Nonlocal Conductivity Research Articles

Trivial Andreev Band Mimicking Topological Bulk Gap Reopening in the Nonlocal Conductance of Long Rashba Nanowires.

We consider a one-dimensional Rashba nanowire in which multiple Andreev bound states in the bulk of the nanowire form an Andreev band. We show that, under certain circumstances, this trivial Andreev band can produce an apparent closing and reopening signature of the bulk band gap in the nonlocal conductance of the nanowire. Furthermore, we show that the existence of the trivial bulk reopening signature in nonlocal conductance is essentially unaffected by the additional presence of trivial zero-bias peaks in the local conductance at either end of the nanowire. The simultaneous occurrence of a trivial bulk reopening signature and zero-bias peaks mimics the basic features required to pass the so-called "topological gap protocol." Our results therefore provide a topologically trivial minimal model by which the applicability of this protocol can be benchmarked.

Giant nonlocal edge conduction in the axion insulator state of MnBi2Te4

The recently discovered antiferromagnetic (AFM) topological insulator (TI) MnBi2Te4 represents a versatile material platform for exploring exotic topological quantum phenomena in nanoscale devices. It has been proposed that even-septuple-layer (even-SL) MnBi2Te4 can host helical hinge currents with unique nonlocal behavior, but experimental confirmation is still lacking. In this work, we report transport studies of exfoliated MnBi2Te4 flakes with varied thicknesses down to the few-nanometer regime. We observe giant nonlocal transport signals in even-SL devices when the system is in the axion insulator state but vanishingly small nonlocal signal in the odd-SL devices at the same magnetic field range. In conjunction with theoretical calculations, we demonstrate that the nonlocal transport is via the helical edge currents mainly distributed at the hinges between the side and top/bottom surfaces. The helical edge currents in the axion insulator state may find unique applications in topological quantum devices.

Non-local Andreev reflection through Andreev molecular states in graphene Josephson junctions

We propose that a device composed of two vertically stacked monolayer graphene Josephson junctions can be used for Cooper pair splitting. The hybridization of the Andreev bound states of the two Josephson junction can facilitate non-local transport in this normal-superconductor hybrid structure, which we study by calculating the non-local differential conductance. Assuming that one of the graphene layers is electron and the other is hole doped, we find that the non-local Andreev reflection can dominate the differential conductance of the system. Our setup does not require the precise control of junction length, doping, or super conducting phase difference, which could be an important advantage for experimental realization.

The nonlocal thermo‐hydro‐mechanical model for cracking behaviors of quasi‐brittle materials in the framework of advanced general particle dynamics

AbstractA novel nonlocal thermo‐hydro‐mechanical coupling model is proposed to investigate cracking behaviors of quasi‐brittle materials in the framework of advanced general particle dynamics (GPD). The nonlocal thermal conduction equation and the nonlocal flow diffusion equation are derived based on nonlocal vector calculus and the microscopic constitutive equation. Moreover, the coupling influences are considered based on the nonlocal equation and the coupling principle. The governing equation of the coupling system is established in the framework of GPD. The correctness of the proposed model is verified through comparing with the corresponding experimental data, and the numerical results are in good agreement with experimental results. Finally, the proposed model is applied to analyze the deformation and cracking behaviors of rock mass around tunnels, and the stress redistribution is revealed under thermo‐hydro‐mechanical coupling condition.

Wave propagation in a non-local magneto-thermoelastic medium permeated by heat source

In this paper, we consider the new concept of non-local heat conduction equation to generalized magneto-thermoelastic problem of two dimensional isotropic and homogeneous half-space in presence of heat-flux at the boundary surface. By using the harmonic plane waves, the governing equations are transformed to the vector matrix differential equation which is then solved by eigenvalue method. The analytical closed form solutions for displacement component, temperature distribution and stress components have been made and comparisons are also illustrated graphically with the theory of non-local dual-phase-lag (NLDPL) and non-local Lord-Shulman (NLLS) theory for different values of physical parameters. The significant effects of non-local variables as well as phase lagging parameters on displacements, temperature distribution and stress components are studied by means of graphically and concluding remarks are drawn.

Nonlocal optical conductivity of Fermi surface nesting materials

We investigate the nonlocal optical conductivity of Fermi surface nesting materials that support charge density waves (CDWs) or spin density waves (SDWs). The nonlocal optical conductivity contains information on correlations in electron fluids, which could not be accessed by standard optical probes. A half-metal emerges from doping a CDW, and similarly, a spin-valley half-metal emerges from doping an SDW. Based on the parabolic band approximation, we find that the Drude peak is shifted to a higher frequency and splits into two peaks in the nonlocal optical conductivity. We attribute this to the two Fermi velocities in the half-metal or spin-valley half-metal states.

Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions.

We report simultaneously acquired local and nonlocal transport spectroscopy in a phase-biased planar Josephson junction based on an epitaxial InAs-Al hybrid two-dimensional heterostructure. Quantum point contacts at the junction ends allow measurement of the 2×2 matrix of local and nonlocal tunneling conductances as a function of magnetic field along the junction, phase difference across the junction, and carrier density. A closing and reopening of a gap was observed in both the local and nonlocal tunneling spectra as a function of magnetic field. For particular tunings of junction density, gap reopenings were accompanied by zero-bias conductance peaks (ZBCPs) in local conductances. End-to-end correlation of gap reopening was strong, while correlation of local ZBCPs was weak. A model of the device, with disorder treated phenomenologically, shows comparable conductance matrix behavior associated with a topological phase transition. Phase dependence helps distinguish possible origins of the ZBCPs.

Conductance spectroscopy of Majorana zero modes in superconductor-magnetic insulator nanowire hybrid systems

There has been recent interest in superconductor-magnetic insulator hybrid Rashba nanowire setups for potentially hosting Majorana zero modes at smaller external Zeeman fields. Using the non-equilibrium Green’s function technique, we develop a quantum transport model that accounts for the interplay between the quasiparticle dynamics in the superconductor-magnetic insulator bilayer structure and the transport processes through the Rashba nanowire. We provide an analysis of three-terminal setups to probe the local and non-local conductance in clean and disordered nanowires. We uncover the gap closing and reopening followed by the emergence of near-zero energy states, which can be attributed to topological zero modes in the clean limit. In the presence of a disordered potential, trivial Andreev bound states may form with signatures reminiscent of topological zero modes. Our results provide transport-based analysis of regimes that support the formation of Majorana modes in these hybrid systems while investigating the effect of disorder on devices.

Investigation on buckling of Timoshenko nanobeams resting on Winkler-Pasternak foundations in a non-uniform thermal environment via stress-driven nonlocal elasticity and nonlocal heat conduction

This study investigates the size-dependent buckling behavior of Timoshenko nanobeams resting on Winkler-Pasternak foundations in a non-uniform thermal environment. A non-uniform temperature distribution is established through nonlocal heat conduction. Subsequently, the equivalent thermal load due to the obtained temperature distribution and boundary constraints is derived using the governing equations of the axial thermal deformation of the beams based on the stress-driven nonlocal elastic model. To obtain the critical buckling load of the nanobeams, the quadrature element method is used to numerically resolve the eigenvalue problem. In the numerical simulation section, we have presented a series of examples to analyze the effects of length-to-height ratios, nonlocal scale parameters, and Winkler-Pasternak foundation parameters on the buckling loads of the nanobeams under various boundary conditions. Moreover, we examine the effect of comprehensively considering both the elastic and thermal nonlocality on the thermal loads and finally mechanical buckling loads.

Detecting Majorana zero modes with transport measurements

Topological superconductors have attracted much research interest, because they were proposed to host non-abelian Ising Anyon Majorana zero modes and thus can be used to construct fault-tolerant topological quantum computers. This paper mainly reviews the electrical transport methods for detecting the presence of Majorana zero modes. First, the basic concepts of topological superconductivity, Majorana zero modes and non-Abelian statistics are introduced, followed by a summary of various schemes for implementing topological superconductivity. Then, the experimental methods for detecting topological superconductivity or Majorana zero modes by using low-temperature transport methods, including electron tunneling spectroscopy, Coulomb blockade spectroscopy and non-local conductance detection, which are widely used in superconductor/nanowire hybrid systems, are discussed. On the other hand, the measurements of the (inverse) AC Josephson effect and current (energy) phase relationships are also reviewed to identify Majorana zero modes in Josephson devices. Meanwhile, to deepen our understanding of Majorana zero modes, some mechanisms for explaining the experimental data observed in the above experiments are provided. Finally, a brief summary and outlook of the electrical transport methods of Majorana zero modes are presented.

Pressure-induced negative capacitance and enhanced grain boundary conductivity in nanocrystalline solid electrolyte BaZrO3

Proton-conducting BaZrO3-doped electrolytes are considered as potential high temperature proton conductors due to their high ionic conductivity and electrical efficiency in the operating temperature range of solid oxide fuel cells. However, doping leads to a decrease in grain boundary conductivity and greatly limits its applications. Here, the charge transport properties of sub-micro and nano-BaZrO3 electrolytes were studied by in situ high-pressure impedance measurements and first-principles calculations. Mixed ionic-electronic conduction was found in both samples in the whole pressure range. Pressure-induced negative capacitance in the tetragonal phase of nano-BaZrO3 was observed, which was related to the space charge layer of grain boundaries as well as the electrostrictive strain of grains. The enhanced electrostrictive effect was attributed to the existence of polar nano-domains in nano-BaZrO3. Furthermore, the coincident imaginary part of impedance and modulus peaks on the frequency scale indicated a non-localized carrier conduction in the tetragonal phase of nano-BaZrO3. The grain boundary conductivity of nano-BaZrO3 was enhanced by four orders of magnitude, and the impedance response changed from a constant phase element to an ideal capacitance, which was accompanied by the cubic to tetragonal phase transition. At a switching frequency of 0.1 Hz, the real part of the dielectric function of nano-BaZrO3 increases sharply with frequencies from negative to positive values, exhibiting a plasma-like Drude behavior. Our results provide insight into the optimization and application of BaZrO3-based proton conductors in solid oxide fuel cells.

Multiterminal transport spectroscopy of subgap states in Coulomb-blockaded superconductors

Subgap states are responsible for the low-bias transport features of hybrid superconducting--semiconducting devices. Here, we analyze the local and nonlocal differential conductance of Coulomb-blockaded multiterminal superconducting islands that host subgap states with different spatial structures. The emerging patterns of their transport spectroscopy are used to characterize the possible topological nature of these devices and offer the possibility of controlling their transport properties. We develop a next-to-leading order master equation to describe the multiterminal transport in superconductors with both strong Coulomb interactions and multiple subgap states, coupled with metallic leads. We show that the nonlocal differential conductance characterizes the spatial extension of the subgap states and signals the presence of degenerate bound states with a finite support on different parts of the device. Additionally, it displays sharp sign changes as a function of the induced charge of the superconductor, signaling energy crossings among its lowest excited states.

Nonlocal conductance spectroscopy of Andreev bound states in gate-defined InAs/Al nanowires

Andreev bound states emerge as excitations in semiconducting InAs, proximitized by superconducting Al. These states can be a mixture of electron and hole and their structure is determined by material parameters, external magnetic field, and gate voltages. Nonlocal conductance is a differential measurement of the current carried by Andreev bound states through a quasi-one-dimensional nanowire, and it can reveal the charge character of the states given by the BCS charge.

The Effect of a Nonlocal Thermoelastic Model on a Thermoelastic Material under Fractional Time Derivatives

This article develops a novel nonlocal theory of generalized thermoelastic material based on fractional time derivatives and Eringen’s nonlocal thermoelasticity. An ultra-short pulse laser heats the surface of the medium’s surrounding plane. Using the Laplace transform method, the basic equations and their accompanying boundary conditions were numerically solved. The distribution of thermal stress, temperature and displacement are physical variables for which the eigenvalues approach was employed to generate the analytical solution. Visual representations were used to examine the influence of the nonlocal parameters and fractional time derivative parameters on the wave propagation distributions of the physical fields for materials. The consideration of the nonlocal thermoelasticity theory (nonlocal elasticity and heat conduction) with fractional time derivatives may lead us to conclude that the variations in physical quantities are considerably impacted.

Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions

For a nonlocal initial-boundary value problem for a one-dimensional heat equation with not strongly regular boundary conditions of general type, an approximate difference scheme with weights is constructed. A correct and stable algorithm for the numerical solving of the difference problem is proposed. It is proven that the difference scheme with weights is stable and its solution converges to the exact solution of the differential problem in the grid L2h-norm. Stability conditions are established. An estimate of the numerical solution with respect to the initial data and the right-hand side of the difference problem is given.

Microstructure size-dependent contact behavior of a thermoelectric film bonded to an elastic substrate with couple stress theory

Thermoelectric films linked to elastic substrates are typical engineering structures and have applications in heat recovery systems. This article uses the nonlocal heat conduction and couple stress theory to investigate the electric-thermal-elastic behavior of the thermoelectric film placed on the elastic half-plane. The internal characteristic lengths of both the thermoelectric film and the elastic substrate are introduced to reveal the scale effects. The coupling governing integro-differential equations in terms of the interface shear stress and tensile stress are derived for the thermoelectric film and the elastic substrate. The numerical results show how the distribution of the tensile and shear stress intensity factors is affected by the stiffness ratio of the substrate to the thermoelectric film, the internal characteristic lengths of the thermoelectric film and the elastic substrate, and the thickness to length ratio of the thermoelectric film. Compared with the classical model for a thicker thermoelectric film and stiffer elastic substrate, the present study demonstrates the necessity of taking into account the microstructure lengths of the thermoelectric film and the elastic substrate.

Ballistic-to-hydrodynamic transition and collective modes for two-dimensional electron systems in magnetic field

The recent demonstrations of viscous hydrodynamic electron flow in two-dimensional electron systems poses serious questions to the validity of existing transport theories, including the ballistic model, the collision-induced and collisionless hydrodynamics. While the theories of transport at hydrodynamic-to-ballistic crossover for free 2d electrons are well established, the same is not true for electrons in magnetic fields. In this work, we develop an analytically solvable model describing the transition from ballistic to hydrodynamic transport with changing the strength of electron-electron collisions in magnetic fields. Within this model, we find an expression for the high-frequency non-local conductivity tensor of 2d electrons. It is valid at arbitrary relation between frequency of external field $\omega$, the cyclotron frequency $\omega_c$, and the frequency of e-e collisions $\tau^{-1}_{ee}$. We use the obtained expression to study the transformation of 2d magnetoplasmon modes at hydrodynamic-to-ballistic crossover. In the true hydrodynamic regime, $\omega\tau_{ee} \ll 1$, the 2DES supports a single magnetoplasmon mode that is not split at cyclotron harmonics. In the ballistic regime, $\omega\tau_{ee} \gg 1$, the plasmon dispersion develops splittings at cyclotron harmonics, forming the Bernstein modes. A formal long-wavelength expansion of kinetic equations ("collisionless hydrodynamics") predicts the first splitting of plasmon dispersion at $\omega\approx 2\omega_c$. Still, such expansion fails to predict the zero and negative group velocity sections of true magnetoplasmon dispersion, for which the full kinetic model is required.

Probing the topological character of superconductors via nonlocal Hanbury Brown and Twiss correlations

Superconductors can be classified as topological or not based on whether time-reversal symmetry, chiral symmetry, and particle-hole symmetry are preserved or not. Further, topological superconductors can also be classified as chiral or helical. In this paper, using Hanbury Brown and Twiss (HBT) shot-noise correlations and the nonlocal conductance, we probe metal and two-dimensional unconventional superconductor and metal junctions to understand better the pairing topological vs nontopological or helical vs chiral or nodal vs gapful. We see that HBT correlations are asymmetric as a function of bias voltage for nontopological superconductors, whereas they are symmetric for topological superconductors irrespective of the barrier strength. Topological superconductors are associated with Majorana fermions which are important for topological quantum computation. By distinguishing topological superconductors from nontopological superconductors, our study will help search for Majorana fermions, which will aid in designing a topological quantum computer.

Terahertz transverse electric modes in graphene with DC current in hydrodynamic regime

The dispersion, excitation, and amplification of electromagnetic transverse electric (TE) modes at terahertz (THz) frequencies in graphene in the hydrodynamic (HD) regime, with a direct electric current flowing perpendicular to the TE mode wavevector, were theoretically investigated. The expression for the nonlocal HD conductivity of graphene with a direct electric current flowing perpendicular to the TE mode wavevector was derived. The direct electric current in graphene leads to the capacitive nature of the graphene HD conductivity at THz frequencies, which makes TE modes exist in this frequency range. The excitation of TE modes in graphene by an incident THz wave was modeled for the attenuated total reflection geometry. A new physical mechanism of TE mode amplification in graphene effective for a low value of carrier drift velocity was predicted. THz lasing regimes with TE modes in graphene structure with direct electric current were found. The results of this work can be used to create miniature technologically feasible sources and amplifiers of THz radiation.

State-space approach to nonlocal thermo-viscoelastic piezoelectric materials with fractional dual-phase lag heat transfer

Purpose The purpose of this study is to develop a comprehensive size-dependent piezoelectric thermo-viscoelastic coupling model that accounts for two fundamentally distinct size-dependent models that govern fractional dual-phase lag heat transfer and viscoelastic deformation, respectively. Design/methodology/approach The fractional calculus has recently been shown to capture precisely the experimental effects of viscoelastic materials. The governing equations are combined into a unified system, from which certain theorems results on linear coupled and generalized theories of thermo-viscoelasticity may be easily established. Laplace transforms and state–space approach will be used to determine the generic solution when any set of boundary conditions exists. The derived formulation is used to two concrete different problems for a piezoelectric rod. The numerical technique for inverting the transfer functions is used to generate observable numerical results. Findings Some analogies of impacts of nonlocal thermal conduction, nonlocal elasticity and DPL parameters as well as fractional order on thermal spreads and thermo-viscoelastic response are illustrated in the figures. Originality/value The results in all figures indicate that the nonlocal thermal and viscoelastic parameters have a considerable influence on all field values. This discovery might help with the design and analysis of thermal-mechanical aspects of nanoscale devices.