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Published: 2017-11-21T20:30:00-05:00
A method to study strongly interacting quantum many-body systems at and away from criticality is proposed. The method is based on a MERA-like tensor network that can be efficiently and reliably contracted on a noisy quantum computer using a number of qubits that is much smaller than the system size. We prove that the outcome of the contraction is stable to noise and that the estimated energy upper bounds the ground state energy. The stability, which we numerically substantiate, follows from the positivity of operator scaling dimensions under renormalization group flow. The variational upper bound follows from a particular assignment of physical qubits to different locations of the tensor network plus the assumption that the noise model is local. We postulate a scaling law for how well the tensor network can approximate ground states of lattice regulated conformal field theories in d spatial dimensions and provide evidence for the postulate. Under this postulate, a $O(\log^{d}(1/\delta))$-qubit quantum computer can prepare a valid quantum-mechanical state with energy density $\delta$ above the ground state. In the presence of noise, $\delta = O(\epsilon \log^{d+1}(1/\epsilon))$ can be achieved, where $\epsilon$ is the noise strength.
We find that localised perturbations in a chaotic classical many-body system-- the classical Heisenberg spin chain -- spread ballistically with a finite speed and little change in form as a function of distance from the origin of the perturbation even when the local spin dynamics is diffusive. We study this phenomenon by shedding light on the two complementary aspects of this butterfly effect-- the rapid growth of perturbations and its simultaneous ballistic (light-cone) spread, as characterised by the Lyapunov exponents and the butterfly speed respectively. We connect this to recent studies of the out-of-time-ordered correlator (OTOC), which have been proposed as an indicator of chaos in a quantum system. We provide a straightforward identification of the OTOC with a correlator in our system and demonstrate that most of the interesting qualitative features -- with the exception of the physics of entanglement -- are present in the classical system. We present mostly results for the infinite temperature case but also discuss finite temperatures, where our results remain valid.
We investigate, in the Luttinger model with fixed box potential, the time evolution of an inhomogeneous state prepared as a localized fermion added to the noninteracting ground state. We proved that, if the state is evolved with the interacting Hamiltonian, the averaged density has two peaks moving in opposite directions, with a constant but renormalized velocity. We also proved that a dynamical `Landau quasi-particle weight' appears in the oscillating part of the averaged density, asymptotically vanishing with large time. The results are proved with the Mattis-Lieb diagonalization method. A simpler proof with the exact Bosonization formulas is also provided.
Atomic systems display a rich variety of quantum dynamics due to the different possible symmetries obeyed by the atoms. These symmetries result in selection rules that have been essential for the quantum control of atomic systems. Superconducting artificial atoms are mainly governed by parity symmetry. Its corresponding selection rule limits the types of quantum systems that can be built using electromagnetic circuits at their optimal coherence operation points ("sweet spots"). Here, we use third-order nonlinear coupling between the artificial atom and its readout resonator to drive transitions forbidden by the parity selection rule for linear coupling to microwave radiation. A Lambda-type system emerges from these newly accessible transitions, implemented here in the fluxonium artificial atom coupled to its "antenna" resonator. We demonstrate coherent manipulation of the fluxonium artificial atom at its sweet spot by stimulated Raman transitions. This type of transition enables the creation of new quantum operations, such as the control and readout of physically protected artificial atoms.
Conventional crystalline magnets are characterized by symmetry breaking and normal modes of excitation called magnons with quantized angular momentum $\hbar$. Neutron scattering correspondingly features extra magnetic Bragg diffraction at low temperatures and dispersive inelastic scattering associated with single magnon creation and annihilation. Exceptions are anticipated in so-called quantum spin liquids as exemplified by the one-dimensional spin-1/2 chain which has no magnetic order and where magnons accordingly fractionalize into spinons with angular momentum $\hbar/2$. This is spectacularly revealed by a continuum of inelastic neutron scattering associated with two-spinon processes and the absence of magnetic Bragg diffraction. Here, we report evidence for these same key features of a quantum spin liquid in the three-dimensional Heisenberg antiferromagnet NaCaNi$_2$F$_7$. Through specific heat and neutron scattering measurements, Monte Carlo simulations, and analytic approximations to the equal time correlations, we show that NaCaNi$_2$F$_7$ is an almost ideal realization of the spin-1 antiferromagnetic Heisenberg model on a pyrochlore lattice with weak connectivity and frustrated interactions. Magnetic Bragg diffraction is absent and 90\% of the spectral weight forms a continuum of magnetic scattering not dissimilar to that of the spin-1/2 chain but with low energy pinch points indicating NaCaNi$_2$F$_7$ is in a Coulomb phase. The residual entropy and diffuse elastic scattering points to an exotic state of matter driven by frustration, quantum fluctuations and weak exchange disorder.
Low energy consumption enabled by charge-free information transport, which is free from ohmic heating, and the ability to process phase-encoded data by nanometer-sized interference devices at GHz and THz frequencies are just a few benefits of spin-wave-based technologies. Moreover, when approaching cryogenic temperatures, quantum phenomena in spin-wave systems pave the path towards quantum information processing. In view of these applications, the lifetime of magnons$-$spin-wave quanta$-$is of high relevance for the fields of magnonics, magnon spintronics and quantum computing. Here, the relaxation behavior of parametrically excited magnons having wavenumbers from zero up to $6\cdot 10^5 \mathrm{rad~cm}^{-1}$ was experimentally investigated in the temperature range from 20 K to 340 K in single crystal yttrium iron garnet (YIG) films epitaxially grown on gallium gadolinium garnet (GGG) substrates as well as in a bulk YIG crystal$-$the magnonic materials featuring the lowest magnetic damping known so far. As opposed to the bulk YIG crystal in YIG films we have found a significant increase in the magnon relaxation rate below 150 K$-$up to 10.5 times the reference value at 340 K$-$in the entire range of probed wavenumbers. This increase is associated with rare-earth impurities contaminating the YIG samples with a slight contribution caused by coupling of spin waves to the spin system of the paramagnetic GGG substrate at the lowest temperatures.
We numerically simulate the free decay of two-dimensional quantum turbulence in a large, homogeneous Bose-Einstein condensate. The large number of vortices, the uniformity of the density profile and the absence of boundaries (where vortices can drift out of the condensate) isolate the annihilation of vortex-antivortex pairs as the only mechanism which reduces the number of vortices, $N_{\rm v}$, during the turbulence decay. The results clearly reveal that vortex annihilations is a four-body process, confirming the decay law $N_{\rm v} \sim t^{-1/3}$ where $t$ is time, which was inferred from experiments with relatively few vortices in small harmonically trapped condensates.
The present work reports about the dynamics of a collection of randomly distributed, and randomly oriented, oscillators in 3D space, coupled by an interaction potential falling as $1/r^3$, where r stands for the inter-particle distance. This model schematically represents a collection of identical biomolecules, coherently vibrating at some common frequency, coupled with a $1/r^3$ potential stemming from the electrodynamic interaction between oscillating dipoles. The oscillating dipole moment of each molecule being a direct consequence of its coherent (collective) vibration. By changing the average distance among the molecules, neat and substantial changes in the power spectrum of the time variation of a collective observable are found. As the average intermolecular distance can be varied by changing the concentration of the solvated molecules, and as the collective variable investigated is proportional to the projection of the total dipole moment of the model biomolecules on a coordinate plane, we have found a prospective experimental strategy of spectroscopic kind to check whether the mentioned intermolecular electrodynamic interactions can be strong enough to be detectable, and thus to be of possible relevance to biology.
We present design and simulation of a Josephson parametric amplifier with bandwidth exceeding 1.6 GHz, and with high saturation power approaching -90 dBm at a gain of 22.8 dB. An improvement by a factor of roughly 50 in bandwidth over the state of the art is achieved by using well-established impedance matching techniques. An improvement by a factor of roughly 100 in saturation power over the state of the art is achieved by implementing the Josephson nonlinear element as an array of rf-SQUIDs with a total of 40 junctions. WRSpice simulations of the circuit are in excellent agreement with the calculated gain and saturation characteristics.
This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.
Copper-doped zinc sulphide (ZnS:Cu) thin films were synthesized through pulsed laser ablation in an inert background gas on stationary and rotating substrates, and a comprehensive opto-electrical characterisation is presented. The Cu$_x$Zn$_{1-x}$S films demonstrated comparable conductivity and transparency to other leading p-type transparent conducting materials, with a peak conductivity of 49.0 Scm$^{-1}$ and a hole mobility of 1.22 cm$^2$V$^{-1}$s$^{-1}$ for films alloyed with an x = 0.33 copper content. The most conducting films displayed a transparency of 71.8$\%$ over the visible range at a thickness of 100 nm, and band gaps were found in the range 3.22-3.52 eV, which showed a strong negative correlation with copper content. The effects of sulphur-rich rapid thermal annealing on the synthesized compound are reported, with films reliably displaying an increase in conductivity and carrier mobility. Films grown using a stationary substrate possessed large spatial thickness distributions and displayed sub-band gap absorption, which is discussed with respect to inhomogeneous copper substitution. Films deposited at 450$^\circ$C were found to be in the zincblende phase before and after annealing, with no occurrence of a phase change to wurtzite structure.
We develop an improved variant of $U(1)$-symmetric infinite projected entangled-pair states (iPEPS) ansatz to investigate the ground state phase diagram of the spin-$1/2$ square $J_{1}$-$J_{2}$ Heisenberg model. In order to improve the accuracy of the ansatz, we discuss a simple strategy to select automatically relevant symmetric sectors and also introduce an optimization method to treat second-neighbor interactions more efficiently. We show that variational ground-state energies of the model obtained by the $U(1)$-symmetric iPEPS ansatz (for a fixed bond dimension $D$) set a better upper bound, improving previous tensor-network-based results. By studying N\'{e}el order parameter and correlation function in the large-$D$ limit, we find that a deconfined quantum-critical point occurs at $J^{c_1}_{2}=0.530(5)$, where the correlation length of the system diverges as $\xi \sim D^{1.2}$. The estimated critical anomalous exponents $\eta_{s}=0.65(5)$ and $\eta_{d}=1.9(1)$ for spin and dimer correlations respectively show strong deviation from those of the well-known $\mathcal{J}$-$\mathcal{Q}$ model, suggesting possibly a different universality class. The pattern of local bond energy for the intermediate phase is compatible with the columnar valence bond solid (VBS) state, with a quite competitive variational ground-state energy in comparison with plaquette VBS one predicted by the density matrix renormalization group. We show that the associated VBS order parameter first monotonically increases with $J_2$ and finally a first-order quantum phase transition takes place at $J^{c_2}_{2}=0.610(3)$ to the conventional Stripe phase. We compare our results with earlier DMRG and PEPS studies and suggest future directions for resolving remaining issues.
Tantalum pentoxide (Ta2O5) is a wide-gap semiconductor which has important technological applications. Despite the enormous efforts from both experimental and theoretical studies, the ground state crystal structure of Ta2O5 is not yet uniquely determined. Based on first-principles calculations in combination with evolutionary algorithm, we identify a triclinic phase of Ta2O5, which is energetically much more stable than any phases or structural models reported previously. Characterization of the static and dynamical properties of the new phase reveals the common features shared with previous metastable phases of Ta2O5. In particular, we show that the d-spacing of ~ 3.8 {\AA} found in the X-ray diffraction (XRD) patterns of many previous experimental works, is actually the radius of the second Ta-Ta coordination shell as defined by radial distribution functions.
The surface tension of flowing soap films is measured with respect to the film thickness and the concentration of soap solution. We perform this measurement by measuring the curvature of the nylon wires that bound the soap film channel and use the measured curvature to parametrize the relation between the surface tension and the tension of the wire. We find the surface tension of our soap films increases when the film is relatively thin or made of soap solution of low concentration, otherwise it approaches an asymptotic value 30 mN/m. A simple adsorption model with only two parameters describes our observations reasonably well. With our measurements, we are also able to measure Gibbs elasticity for our soap film.
Recent years have seen many examples of how the strong spin-orbit coupling (SOC) present in iridates can stabilize new emergent states that are difficult or impossible to realize in more conventional materials. In this review we outline a representative set of studies detailing how heterostructures based on Ruddlesden-Popper (RP) and perovskite iridates can be used to access yet more novel physics. Beginning with a short synopsis of iridate thin film growth, the effects of the heterostructure morphology on the RP iridates including Sr2IrO4 and SrIrO3 are discussed. Example studies explore the effects of epitaxial strain, laser-excitation to access transient states, topological semimetallicity in SrIrO3, 2D magnetism in artificial RP iridates, and interfacial magnetic coupling between iridate and neighboring layers. Taken together, these works show the fantastic potential for controlled engineering of novel quantum phenomena in iridate heterostructures.
Voltage modulation of YIG with compactness, high speed response and energy efficiency is of great importance for YIG's widely applications in electronics, spintronics and even optoelectronics. Nevertheless, it is extremely challenging because of YIG's low magnetostriction and difficulty of epitaxial growth on various ferroelectric substrates. Here we initial an ionic liquid (IL) gating process on YIG-Pt bilayer heterostructures grown on GGG substrates, where the Pt capping would influence the FMR field position as well as linewidth significantly. Giant FMR field shifts of 400 Oe YIG-Pt multilayer heterostructures under a small voltage bias of 4.5 V across the IL layer. Our results overwhelm the state of the art YIG tunability in 1 order magnification, corresponding to a great ME coupling figure of merit (the ratio between ME tunability and FMR linewidth, FOM = Heff\dH = 10). We relate this record high ME tunability to the electrical modification ferromagnetic ordering in metal layers Pt during the IL gating process. This work shows great potential in voltage tunable YIG based RF and microwave devices, additionally, it opens a door toward abundant interfacial magnetism gating physics, which requires further investigation in near future.
One recent breakthrough in the field of magnonics is the experimental realization of reconfigurable pin-wave nanochannels formed by magnetic domain wall with a width of 10-100 nm. This remarkable progress enables an energy-efficient spin-wave propagation with a well-defined wave vector along its propagating path inside the wall. A micro-focus Brillouin light scattering spectroscopy is taken in a line-scans manner to measure the frequency of the bounded spin wave. Due to their localization nature, the confined spin waves can hardly be detected outside the wall channel, which guarantees the information security to some extent. In this work, we propose a scheme to detect/eavesdrop on the spin waves inside the domain-wall nanochannel via nonlinear three-magnon processes. We send a spin wave in one magnetic domain to interact with the bounded mode in the wall. Two kinds of three-magnon processes, i.e., confluence and splitting, are expected to occur. The confluence process is conventional, while the three magnon splitting is highly nontrivial. We uncover a stimulated three-magnon splitting (or "magnon laser") effect, assisted by the bounded magnon moving in the wall channel. Micromagnetic simulations confirm our theoretical analysis. Our results demonstrate that one is able to uniquely infer the spectrum of the spin-wave in the domain-wall nanochannel once we know both the injection and the transmitted waves.
We study deformability-based sorting of red blood cells via deep deterministic lateral displacement (DLD) using an in-house integral equation solver. Our goal is to quantitatively characterize the physical mechanisms enabling the cell separation. To this end, we systematically investigate the effects of the interior fluid viscosity and the membrane elasticity of a cell on its behavior. In particular, we consider deep devices in which a cell can show rich dynamics such as taking a particular angular orientation depending on its mechanical property. We have found out that cells moving with a sufficiently high positive inclination angle with respect to the flow direction displace laterally while those with smaller angles travel with the flow streamlines. Thereby, deformability-based cell sorting is possible. The underlying mechanism here is cell migration due to the cell's positive inclination and the shear gradient. The higher the inclination is, the farther the cell can travel laterally. We also assess the efficiency of the technique for dense suspensions. It turns out that most of the cells in dense suspensions does not displace in the lateral direction no matter what their deformability is. As a result, separating cells using a DLD device becomes harder.
In this paper I have studied the fiber bundle model with a fraction {\alpha} of infinitely strong fibers. Inclusion of such unbreakable fraction has been proven to affect the failure process in early studies, especially around a critical value {\alpha}_c . The present work has a twofold purpose: (i) study of failure abruptness, mainly the brittle to quasi-brittle transition point ({\delta}_c ) with varying {\alpha} and (ii) variation of {\alpha}_c as we change the disorder introduced in the model. The brittle to quasi-brittle transition is confirmed from the failure abruptness. On the other hand, the {\alpha}_c is obtained from the knowledge of failure abruptness and statistics of avalanches. It is observed that {\delta}_c scales to lower values, suggesting more quasi-brittle like continuous failure even at low strength of disorder, when {\alpha} is increased. Also, the critical fraction {\alpha}_c, required to make the model deviate from the conventional results, increases with decreasing {\delta} values. The analytical expression for {\alpha}_c shows good agreement with the numerical result. Finally, the findings in the paper are compared with previous results as well as with the real life application of composite materials.
Ferroelectric materials possess spontaneous polarization that can be used for multiple applications. Owing to a long term development for reducing the sizes of devices, the preparation of ferroelectric materials and devices are entering nanometer-scale regime. Accordingly, to evaluate the ferroelectricity, there is a need to investigate the polarization charge at the nanoscale. Nonetheless, it has been generally accepted that the detection of polarization charges using a conventional conductive atomic force microscopy (CAFM) without a top electrode is not feasible because the nanometer-scale radius of an atomic force microscopy (AFM) tip yields a very low signal-to-noise ratio. However, the detection is unrelated to the radius of an AFM tip, and in fact, a matter of the switched area. In this work, we demonstrate the direct probing of the polarization charge at the nanoscale using the Positive-Up-Negative-Down method based on the conventional CAFM approach without additional corrections or circuits to reduce the parasitic capacitance. We successfully probed the polarization charge densities of 73.7 and 119.0 uC/cm2 in ferroelectric nanocapacitors and thin films, respectively. The obtained results show the feasibility of the evaluation of the polarization charge at the nanoscale and provide a new guideline for evaluating the ferroelectricity at the nanoscale.
Superconducting nanowire single-photon detectors (SNSPDs) have an absolute advantage over other types of single photon detectors except the low operating temperature. Therefore, many efforts have been devoted to find high-temperature superconducting materials that are suitable for preparing SNSPDs. Copper-based and MgB2 ultra-thin superconducting nanowires have been already reported. However, the transport properties of iron-based ultra-thin superconducting nanowires have not been studied. In this work, a 10 nm thick 200 nm wide 30 {\mu}m long high quality superconducting nanowire was fabricated from ultrathin BaFe1.84Co0.16As2 films by a lift-off process. The precursor BaFe1.84Co0.16As2 film with a thickness of 10 nm and root-mean-square roughness of 1 nm was grown on CaF2 substrates by pulsed laser deposition. The nanowire shows a high superconducting critical temperature Tzero c=20 K with a narrow transition width of Delta T=2.5 K and exhibits a high critical current density Jc of 1.8E7 A/cm2 at 10 K. These results of ultrathin BaFe1.84Co0.16As2 nanowire will attract interest in electronic applications, including SNSPDs
In first-principles calculations, hybrid functional is often used to improve accuracy from local exchange correlation functionals. A drawback is that evaluating the hybrid functional needs significantly more computing effort. When spin-orbit coupling (SOC) is taken into account, the non-collinear spin structure increases computing effort by at least eight times. As a result, hybrid functional calculations with SOC are intractable in most cases. In this paper, we present an approximate solution to this problem by developing an efficient method based on a mixed linear combination of atomic orbital (LCAO) scheme. We demonstrate the power of this method using several examples and we show that the results compare very well with those of direct hybrid functional calculations with SOC, yet the method only requires a computing effort similar to that without SOC. The presented technique provides a good balance between computing efficiency and accuracy, and it can be extended to magnetic materials.
We present optical study of MAPbBr3 single crystals grown from solution by inverse temperature crystallization method. Photoluminescence temperature dependence of narrow and isolated exciton resonance showed encouragingly low inhomogeneous broadening {\Gamma} ~ 0.5 meV, which is comparable to those of MBE-grown III-V heterostructures, indicating high quality of the solution-grown perovskite. Excitonic origin of the resonance was proved by its superlinear pump intensity dependence in contrast to the linear behavior of the defect-assisted recombination bands. In addition, for the first time phonon replicas were resolved in MAPbBr3 photoluminescence spectra and attributed to the known lattice vibrational modes by comparison with Raman scattering spectra.
Understanding the evolution of spin-orbit torque (SOT) with increasing heavy-metal thickness in ferromagnet/normal metal (FM/NM) bilayers is critical for the development of magnetic memory based on SOT. However, several experiments have revealed an apparent discrepancy between damping enhancement and damping-like SOT regarding their dependence on NM thickness. Here, using linewidth and phase-resolved amplitude analysis of vector network analyzer ferromagnetic resonance (VNA-FMR) measurements, we simultaneously extract damping enhancement and both field-like and damping-like inverse SOT in Ni$_{80}$Fe$_{20}$/Pt bilayers as a function of Pt thickness. By enforcing an interpretation of the data which satisfies Onsager reciprocity, we find that both the damping enhancement and damping-like inverse SOT can be described by a single spin diffusion length ($\approx$ 4 nm), and that we can separate the spin pumping and spin memory loss (SML) contributions to the total damping. This analysis indicates that less than 40% of the angular momentum pumped by FMR through the Ni$_{80}$Fe$_{20}$/Pt interface is transported as spin current into the Pt. On account of the SML and corresponding reduction in total spin current available for spin-charge transduction in the Pt, we determine the Pt spin Hall conductivity ($\sigma_\mathrm{SH} = (2.36 \pm 0.04)\times10^6 \Omega^{-1} \mathrm{m}^{-1}$) and bulk spin Hall angle ($\theta_\mathrm{SH}=0.387 \pm0.008$) to be larger than commonly-cited values. These results suggest that Pt can be an extremely useful source of SOT if the FM/NM interface can be engineered to minimize SML. Lastly, we find that self-consistent fitting of the damping and SOT data is best achieved by a model with Elliott-Yafet spin relaxation and extrinsic inverse spin Hall effect, such that both the spin diffusion length and spin Hall conductivity are proportional to the Pt charge conductivity.
We show that the optimal trial wave function of a fractional Chern insulator depends on the form of its interaction. The gauge of single particle Bloch bases for constructing the optimal wave trail function is obtained by applying the variational principle proposed by Zhang et al.. We consider a short-range interaction, the Coulomb interaction, and an interpolation between them, and determine the evolution of the optimal gauge with the different interactions. We compare the optimal gauge with those proposed by Qi and Wu et al., and find that Wu et al.'s gauge is close to the optimal gauge when the interaction is a certain mixture of the Coulomb interaction and the short-range interaction, while Qi's gauge is qualitatively different from the optimal gauge in all the cases. Both the gauges deviate significantly from the optimal gauge when the short range component of the interaction becomes more prominent.
The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantum-limited readout. The inductance is either set by tailoring the metal-oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local current-biased flux lines. JJs based on superconductor-semiconductor hybrids represent a tantalizing all-electric alternative. The gatemon is a recently developed transmon variant which employs locally gated nanowire (NW) superconductor-semiconductor JJs for qubit control. Here, we go beyond proof-of-concept and demonstrate that semiconducting channels etched from a wafer-scale two-dimensional electron gas (2DEG) are a suitable platform for building a scalable gatemon-based quantum computer. We show 2DEG gatemons meet the requirements by performing voltage-controlled single qubit rotations and two-qubit swap operations. We measure qubit coherence times up to ~2 us, limited by dielectric loss in the 2DEG host substrate.
We study the relation between the microscopic properties of a many-body system and the electron spectra, experimentally accessible by photoemission. In a recent paper [Phys. Rev. Lett. 114, 236402 (2015)], we introduced the "fluctuation diagnostics" approach, to extract the dominant wave vector dependent bosonic fluctuations from the electronic self-energy. Here, we first reformulate the theory in terms of fermionic modes, to render its connection with resonance valence bond (RVB) fluctuations more transparent. Secondly, by using a large-U expansion, where U is the Coulomb interaction, we relate the fluctuations to real space correlations. Therefore, it becomes possible to study how electron spectra are related to charge, spin, superconductivity and RVB-like real space correlations, broadening the analysis of an earlier work [Phys. Rev. B 89, 245130 (2014)]. This formalism is applied to the pseudogap physics of the two-dimensional Hubbard model, studied in the dynamical cluster approximation. We perform calculations for embedded clusters with up to 32 sites, having three inequivalent K-points at the Fermi surface. We find that as U is increased, correlation functions gradually attain values consistent with an RVB state. This first happens for correlation functions involving the antinodal point and gradually spreads to the nodal point along the Fermi surface. Simultaneously a pseudogap opens up along the Fermi surface. We relate this to a crossover from a Kondo-like state to an RVB-like localized cluster state and to the presence of RVB and spin fluctuations. These changes are caused by a strong momentum dependence in the cluster bath-couplings along the Fermi surface. We also show, from a more algorithmic perspective, how the time-consuming calculations in fluctuation diagnostics can be drastically simplified.
Motivated by the close analogy with the fractional quantum Hall states (FQHSs), fractional Chern insulators (FCIs) are envisioned as strongly correlated, incompressible states emerging in a fractionally filled, (nearly) flat band with non-trivial Chern number. Built upon this vision, fractional topological insulators (FTIs) have been proposed as being composed of two independent copies of the FCI with opposite Chern numbers for different spins, preserving the time-reversal symmetry as a whole. An important question is if the correlation between electrons with different spins can be really ignored. To address this question, we investigate the effects of correlation in the presence of spin-dependent holomorphicity, i.e., electrons of one spin species reside in the holomorphic lowest Landau level, while those of the other in the antiholomorphic counterpart. By constructing and performing exact diagonalization of an appropriate model Hamiltonian, here, we show that generic, strongly correlated, fractionally filled states with spin-dependent holomorphicity cannot be described as two independent copies of the FQHS, suggesting that FTIs in the lattice cannot be described as those of the FCI either. Fractionally filled states in this system are generally compressible except at half filling, where an insulating state called the half-filled spin-holomorphic FTI occurs. It is predicted that the half-filled spin-holomorphic FTI is susceptible to an inherent spontaneous symmetry breaking, leading to the spatial separation of spins.
We study quasi-two-dimensional dipolar Bose-Einstein condensates, in which the Bogoliubov excitation spectrum displays, at sufficiently large gas density, a deep roton minimum due to the spatially anisotropic behavior of the dipolar two-body potential. A rapid quench, performed on the speed of sound of excitations propagating on the condensate background, leads to the dynamical Casimir effect, which can be characterized by measuring the density-density correlation function. It is shown, for both zero and finite initial temperatures, that the continuous-variable bipartite quantum state of the created quasiparticle pairs with opposite momenta, resulting from the quench, displays an enhanced potential for the presence of entanglement and steering, when compared to a gas with repulsive contact interactions. Steered quasiparticle pairs contain momenta from close to the roton, and hence nonlocal quantum correlations significantly increase in the presence of a deep roton minimum.
Spin polarization induced by a temperature gradient (heat-current) in a magnetized two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction is considered theoretically within the linear response theory. Using the Matsubara Green function formalism we calculate the temperature dependence of the spin polarization for arbitrary orientation of the exchange field. The limit of a nonmagnetic 2DEG (zero exchange field) is also considered. The physical mechanisms of the spin polarization within our scheme are discussed.
Using the Matsubara Green's function formalism we calculate the temperature dependence of the nonequilibrium spin polarization induced by an external electric field in the presence of spin-orbit coupling. The model Hamiltonian includes an isotropic k-cubed form of the Rashba spin-orbit interaction. Such a Hamiltonian captures the electronic and spin properties of two-dimensional electron (hole) gas at the surfaces or interfaces of transition metal oxides or in p-doped semiconductor heterostructures. The induced spin polarization is calculated for the nonmagnetic as well as magnetic electron/hole gas. Relation of the spin polarization to the Berry curvature is also discussed.
In the theory of antiferromagnetism, the staggered field---an external magnetic field that alternates in sign on atomic length scales---is used to select the classical N\'eel state from a quantum magnet, but justification is missing. This work examines, within the decoherence framework, whether repeated $local$ measurement can replace a staggered field. Accordingly, the conditions under which local decoherence can be considered a continuous measurement are studied. By applying this idea to an approximate low-energy description of antiferromagnets, it is found that local decoherence can lead to (symmetry-broken) order similar to order resulting from a staggered field.
The interplay of multiple length- and energy-scales is crucial for the understanding of the properties of many physical systems. Artificial ferroic structures can serve as model systems for investigating the outcome of such an interplay. These offer an experimental framework for the definition and tuning of length- and energy-scales by geometry design, while simultaneously facilitating direct access to the system microstates. Here we employ artificial magnetic nano-structures, with varying length-scales of the interacting elements in an attempt to experimentally highlight the importance of distinct energy-scales on the collective magnetic ordering. Utilizing the mesoscopic nature of these architectures and magnetic microscopy techniques, we image the magnetic states in thermal realizations of such systems. In combination with reciprocal space analysis tools, like the magnetic spin structure factor, we reveal the impact of the combination of distinct energy- and length-scales on the magnetic ordering. Our findings provide a conceptual and experimental framework for understanding the role that the energy-scale hierarchy plays in the short-range order of artificial magnetic architectures and beyond.
The coupling between defects in diamond and a superconducting microwave resonator is studied in the nonlinear regime. Both negatively charged nitrogen-vacancy and P1 defects are explored. The measured cavity mode response exhibits strong nonlinearity near a spin resonance. Data is compared with theoretical predictions and a good agreement is obtained. The nonlinear effect under study in the current paper is expected to play a role in any cavity-based magnetic resonance imaging technique and to impose a fundamental limit upon its sensitivity.
Micro-/nano-indentations have been widely used to measure the mechanical properties of biological cells and tissues, but direct application of classical Hertzian contact model would lead to overestimation of elastic modulus due to the influence of finite thickness and surface energy. In this work, we analyze spherical indentation of biological films considering both large deformation and surface energy. The hyperelastic behavior of biological films is characterized by neo-Hookean model, and the influence of surface energy is addressed through finite element simulation. Based on dimensional analysis, the explicit expressions of load-depth relation accounting for film thickness, large deformation and surface energy are achieved for bonded or non-bonded films. Under a specific load, the consideration of large deformation increases the indent depth, while the finite thickness of films tends to decrease the indent depth, compared to the linear elastic Hertzian solution. More importantly, surface energy evidently alters the load-depth relation for micro-/nano-indentations, which reduces the indent depth and makes the films seemingly stiffer. These results provide a fundamental relationship to accurately extract the mechanical properties of biological films from indentation tests.
We study the dynamics of microscopic quantum correlations, viz., bipartite entanglement and quantum discord, in Ising spin chain with periodically varying external magnetic field along the transverse direction. Depending upon system parameters, the local quantum correlations in the evolved states of such systems may get saturated to non-zero values after sufficiently large number of driving cycles. Moreover, we investigate convergence of the local density matrices, from which the quantum correlations under study originate, towards the final steady-state density matrices as a function of driving cycles. We find that the geometric distance between the non-equilibrium and the steady-state reduced density matrices obey power-law scaling. The steady-state quantum correlations corresponding to various initial states in thermal equilibrium are studied as a function of drive time period of a square pulsed field. The steady-state quantum correlations are marked by presence of peaks in the frequency domain. The steady-state features can be further understood by probing band structures of Floquet Hamiltonian. Finally, we investigate ergodic properties of the local quantum correlations under study. We find that depending upon the quantum phases of the initial state and the pathway of the driving Hamiltonian, quantum correlations may go through ergodic to non-ergodic transitions in the frequency domain.
We study a system of 1D non interacting spinless fermions in a confining trap at finite temperature. We first derive a useful and general relation for the fluctuations of the occupation numbers valid for arbitrary confining trap, as well as for both canonical and grand canonical ensembles. Using this relation, we obtain compact expressions, in the case of the harmonic trap, for the variance of linear statistics $\mathcal{L}=\sum_n h(x_n)$, where $h$ is an arbitrary function of the fermion coordinates $\{ x_n \}$. As anticipated, we demonstrate explicitly that these fluctuations do depend on the ensemble in the thermodynamic limit, as opposed to averaged quantities, which are ensemble independent. We have applied our general formalism to compute the fluctuations of the number of fermions $\mathcal{N}_+$ on the positive axis at finite temperature. Our analytical results are compared to numerical simulations.
Polynomial approximations of hysteresis curves were studied for systems exhibiting the return point memory. An extended Rayleigh law that uses polynomials of the third degree, and Rayleigh-like equations describing the energy dependence on the applied magnetic field are proposed. The results were compared with numerical experiments on a zero temperature random bond Ising model.
We present results for the fluctuations of the displacement of a tracer particle on a planar lattice pulled by a step force in the presence of impenetrable, immobile obstacles. The fluctuations perpendicular to the applied force are evaluated exactly in first order of the obstacle density for arbitrarily strong pulling and all times. The complex time-dependent behavior is analyzed in terms of the diffusion coefficient, local exponent, and the non-Skellam parameter which quantifies deviations from the dynamics on the lattice in the absence of obstacles. The non-Skellam parameter along the force is analyzed in terms of an asymptotic model and reveals a power law growth for intermediate times.
Interfacial Dzyaloshinskii-Moriya interaction (iDMI) has been investigated in
Co2FeAl (CFA) ultrathin films of various thicknesses (0.8 nm
We report an observation of conductance fuctuations (CFs) in the bipolar regime of quantum hall (QH) plateaus in graphene (p-n-p/n-p-n) devices. The CFs in the bipolar regime are shown to decrease with increasing bias and temperature. At high temperature (above 7 K) the CFs vanishes completely and the flat quantized plateaus are recovered in the bipolar regime. The values of QH plateaus are in theoretical agreement based on full equilibration of chiral channels at the p-n junction. The amplitude of CFs for different filling factors follows a trend predicted by the random matrix theory. Although, there are mismatch in the values of CFs between the experiment and theory but at higher filling factors the experimental values become closer to the theoretical prediction. The suppression of CFs and its dependence has been understood in terms of time dependent disorders present at the p-n junctions.
We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained for a range of salt concentrations for the Joung-Cheatham NaCl force field combined with the SPC/E water model. The calculated nucleation rates are significantly lower than available experimental measurements. The estimates for the nucleation rates in this work do not rely on classical nucleation theory, but the pathways observed in the simulations suggest that the nucleation process is better described by classical nucleation theory than an alternative interpretation based on Ostwald's step rule, in contrast to some prior simulations of related models. In addition to the size of NaCl nucleus, we find that the crystallinity of a nascent cluster plays an important role in the nucleation process. Nuclei with high crystallinity were found to have higher growth probability and longer lifetimes, possibly because they are less exposed to hydration water.
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical mechanics and Gibbs' statistical mechanics follows. The former and the latter are endowed with probability distribution of microstates ruled by power laws and Boltzmann exponentials respectively. We apply our treatment to the relaxed states described by a 1D nonlinear FokkerPlanck equation. If the latter is associated to the stochastic differential equation obtained in the continuous limit from a 1D, autonomous, discrete map affected by noise, then we may ascertain whether if a relaxed state follow a power law distribution (and with which exponent) by looking at both map dynamics and noise level, with no assumptions concerning the additive or multiplicative nature of the noise and with no numerical computation of the orbits. Results agree with the simulations of Sanchez et al. EPJ 143.1 (2007) 141-143 concerning relaxation to a Pareto-like distribution.
Strongly correlated iridate pyrochlores with geometrically frustrated spins have been recognized as a potentially interesting group of oxide materials where novel topological phases may appear. A particularly attractive system is the metallic Pr$_2$Ir$_2$O$_7$, as it is known as a Fermi node semimetal characterized by quadratic band touching at the Brillouin zone center, suggesting that the topology of its electronic states can be tuned by moderate lattice strain. In this work we report the growth of epitaxial Pr$_2$Ir$_2$O$_7$ thin films grown by solid-state epitaxy. We show that the strained parts of the films give rise to a spontaneous Hall effect that persists up to 50 K without having spontaneous magnetization within our experimental accuracy. This indicates that a macroscopic time reversal symmetry (TRS) breaking appears at a temperature scale that is too high for the magnetism to be due to Pr 4$f$ moments, and must thus be related to magnetic order of the iridium 5$d$ electrons. The magnetotransport and Hall analysis results are consistent with the formation of a Weyl semimetal state that is induced by a combination of TRS breaking and cubic symmetry breaking due to lattice strain.
We perform time-dependent analysis of quantum dynamics of dark matter particles in the Solar System. It is shown that this problem has similarities with a microwave ionization of Rydberg atoms studied previously experimentally and analytically. On this basis it is shown that the quantum effects for chaotic dark matter dynamics become significant for dark matter mass ratio to electron mass being smaller than $2 \times 10^{-15}$. Below this border multiphoton diffusion over Rydberg states of dark matter atom becomes exponentially localized in analogy with the Anderson localization in disordered solids. The life time of dark matter in the Solar System is determined in dependence on mass ratio in the localized phase and a few photon ionization regime. Various implications of these quantum results are discussed for the capture of dark matter from Galaxy and its steady-state density distribution.
Clarifying the impact of quantumness in the operation and properties of thermal machines represents a major challenge. Here we envisage a toy model acting either as an information-driven fridge or as heat-powered information eraser in which coherences can be naturally introduced in by means of squeezed thermal reservoirs. We study the validity of the transient entropy production fluctuation theorem in the model with and without squeezing as well as its decomposition into adiabatic and non-adiabatic contributions. Squeezing modifies fluctuations and introduces extra mechanisms of entropy exchange. This leads to enhancements in the cooling performance of the refrigerator, and to overcoming Landauer's bound in the setup.
We describe electromagnetic propagation in a relativistic electron gas at finite temperatures and carrier densities. Using quantum electrodynamics at finite temperatures, we obtain electric and magnetic responses and general constitutive relations. Rewriting the propagator for the electromagnetic field in terms of the electric and magnetic responses, we identify the modes that propagate in the gas. As expected, we obtain the usual collective excitations, i.e., a longitudinal electric and two transverse magnetic plasmonic modes. In addition, we find a purely photonic mode that satisfies the wave equation in vacuum, for which the electron gas is transparent. We present dispersion relations for the plasmon modes at zero and finite temperatures and identify the intervals of frequency and wavelength where both electric and magnetic responses are simultaneously negative, a behavior previously thought not to occur in natural systems.
In the weak-coupling theory of superconductivity, the diagonal self-energy term is usually disregarded so that this term is already included in the renormalized chemical potential. Using the bulk solution, we can easily see that the term vanishes in the quasiclassical level. However, the validity of this treatment is obscured in non-uniform systems, such as quantized vortices.
In this paper, we study an isolated vortex both analytically and numerically by the quasiclassical theory and demonstrate that the finite magnitude of the self-energy can emerge within a vortex in some odd-parity superconductors. We also find that the existence of diagonal self-energy can induce the breaking of axisymmetry of vortices in chiral p-wave superconductors. This implies that the diagonal self-energy is not negligible within a vortex in odd-parity superconductors in general, even in the weak-coupling limit.
When chiral liquid crystals or magnets are subjected to applied fields or other anisotropic environments, the competition between favored twist and anisotropy leads to the formation of complex defect structures. In some cases, the defects are skyrmions, which have 180{\deg} double twist going outward from the center, and hence can pack together without singularities in the orientational order. In other cases, the defects are merons, which have 90{\deg} double twist going outward from the center; packing such merons requires singularities in the orientational order. In the liquid crystal context, a lattice of merons is regarded as a blue phase. Here, we perform theoretical and computational studies of skyrmions and merons in chiral liquid crystals and magnets. Through these studies, we calculate the phase diagrams for liquid crystals and magnets in terms of dimensionless ratios of energetic parameters. We also predict the range of metastability for liquid crystal skyrmions, and show that these skyrmions can move and interact as effective particles. The results show how the properties of skyrmions and merons depend on the vector or tensor nature of the order parameter.
Quantum information theory has considerably helped in the understanding of quantum many-body systems. Since the early 2000s various measures of quantum entanglement have been employed to characterise the features of the ground and excited states of quantum matter. Furthermore, the scaling of entanglement entropy with the size of a system has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the knowledge and the methods brought by quantum information do not end with bipartite entanglement. There are other forms of quantum correlations that emerge "for free" in the ground and thermal states of condensed matter models and that can be exploited as resources for quantum technologies. The goal of this work is to review the most recent development on quantum correlations for quantum many-body systems focussing on multipartite entanglement, quantum non locality, quantum discord, mutual information but also other non classical resources like quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.
Multiphoton interaction of coherent electromagnetic radiation with 2D metallic carriers confined on the surface of the 3D topological insulator is considered. A microscopic theory describing the nonlinear interaction of a strong wave and metallic carriers with many-body Coulomb interaction is developed. The set of integrodifferential equations for the interband polarization and carrier occupation distribution is solved numerically. Multiphoton excitation of Fermi-Dirac sea of 2D massless carriers is considered for a THz pump wave. It is shown that in the moderately strong pump wave field along with multiphoton interband/intraband transitions the intense radiation of high harmonics takes place.
We review a simple mechanism for the formation of plateaux in the fractional quantum Hall effect. It arises from a map of the microscopic Hamiltonian in the thin torus limit to a lattice gas model, solved by Hubbard. The map suggests a Devil's staircase pattern, and explains the observed asymmetries in the widths. Each plateau is a new ground state of the system: a periodic Slater state in the thin torus limit. We provide the unitary operator that maps such limit states to the full, effective ground states with same filling fraction. These Jack polynomials generalise Laughlin's ansatz, and are exact eigenstates of the Laplace-Beltrami operator. Why are Jacks sitting on the Devil's staircase? This is yet an intriguing problem.
We construct model wavefunctions for the half-filled Landau level parameterized by "composite fermion occupation-number configurations" in a two-dimensional momentum space which correspond to a Fermi sea with particle-hole excitations. When these correspond to a weakly-excited Fermi sea, they have large overlap with wavefunctions obtained by exact diagonalization of lowest-Landau-level electrons interacting with a Coulomb interaction, allowing exact states to be identified with quasiparticle configurations. We then formulate a many-body version of the single-particle Berry phase for adiabatic transport of a single quasiparticle around a path in momentum space, and evaluate it using a sequence of exact eigenstates in which a single quasiparticle moves incrementally. In this formulation the standard free-particle construction in terms of the overlap between "periodic parts of successive Bloch wavefunctions" is reinterpreted as the matrix element of a "momentum boost" operator between the full Bloch states, which becomes the matrix elements of a Girvin-MacDonald-Platzman density operator in the many-body context. This allows computation of the Berry phase for transport of a single composite fermion around the Fermi surface. In addition to a phase contributed by the density operator, we find a phase of exactly $\pi$ for this process.
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems exactly solvable. We illustrate this with: random surfaces, lattice models, and structure constants in representation theory.
We investigate the interplay of the time resolution and memory in dynamic scaling properties of temporal networks, where we present an activity-driven network model with memory. We also show how to control the time resolution and memory. Temporal networks are time series of static subnetworks. The time resolution in analyzing networks plays an important role in determining the dynamic topologies of networks. Performing the random-walk (RW) process on coarse-grained networks, we explore the role of memory in the diffusion properties on the RW process. In particular, we focus on the evolution of dynamic topologies in temporal networks with and without memory. Based on the temporal percolation concept in time-aggregated networks, we discuss the relation between the growth patterns of the largest cluster size and the diffusion properties of the RW process. Finally, we propose the finite-size scaling (FSS) form in the dynamic topologies of temporal networks, which are numerically confirmed with analytic conjectures.
We study the differential conductance of a time-reversal symmetric Weyl semimetal-superconductor (N-S) junction with an s-wave superconducting state. We find that there exists an extended regime where the zero-bias differential conductance acquires the universal value $e^{2}/h$ per unit channel, independent of the pairing and chemical potentials on each side of the junction, due to a perfect cancellation of Andreev and normal reflection contributions. This universal conductance can be attributed to the interplay of the unique spin/orbital-momentum locking and s-wave pairing that couples Weyl nodes of the same chirality. We expect that the universal conductance can serve as a robust and distinct signature for time-reversal symmetric Weyl fermions, and be observed in the recently discovered time-reversal symmetric Weyl semimetals.
We study the dynamics of the Fermi-Hubbard model driven by a time-periodic modulation of the interaction within nonequilibrium Dynamical Mean-Field Theory. For moderate interaction, we find clear evidence of thermalization to a genuine infinite-temperature state with no residual oscillations. Quite differently, in the strongly correlated regime, we find a quasi-stationary extremely long-lived state with oscillations synchronized with the drive (Floquet prethermalization). Remarkably, the nature of this state dramatically changes upon tuning the drive frequency. In particular, we show the existence of a critical frequency at which the system rapidly thermalizes despite the large interaction. We characterize this resonant thermalization and provide an analytical understanding in terms of a break down of the periodic Schrieffer-Wolff transformation.
Intervalley scattering of carriers in graphene at `top' adatoms may give rise to a hidden Kekul\'e ordering pattern in the adatom positions. This ordering is the result of a rapid modulation in the electron-mediated interaction between adatoms at the wavevector $K- K'$, which has been shown experimentally and theoretically to dominate their spatial distribution. Here we show that the adatom interaction is extremely sensitive to strain in the supporting graphene, which leads to a characteristic spatial modulation of the Kekul\'e order as a function of adatom distance. Our results suggest that the spatial distributions of adatoms could provide a way to measure the type and magnitude of strain in graphene and the associated pseudogauge field with high accuracy.
Due to its strong bonds graphene can stretch up to 25% of its original size without breaking. Furthermore, mechanical deformations lead to the generation of pseudo-magnetic fields (PMF) that can exceed 300 T. The generated PMF has opposite direction for electrons originating from different valleys. We show that valley-polarized currents can be generated by local straining of multi-terminal graphene devices. The pseudo-magnetic field created by a Gaussian-like deformation allows electrons from only one valley to transmit and a current of electrons from a single valley is generated at the opposite side of the locally strained region. Furthermore, applying a pressure difference between the two sides of a graphene membrane causes it to bend/bulge resulting in a resistance change. We find that the resistance changes linearly with pressure for bubbles of small radius while the response becomes non-linear for bubbles that stretch almost to the edges of the sample. This is explained as due to the strong interference of propagating electronic modes inside the bubble. Our calculations show that high gauge factors can be obtained in this way which makes graphene a good candidate for pressure sensing.
We present numerical results for the six-vertex model with a variety of boundary conditions. Adapting an algorithm proposed by Allison and Reshetikhin for domain wall boundary conditions, we examine some modifications of these boundary conditions. To be precise, we discuss partial domain wall boundary conditions, reflecting ends and half turn boundary conditions (domain wall boundary conditions with half turn symmetry).
We present a wafer trimming technique for producing superconducting micro-resonator arrays with highly uniform frequency spacing. With the light-emitting diode (LED) mapper technique demonstrated previously, we first map the measured resonance frequencies to the physical resonators. Then, we fine-tune each resonator's frequency by lithographically trimming a small length, calculated from the deviation of the measured frequency from its design value, from the interdigitated capacitor. We demonstrate this technique on a 127-resonator array made of titanium-nitride (TiN) and show that the uniformity of frequency spacing is greatly improved. The array yield in terms of frequency collisions improves from 84% to 97%, while the quality factors and noise properties are unaffected. The wafer trimming technique provides an easy-to-implement tool to improve the yield and multiplexing density of large resonator arrays, which is important for various applications in photon detection and quantum computing.
Within the framework of Oseen-Frank theory, we analyse the static configurations for chiral liquid crystals. In particular, we find numerical solutions for localised axisymmetric states in confined chiral liquid crystals with weak homeotropic anchoring at the boundaries. These solutions describe the distortions of two-dimensional skyrmions, known as either \textit{spherulites} or \textit{cholesteric bubbles}, which have been observed experimentally in these systems. Relations with nonlinear integrable equations have been outlined and are used to study asymptotic behaviors of the solutions. By using analytical methods, we build approximated solutions of the equilibrium equations and we analyse the generation and stabilization of these states in relation to the material parameters, the external fields and the anchoring boundary conditions.
We investigate equilibrium properties, including structure of the order parameter, superflow patterns, and thermodynamics of low-temperature surface phases of layered d_{x^2-y^2}-wave superconductors in magnetic field. At zero external magnetic field, time-reversal symmetry and continuous translational symmetry along the edge are broken spontaneously in a second order phase transition at a temperature $T^*\approx 0.18 T_c$, where $T_c$ is the superconducting transition temperature. At the phase transition there is a jump in the specific heat that scales with the ratio between the edge length $D$ and layer area ${\cal A}$ as $(D\xi_0/{\cal A})\Delta C_d$, where $\Delta C_d$ is the jump in the specific heat at the d-wave superconducting transition and $\xi_0$ is the superconducting coherence length. The phase with broken symmetry is characterized by a gauge invariant superfluid momentum ${\bf p}_s$ that forms a non-trivial planar vector field with a chain of sources and sinks along the edges with a period of approximately $12\xi_0$, and saddle point disclinations in the interior. To find out the relative importance of time-reversal and translational symmetry breaking we apply an external field that breaks time-reversal symmetry explicitly. We find that the phase transition into the state with the non-trivial ${\bf p}_s$ vector field keeps its main signatures, and is still of second order. In the external field, the saddle point disclinations are pushed towards the edges, and thereby a chain of edge motifs are formed, where each motif contains a source, a sink, and a saddle point. Due to a competing paramagnetic response at the edges, the phase transition temperature $T^*$ is slowly suppressed with increasing magnetic field strength, but the phase with broken symmetry survives into the mixed state.
We present an experimental study of nanowire transmons at zero and applied in-plane magnetic field. With Josephson non-linearities provided by the nanowires, our qubits operate at higher magnetic fields than standard transmons. Nanowire transmons exhibit coherence up to 70 mT, where the induced superconducting gap in the nanowire closes. We demonstrate that on-chip charge noise coupling to the Josephson energy plays a dominant role in the qubit dephasing. This takes the form of strongly-coupled two-level systems switching on 100 ms timescales and a more weakly coupled background producing $1/f$ noise. Several observations, including the field dependence of qubit energy relaxation and dephasing, are not fully understood, inviting further experimental investigation and theory. Using nanowires with a thinner superconducting shell will enable operation of these circuits up to 0.5 T, a regime relevant for topological quantum computation.
Current-induced spin-orbit torques in Co$_2$FeAl/Pt ultrathin bilayers are studied using a magnetoresistive harmonic response technique, which distinguishes the dampinglike and fieldlike contributions. The presence of a temperature-dependent magnetic proximity effect is observed through the anomalous Hall and anisotropic magnetoresistances, which are enhanced at low temperatures for thin platinum thicknesses. The fieldlike torque efficiency decreases steadily as the temperature is lowered for all Pt thicknesses studied, which we propose is related to the influence of the magnetic proximity effect on the fieldlike torque mechanism.
We present a Gutzwiller von Neumann dynamics (GvND) method for simulating equilibrium and nonequilibrium phenomena in strongly correlated electron systems. Our approach is a real-space formulation of the time-dependent Gutzwiller approximation method. Applying the GvND method to simulate interaction quenches in the Peierls-Hubbard model, we demonstrate the amplification of initial inhomogeneities, which in turn results in the collapse of quench-induced synchronized oscillation. Moreover, we find a dynamical phase transition separating two quasi-stationary regimes with rather distinct spatial distributions of physical quantities after the collapsed oscillation. In particular, in the strong-coupling regime, the system exhibits a dynamic phase separation in the quasi-stationary state. Our results thus underscore the importance of spatial fluctuations in the nonequilibrium dynamics of strongly correlated systems.
Topological Kondo insulators (TKIs) are new type of symmetry-protected topological insulators, which develop through the interplay of strong correlations and spin-orbit interactions. In these materials, the bulk is a perfect band insulator due to Kondo screening of localized moments via conduction electrons. Furthermore, strong spin-orbit coupling (SOC) and crystal field effect (CFE) of the localized moments result in a nonlocal odd-parity, time-reversal invariant hybridization between the local-moments and conduction bands, which creates a ground-state with nontrivial topology and gapless surface excitations (Physical Review Letters 104 (2010) 106408). In the present work, we develop a self-consistent theory to study topological Kondo insulators at the mean-field level. To achieve this, we apply slave-boson mean-field theory for a system with and without periodic boundary conditions, in order to study the system at bulk and slab geometry configuration. This enables us to observe a clear signature of protected edge states through band structure and calculation of spectral functions.
Recent developments in the techniques of ultrafast pump-probe photoemission have made possible the search for collective modes in strongly correlated systems out of equilibrium. Including inelastic scattering processes and a retarded interaction, we simulate time- and angle- resolved photoemission spectroscopy (trARPES) to study the amplitude mode of a d-wave superconductor, a collective mode excited through the nonlinear light-matter coupling to the pump pulse. We find that the amplitude mode oscillations of the d-wave order parameter occur in phase at a single frequency that is twice the quasi-steady-state maximum gap size after pumping. We comment on the necessary conditions for detecting the amplitude mode in trARPES experiments.
We develop an approximation formula for the cross-validation error (CVE) of a sparse linear regression penalized by $\ell_1$-norm and total variation terms, which is based on a perturbative expansion utilizing the largeness of both the data dimensionality and the model. The developed formula allows us to reduce the necessary computational cost of the CVE evaluation significantly. The practicality of the formula is tested through application to simulated black-hole image reconstruction on the event-horizon scale with super resolution. The results demonstrate that our approximation reproduces the CVE values obtained via literally conducted cross-validation with reasonably good precision.
We report on the fabrication and characterization of a Fabry-Perot microcavity enclosing a thin diamond membrane at cryogenic temperatures. The cavity is designed to enhance resonant emission of single nitrogen-vacancy centers by allowing spectral and spatial tuning while preserving the optical properties observed in bulk diamond. We demonstrate cavity finesse at cryogenic temperatures within the range of F = 4,000-12,000 and find a sub-nanometer cavity stability. Modeling shows that coupling nitrogen-vacancy centers to these cavities could lead to an increase of remote entanglement success rates by three orders of magnitude.
Exotic spin-multipolar ordering in spin transition metal insulators has so far eluded unambiguous experimental observation. A less studied, but perhaps more feasible fingerprint of multipole character emerges in the excitation spectrum in the form of quadrupolar transitions. Such multipolar excitations are desirable as they can be manipulated with the use of light or electric field and can be captured by means of conventional experimental techniques. Here we study single crystals of multiferroic Sr$_2$CoGe$_2$O$_7$, and show that due to its nearly isotropic nature a purely quadrupolar bimagnon mode appears in the electron spin resonance (ESR) spectra. This non-magnetic spin-excitation couples to the electric field of the light and becomes observable for a specific experimental configuration, in full agreement with a theoretical analysis of the selection rules.
Nanomechanical devices have attracted the interest of a growing interdisciplinary research community, since they can be used as highly sensitive transducers for various physical quantities. Exquisite control over these systems facilitates experiments on the foundations of physics. Here, we demonstrate that an optically trapped silicon nanorod, set into rotation at MHz frequencies, can be locked to an external clock, transducing the properties of the time standard to the rod's motion with the remarkable frequency stability $f_{\rm r}/\Delta f_{\rm r}$ of $7.7 \times 10^{11}$. While the dynamics of this periodically driven rotor generally can be chaotic, we derive and verify that stable limit cycles exist over a surprisingly wide parameter range. This robustness should enable, in principle, measurements of external torques with sensitivities better than 0.25zNm, even at room temperature. We show that in a dilute gas, real-time phase measurements on the locked nanorod transduce pressure values with a sensitivity of 0.3%.
By comparing femtosecond laser pulse induced ferro- and antiferromagnetic dynamics in one and the same material - metallic dysprosium - we show both to behave fundamentally different. Antiferromagnetic order is considerably faster and much more efficiently manipulated by optical excitation than its ferromagnetic counterpart. We assign the fast and extremely efficient process in the antiferromagnet to an interatomic transfer of angular momentum within the spin system. Our findings do not only reveal this angular momentum transfer channel effective in antiferromagnets and other magnetic structures with non-parallel spin alignment, they also point out a possible route towards energy-efficient spin manipulation for magnetic devices.
Mobile impurity atoms immersed in Bose-Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable microscopic parameters and to explore equilibrium and dynamical properties of polarons using a rich toolbox of atomic physics. In this paper we present a detailed theoretical analysis of Bose polarons in one dimensional systems of ultracold atoms. By combining a non-perturbative renormalization group approach with numerically exact diffusion Monte Carlo calculations we obtain not only detailed numerical results over a broad range of parameters but also qualitative understanding of different regimes of the system. We find that an accurate description of Bose polarons requires the inclusion of two-phonon scattering terms which go beyond the commonly used Fr\"ohlich model. Furthermore we show that when the Bose gas is in the strongly interacting regime, one needs to include interactions between the phonon modes. We use several theoretical approaches to calculate the polaron energy and its effective mass. The former can be measured using radio-frequency spectroscopy and the latter can be studied experimentally using impurity oscillations in a harmonic trapping potential. We compare our theoretical results for the effective mass to the experiments by Catani et al. [PRA 85, 023623 (2012)]. In the weak-to-intermediate coupling regimes we obtain excellent quantitative agreement between theory and experiment, without any free fitting parameter. We supplement our analysis by full dynamical simulations of polaron oscillations in a shallow trapping potential. We also use our renormalization group approach to analyze the full phase diagram and identify regions that support repulsive and attractive polarons, as well as multi-particle bound states.
The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolutions, as given by quantum maps. Third, it brings out the full connection between the FDT and the Quantum Fisher information, the figure of merit in quantum metrology.
The low-energy behaviors of gapless double- and triple-Weyl fermions caused by the interplay of long-range Coulomb interaction and quenched disorder are studied by performing a renormalization group analysis. It is found that an arbitrarily weak disorder drives the double-Weyl semimetal to undergo a quantum phase transition into a compressible diffusive metal, independent of the disorder type and the Coulomb interaction strength. In contrast, the nature of the ground state of triple-Weyl fermion system relies sensitively on the specific disorder type in the noninteracting limit: The system is turned into a compressible diffusive metal state by an arbitrarily weak random scalar potential or $z$ component of random vector potential but exhibits stable critical behavior when there is only $x$ or $y$ component of random vector potential. In case the triple-Weyl fermions couple to random scalar potential, the system becomes a diffusive metal in the weak interaction regime but remains a semimetal if Coulomb interaction is sufficiently strong. Interplay of Coulomb interaction and $x$, or $y$, component of random vector potential leads to a stable infrared fixed point that is likely to be characterized by critical behavior. When Coulomb interaction coexists with the $z$ component of random vector potential, the system flows to the interaction-dominated strong coupling regime, which might drive a Mott insulating transition. It is thus clear that double- and triple-Weyl fermions exhibit distinct low-energy behavior in response to interaction and disorder. The physical explanation of such distinction is discussed in detail. The role played by long-range Coulomb impurity in triple-Weyl semimetal is also considered.
We characterize the soft modes of the dynamical matrix at the depinning transition, and compare it with the properties of the Anderson model (and long--range generalizations). The density of states at the edge of the spectrum displays a universal linear tail, different from the Lifshitz tails. The eigenvectors are instead very similar in the two matrix ensembles. We focus on the ground state (soft mode), which represents the epicenter of avalanche instabilities. We expect it to be localized in all finite dimensions, and make a clear connection between its localization length and the Larkin length of the depinning model. In the fully connected model, the weak--strong pinning transition coincides with a peculiar localization transition of the ground state.
We study the spin-charge conversion mechanisms in a two-dimensional gas of electrons moving in a smooth disorder potential by accounting for both Rashba-type and Mott's skew scattering contributions. We find that quantum interference effects between spin-flip and skew scattering give rise to anisotropic spin precession scattering (ASP), a direct spin-charge conversion mechanism that was discovered in an earlier study of graphene decorated with adatoms [C. Huang \emph{et al.} Phys.~Rev.~B \textbf{94} 085414.~(2016)]. Our findings suggest that, together with other spin-charge conversion mechanisms such as the inverse galvanic effect, ASP is a fairly universal phenomenon that should be present in disordered two-dimensional systems lacking inversion symmetry.
We develop a new first-principles approach to predict and understand rates of singlet fission with an ab initio Green's-function formalism based on many-body perturbation theory. Starting with singlet and triplet excitons computed from a GW plus Bethe-Salpeter equation approach, we calculate the exciton--bi-exciton coupling to lowest order in the Coulomb interaction, assuming a final state consisting of two non-interacting spin-correlated triplets with finite center-of-mass momentum. For crystalline pentacene, symmetries dictate that the only purely Coulombic fission decay from a bright singlet state requires a final state consisting of two inequivalent nearly degenerate triplets of nonzero, equal and opposite, center-of-mass momenta. For such a process, we predict a singlet lifetime of 40 to 150 fs, in very good agreement with experimental data, indicating that this process can dominate singlet fission in crystalline pentacene. Our approach is general and provides a framework for predicting and understanding multiexciton interactions in solids.
A free surface of a dilute $^3$He-$^4$He liquid mixture is a unique system where two Fermi liquids with distinct dimensions coexist: a three-dimensional (3D) $^3$He Fermi liquid in bulk and a two-dimensional (2D) $^3$He Fermi liquid at the surface. To investigate a novel effect generated by the interaction between the two Fermi liquids, mobility of a Wigner crystal of electrons formed on the free surface of the mixture is studied. An anomalous enhancement of the mobility, compared with the case where the 3D and 2D systems do not interact with each other, is observed. The enhancement is explained by non-trivial reflection of 3D quasiparticles from the surface covered with the 2D $^3$He system.
We study the anomalous Nernst and thermal Hall effects in a linearized low-energy model of a tilted Weyl semimetal, with two Weyl nodes separated in momentum space. For inversion symmetric tilt, we give analytic expressions in two opposite limits: for a small tilt, corresponding to a type-I Weyl semimetal, the Nernst conductivity is finite and independent of the Fermi level, while for a large tilt, corresponding to a type-II Weyl semimetal, it acquires a contribution depending logarithmically on the Fermi energy. This result is in a sharp contrast to the nontilted case, where the Nernst response is known to be zero in the linear model. The thermal Hall conductivity similarly acquires Fermi surface contributions, which add to the Fermi level independent, zero tilt result, and is suppressed as one over the tilt parameter at half filling in the Type-II phase. In the case of inversion breaking tilt, with the tilting vector of equal modulus in the two Weyl cones, all Fermi surface contributions to both anomalous responses cancel out, resulting in zero Nernst conductivity. We discuss two possible experimental setups, representing open and closed thermoelectric circuits.
In the context of a discrete analogue of the classical Heisenberg model, we investigate critical behavior of the icosahedron model, where the interaction energy is defined as the inner product of neighboring vector spins of unit length pointing to vertices of the icosahedron. Effective correlation length and magnetization of the model are calculated by means of the corner-transfer matrix renormalization group (CTMRG) method. Scaling analysis with respect to the cutoff dimension $m$ in CTMRG reveals the second-order phase transition characterized by the exponents $\nu = 1.62\pm0.02$ and $\beta = 0.12\pm0.01$. We also extract the central charge from the classical analogue of the entanglement entropy as $c = 1.90\pm0.02$, which cannot be explained by the minimal series of conformal field theory.
The electronic nematic phase is characterized as an ordered state of matter with rotational symmetry breaking and has been well studied in the quantum Hall system and the under-doped high-$T_c$ superconductors, regardless of cuprate or pnictide family. The nematic state in high-$T_c$ systems is often related to the structural transition or electronic instability in the normal phase. Nevertheless, the electronic states below the superconducting transition is still an open question. With high-resolution scanning tunneling microscope measurements, direct observation of vortex core in FeSe thin films reveals the nematic superconducting state [Song \emph{et al}., Science 332, 1410 (2011)]. Here, motivated by the experiment, we construct the extended Ginzburg-Landau free energy to describe the elliptical vortex, where a mixed isotropic \emph{s}-wave and anisotropic \emph{d}-wave superconducting order is coupled to the nematic order. The nematic order induces the mixture of two superconducting orders and enhance the anisotropic interaction between the two superconducting orders, resulting in a symmetry breaking from $C_4$ to $C_2$. Consequently, the vortex cores are stretched into an elliptical shape. In the equilibrium state, the elliptical vortices assemble an oblique vortex lattice with $r>\sqrt{3}$, being well consistent with experimental results.
We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced, such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.
The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a flat and a spherical rough and textured substrate is theoretically studied in the capillary-controlled spreading regime. A droplet whose scale is much larger than that of the roughness of substrate is considered. The equilibrium contact angle on a rough substrate is modeled by the Wenzel and the Cassie-Baxter model. Only the viscous energy dissipation within the droplet volume is considered, and that within the texture of substrate by imbibition is neglected. Then, the energy balance approach is adopted to derive the evolution equation of the contact angle. When the equilibrium contact angle vanishes, the relaxation of dynamic contact angle $\theta$ of a droplet obeys a power law decay $\theta \sim t^{-\alpha}$ except for the Newtonian and the non-Newtonian shear-thinning liquid of the Wenzel model on a spherical substrate. The spreading exponent $\alpha$ of the non-Newtonian shear-thickening liquid of the Wenzel model on a spherical substrate is larger than others. The relaxation of the Newtonian liquid of the Wenzel model on a spherical substrate is even faster showing the exponential relaxation. The relaxation of the non-Newtonian shear-thinning liquid of Wenzel model on a spherical substrate is fastest and finishes within a finite time. Thus, the topography (roughness) and the topology (flat to spherical) of substrate accelerate the spreading of droplet.
We propose a new approach to understand the time-dependent temperature increasing process of gold-silica core-shell nanoparticles injected into chicken tissues under near-infrared laser irradiation. Gold nanoshells strongly absorb near-infrared radiations and efficiently transform absorbed energy into heat. Temperature rise given by experiments and numerical calculations based on bioheat transfer are in good agreement. Our work improves the analysis of a recent study [Richardson et al., Nano Lett. 9, 1139 (2009)] by including effects of the medium perfusion on temperature increase. The theoretical analysis can also be used to estimate the distribution of nanoparticles in experimental samples and provide a relative accuracy prediction for the temperature profile of new systems. This methodology would provide a novel and reliable tool for speeding up photothermal investigations and designing state-of-the-art photothermal devices.
Large crystals of La$_{2-x}$Ca$_{1+x}$Cu$_2$O$_{6}$ (La-Ca-2126) with $x=0.10$ and 0.15 have been grown and converted to bulk superconductors by high-pressure oxygen annealing. The superconducting transition temperature, $T_c$, is as high as 55~K; this can be raised to 60~K by post-annealing in air. Here we present structural and magnetic characterizations of these crystals using neutron scattering and muon spin rotation techniques. While the as-grown, non-superconducting crystals are single phase, we find that the superconducting crystals contain 3 phases forming coherent domains stacked along the $c$ axis: the dominant La-Ca-2126 phase, very thin (1.5 unit-cell) intergrowths of La$_2$CuO$_4$, and an antiferromagnetic La$_8$Cu$_8$O$_{20}$ phase. We propose that the formation and segregation of the latter phases increases the Ca concentration of the La-Ca-2126, thus providing the hole-doping that supports superconductivity.
As first identified by Poynting, typical elastic solids exhibit axial extension under torsion. Along with related normal stress effects such as rod climbing of non-Newtonian fluids, this depends on the first normal stress difference $N_1$, which is of fundamental importance for a variety of nonlinear deformation and flow phenomena, especially in soft matter. This stress difference is almost always positive for elastic solids and viscoelastic polymer materials. Recent work has shown that biopolymer networks can exhibit negative normal stress, but whether $N_1$ itself can be negative in these networks has remained an open question. We demonstrate that lattice-based 2D and 3D fiber network models, as well as off-lattice 2D networks, can indeed exhibit an anomalous negative $N_1$. We also show that this anomaly becomes most pronounced near a critical point of marginal stability, suggesting the importance of critical fluctuations in driving the change of sign in $N_1$. Finally, we present a phase diagram indicating regimes of anomalous normal stress as a function of strain, network connectivity, and disorder.
Vanadium dioxide (VO$_{2}$) undergoes a first-order metal-insulator transition (MIT) upon cooling near room temperature, concomitant with structural change from rutile to monoclinic. Accurate characterization of lattice vibrations is vital for elucidating the transition mechanism. To investigate the lattice dynamics and thermal transport properties of VO$_{2}$ across the MIT, we present a phonon renormalization scheme based on self-consistent phonon theory through iteratively refining vibrational free energy. Using this technique, we compute temperature-dependent phonon dispersion and lifetimes, and point out the importance of both magnetic and vibrational entropy in driving the MIT. The predicted phonon dispersion and lifetimes show quantitative agreement with experimental measurements. We demonstrate that lattice thermal conductivity of rutile VO$_{2}$ is nearly temperature independent as a result of strong intrinsic anharmonicity, while that of monoclinic VO$_{2}$ varies according to $1/T$. Due to phonon softening and enhanced scattering rates, the lattice thermal conductivity is deduced to be substantially lower in the rutile phase, suggesting that Wiedemann-Franz law might not be strongly violated in rutile VO$_{2}$.
A nematic topological superconductor has an order parameter symmetry, which spontaneously breaks the crystalline symmetry in its superconducting state. This state can be observed, for example, by thermodynamic or upper critical field experiments in which a magnetic field is rotated with respect to the crystalline axes. The corresponding physical quantity then directly reflects the symmetry of the order parameter. We present a study on the superconducting upper critical field of the Nb-doped topological insulator NbxBi2Se3 for various magnetic field orientations parallel and perpendicular to the basal plane of the Bi2Se3 layers. The data were obtained by two complementary experimental techniques, magnetoresistance and DC magnetization, on three different single crystalline samples of the same batch. Both methods and all samples show with perfect agreement that the in-plane upper critical fields clearly demonstrate a two-fold symmetry that breaks the three-fold crystal symmetry. The two-fold symmetry is also found in the absolute value of the magnetization of the initial zero-field-cooled branch of the hysteresis loop and in the value of the thermodynamic contribution above the irreversibility field, but also in the irreversible properties such as the value of the characteristic irreversibility field and in the width of the hysteresis loop. This provides strong experimental evidence that Nb-doped Bi2Se3 is a nematic topological superconductor similar to the Cu- and Sr-doped Bi2Se3.
We consider an effective model for graphene with interface-induced spin-orbit coupling and calculate the quantum Hall effect in the low-energy limit. We perform a systematic analysis of the contribution of the different terms of the effective Hamiltonian to the quantum Hall effect (QHE). By analysing the spin-splitting of the quantum Hall states as a function of magnetic field and gate-voltage, we obtain different scaling laws that can be used to characterise the spin-orbit coupling in experiments. Furthermore, we employ a real-space quantum transport approach to calculate the quantum Hall conductivity and investigate the robustness of the QHE to disorder introduced by hydrogen impurities. For that purpose, we combine first-principles calculations and a genetic algorithm strategy to obtain a graphene-only Hamiltonian that models the impurity.
This Reply is intended as a refutation of the preceding Comment [Oikonomou and Bagci, Phys. Rev. E 96, 056101 (2017)] on our paper [Plastino et al., Phys. Rev. E 94, 012145 (2016).]. We show that the Tsallis probability distribution of our paper does not coincide with the Tsallis distribution studied by Oikonomou and Bagci. Consequently, their findings do not apply to our paper.
Orbital effects of a magnetic field in a proximitized semiconductor nanowire are studied in the context of the spatial extent of Majorana bound states. We develop analytical model that explains the impact of concurring effects of paramagnetic coupling of the nanowire bands via the kinetic energy operator and spin-orbit interaction on the Majorana modes. We find, that the perpendicular field, so far considered as detrimental to the Majorana fermion formation, is in fact helpful in establishing the topological zero-energy-modes in a finite system due to significant decrease of the Majorana decay length.
SrMnSb$_2$ is suggested to be a magnetic topological semimetal. It contains square, 2D Sb planes with non-symmorphic crystal symmetries that could protect band crossings, offering the possibility of a quasi-2D, robust Dirac semi-metal in the form of a stable, bulk (3D) crystal. Here, we report a combined and comprehensive experimental and theoretical investigation of the electronic structure of SrMnSb$_2$, including the first ARPES data on this compound. SrMnSb$_2$ possesses a small Fermi surface originating from highly 2D, sharp and linearly dispersing bands (the Y-states) around the (0,$\pi$/a)-point in $k$-space. The ARPES Fermi surface agrees perfectly with that from bulk-sensitive Shubnikov de Haas data from the same crystals, proving the Y$-$states to be responsible for electrical conductivity in SrMnSb$_2$. DFT and tight binding (TB) methods are used to model the electronic states, and both show excellent agreement with the ARPES data. Despite the great promise of the latter, both theory approaches show the Y-states to be gapped above E$_F$, suggesting trivial topology. Subsequent analysis within both theory approaches shows the Berry phase to be zero, indicating the non-topological character of the transport in SrMnSb$_2$, a conclusion backed up by the analysis of the quantum oscillation data from our crystals.
Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behaviour, however, typically assume that groups and populations consist of identical individuals. In this paper, we develop and analyse a model of merge and split group dynamics, also called fission-fusion dynamics, for heterogeneous populations that contain two types (or species) of individuals. We assume that more heterogeneous groups experience higher split rates than homogeneous groups. We derive a master equation for group size and compositions, and find mean-field steady-state solutions. We predict that there is a critical group size below which groups are more likely to be homogeneous and contain the abundant type/species. Groups larger than the critical size are representative of the global heterogeneity, despite the propensity of heterogeneous groups to split at higher rates. Thus, our model predicts that composition of flocks are group-size dependent. We discuss the implications of our results for current methods used to infer interspecies interactions from mixed-species flock compositions.