The quanta of electrical conductance is derived for a one-dimensional electron gas both by making use of the quasi-classical motion of a quantum fluid and by using arguments related to the uncertainty principle. The result is extended to a nanowire of finite cross-section area and to electrons in magnetic field, and the quantization of the electrical conductance is shown. An additional application is made to the two-dimensional electron gas.
The quantized conductance plateaus and zero conductance fluctuation are the general consequence of electron transport in chiral edge states of Hermitian Chern insulators. Here we show that the physics of electron transport through chiral or helical edge channels becomes much richer when the non-Hermicity is allowed. In the presence of an unbalanced non-Hermicity where the chiral edge states have finite-lifetime, the conductance of the edge channels is not quantized, but its conductance fluctuation is zero. For the balanced non-Hermicity, however, the chiral edge states have infinite-lifetime, …
We report a theoretical investigation on the conductance and its fluctuation of three-dimensional topological insulators (3D TI) in $Bi_2Se_3$ and $Sb_2Te_3$ in the presence of disorders. Extensive numerical simulations are carried out. We find that in the diffusive regime the conductance is quantized with fractional value. Importantly, the conductance fluctuation is also quantized with a universal value. For 3D TI connected by two terminals, three independent conductances $G_{zz}$, $G_{xx}$ and $G_{zx}$ are identified where z is the normal direction of quintuple layer of 3D TI (see inset of F…
We propose a surface-edge state theory for half quantized Hall conductance of surface states in topological insulators. The gap opening of a single Dirac cone for the surface states in a weak magnetic field is demonstrated. We find a new surface state resides on the surface edges and carries chiral edge current, resulting in a half-quantized Hall conductance in a four-terminal setup. We also give a physical interpretation of the half quantized conductance by showing that this state is the product of splitting of a boundary bound state of massive Dirac fermions which carries a conductance quant…
Using the Landauer formulation of transport theory, we predict that dielectric quantum wires should exhibit quantized thermal conductance at low temperatures in a ballistic phonon regime. The quantum of thermal conductance is universal, independent of the characteristics of the material, and equal to $π^2 k^2_B T /3h$ where $k_B$ is the Boltzmann constant, h is Planck's constant and T is the temperature. Quantized thermal conductance should be experimentally observable in suspended nanostructures adiabatically coupled to reservoirs, devices that can be realized at the present time.
We show theoretically that quantized zero-bias conductance peaks should be ubiquitous in superconductor-semiconductor hybrids by employing a zero-dimensional random matrix model with continuous tuning parameters. We demonstrate that a normal metal-superconductor (NS) junction conductance spectra can be generically obtained in this model replicating all features seen in recent experimental results. The theoretical quantized conductance peaks, which explicitly do not arise from spatially isolated Majorana zero modes, are easily found by preparing a contour plot of conductance over several indepe…
We demonstrate switching behavior and quantized conductance at room temperature in percolating films of nanoparticles. Our experiments and complementary simulations show that switching and quantization result from formation of atomic scale wires in gaps between particles. These effects occur only when tunnel gaps are present in the film, close to the percolation threshold.
We introduce a non-linear frequency dependent D+1 terminal conductance that characterizes a D dimensional Fermi gas, generalizing the Landauer conductance in D=1. For a 2D ballistic conductor we show that this conductance is quantized and probes the Euler characteristic of the Fermi sea. We critically address the roles of electrical contacts and of Fermi liquid interactions, and we propose experiments on 2D Dirac materials such as graphene using a triple point contact geometry.
Recently,a half-quantized Hall conductance (HQHC) plateau is experimentally observed in a semi-magnetic topological insulator heterostructure. However,the heterostructure is metallic with a nonzero longitudinal conductance, which contradicts the common belief that quantized Hall conductance is usually observed in insulators.In this work,we systematically study the surface transport of the semi-magnetic topological insulator with both gapped and gapless Dirac surfaces in the presence of dephasing process.In particular, we reveal that the HQHC is directly related to the half-quantized chiral cur…
We study a generic two-dimensional hopping model on a honeycomb lattice with strong spin-orbit coupling, without the requirement that the half-filled lattice be a Topological Insulator. For quarter-(or three-quarter) filling, we show that a state with a quantized Hall conductance generically arises in the presence of a Zeeman field of sufficient strength. We discuss the influence of Hubbard interactions and argue that spontaneous ferromagnetism (which breaks time-reversal) will occur, leading to a quantized anomalous Hall effect.
We show that partially separated Andreev bound states (ps-ABSs), comprised of pairs of overlapping Majorana bound states (MBSs) emerging in quantum dot-semiconductor-superconductor heterostructures, produce robust zero bias conductance plateaus in end-of-wire charge tunneling experiments. These plateaus remain quantized at $2e^2/h$ over large ranges of experimental control parameters. In light of recent experiments reporting the observation of robust $2e^2/h$-quantized conductance plateaus in local charge tunneling experiments, we perform extensive numerical calculations to explicitly show tha…
We report conductance and supercurrent of InAs nanowires coupled to Al-superconducting electrodes with short channel lengths and good Ohmic contacts. The nanowires are suspended 15\,nm above a local gate electrode. The charge density in the nanowires can be controlled by a small change in the gate voltage. For large negative gate voltages, the number of conducting channels is reduced gradually and we observe a stepwise decrease of both conductance and critical current before the conductance vanishes completely.
We report the experimental observation of quantized conductance by Rashba bands at the surface of 50-nm Bi nanowires. With increasing magnetic fields along the wire axis, the wires exhibit a stepwise increase of conductance with as many as four distinct plateaus together with oscillatory thermopower. The observations can be accounted for by the increase of the number of propagating surface modes. The modes have very high mobility and are associated with Aharonov-Bohm interference around the perimeter consistently with theory of quasiballistic one-dimensional nanowires considering that Lorentz …
Majorana zero-modes hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool to identify the presence of Majorana zero-modes, for instance as a zero-bias peak (ZBP) in differential-conductance. The Majorana ZBP-height is predicted to be quantized at the universal conductance value of 2e2/h at zero temperature. Interestingly, this quantization is a direct consequence of the famous Majorana symmetry, 'particle equals antiparticle'. The Majorana symmetry protects the quantization against disorder, interactions, and variations in the…
We propose an objective and robust method to extract the electrical conductance of single molecules connected to metal electrodes from a set of measured conductance data. Our method roots in the physics of tunneling and is tested on octanedithiol using mechanically controllable break junctions. The single molecule conductance values can be deduced without the need for data selection.
We have investigated the conductance of long quantum wires formed in GaAs/AlGaAs heterostructures. Using realistic fluctuation potentials from donor layers we have simulated numerically the conductance of four different kinds of wires. While ideal wires show perfect quantization, potential fluctuations from random donors may give rise to strong conductance oscillations and degradation of the quantization plateaux. Statistically there is always the possibility of having large fluctuations in a sample that may effectively act as a microconstriction. We therefore introduce microconstrictions in t…
Electrical conductance measurements have limited scope in identifying Andreev edge states (AESs), which form the basis for realizing various topological excitations in quantum Hall (QH) - superconductor (SC) junctions. To unambiguously detect AESs, we measure shot noise along with electrical conductance in a graphene based QH-SC junction at integer filling nu=2. Remarkably, we find that the Fano factor of shot noise approaches half when the bias energy is less than the superconducting gap, whereas it is close to zero above the superconducting gap. This is striking, given that, at the same time…
We report on magnetic field dependence of half-integer quantized conductance plateaus (HQPs) in InAs quantum wires. We observed HQPs at zero applied magnetic field in InAs quantum wires fabricated from a high-quality InAs quantum well. The application of in-plane magnetic field causes Zeeman splitting of the HQP features, indicating that the origin of the observed HQP is not spontaneous spin polarization. Additionally we observe that conductance of the split HQPs decreases gradually as the in-plane magnetic field increases. We finally assume electron-electron interaction as a possible mechanis…
Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field is investigated. It is found that chiral surface states parallel to the magnetic field are responsible to the quantized Hall (QH) conductance $(2n+1)\frac{e^2}{h}$ multiplied by the number of Dirac cones. Due to the two-dimension (2D) nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and ev…
The electrical and heat currents flowing through a quantum dot are calculated in the presence of a time-modulated gate voltage with the help of the out-of-equilibrium Green function technique. From the first harmonics of the currents, we extract the electrical and thermoelectrical trans-admittances and ac-conductances. Next, by a careful comparison of the ac-conductances with the finite-frequency electrical and mixed electrical-heat noises, we establish the fluctuation-dissipation relations linking these quantities, which are thus generalized out-of-equilibrium for a quantum system. It is show…
Majorana zero modes can appear at the wire ends of a 1D topological superconductor and manifest themselves as a quantized zero-bias conductance peak in the tunneling spectroscopy of normal-superconductor junctions. However, in superconductor-semiconductor hybrid nanowires, zero-bias conductance peaks may arise owing to topologically trivial mechanisms as well, mimicking the Majorana-induced topological peak in many aspects. In this work, we systematically investigate the characteristics of zero-bias conductance peaks for topological Majorana bound states, trivial quasi-Majorana bound states an…
Quantized conductance is reported in high-crystalline tin oxide (SnO2) nanobelt back-gate field-effect transistors, at low temperatures. The quantized conductance was observed as current oscillations in the drain current vs. gate voltage characteristics, and were analyzed considering the nanobelt as a quantum wire with rectangular cross-section hard-walls. The quantum confinement in the nanowires created conditions for the successive filling of the electron energy-subbands, as the gate voltage increases. When the source-drain voltage is changed the oscillations are not dislocated with respect …
We construct useful sets of one-particle states in the quantum Hall system based on the von Neumann lattice. Using the set of momentum states, we develop a field-theoretical formalism and apply the formalism to the system subjected to a periodic potential. The topological formula of the Hall conductance written by the winding number of propagator is generalized to Bloch electrons. The relation between the winding number and the Chern number is clarified.
Based on the Landauer formalism, we demonstrate that the thermal conductance due to the propagation of surface phonon-polaritons along a polar nanowire is independent of the material characteristics and is given by Pi^2kB^2T/3h. The giant propagation length of these energy carriers establishes that this quantization holds not only for a temperature much smaller than 1 K, as is the case of electrons and phonons, but also for temperatures comparable to room temperature, which can significantly facilitate its observation and application in the thermal management of nanoscale electronics and photo…
The electrical conductance and RHEED intensities as a function of the coverage have been measured during Pb depositions at 105 K on Si(111)-(6x6)Au with up to 4.2 ML of annealed Pb. The experiments show the strong influence of used substrates on the behavior of the conductance during the epitaxy of Pb atoms, especially for very initial stage of growth. Oscillations of the conductance during the layer-by-layer growth are correlated with RHEED intensity oscillations. The analysis of the conductance behavior is made according to the theory described by Trivedi and Aschcroft (Phys.Rev.B 38,12298 (…
We demonstrate that it is possible to distinguish two conductance switching mechanisms in silver sulfide devices at room temperature. Experiments were performed using a Ag$_2$S thin film deposited on a wide Ag bottom electrode, which was contacted by the Pt tip of a scanning tunneling microscope. By applying a positive voltage on the silver electrode the conductance is seen to switch to a state having three orders of magnitude higher conductance, which is related to the formation of a conductive path inside the Ag$_2$S thin film. We argue this to be composed of a metallic silver nanowire accom…
We present measurements of the electrical conductance $G$ at room temperature of mechanically controllable break junctions (MCBJ) fabricated from Au in different solvents (octane, DCM, DMSO, and toluene) and compare with measurements in air and vacuum. In the high conductance regime $G \agt G_0=2e^2/h$, the environment plays a minor role, as proven by the measured conductance histograms, which do not depend on the environment. In contrast, the environment significantly affects the electrical properties in the low conductance (tunneling) regime {$G << G_0$}. Here, we observe a systematic and re…
Superconducting wires without time-reversal and spin-rotation symmetries can be driven into a topological phase that supports Majorana bound states. Direct detection of these zero-energy states is complicated by the proliferation of low-lying excitations in a disordered multi-mode wire. We show that the phase transition itself is signaled by a quantized thermal conductance and electrical shot noise power, irrespective of the degree of disorder. In a ring geometry, the phase transition is signaled by a period doubling of the magnetoconductance oscillations. These signatures directly follow from…
Probing an isolated Majorana zero mode is predicted to reveal a tunneling conductance quantized at $2e^2/h$ at zero temperature. Experimentally, a zero-bias peak (ZBP) is expected and its height should remain robust against relevant parameter tuning, forming a quantized plateau. Here, we report the observation of large ZBPs in a thin InAs-Al hybrid nanowire device. The ZBP height can stick close to $2e^2/h$, mostly within $5\%$ tolerance, by sweeping gate voltages and magnetic field. We further map out the phase diagram and identify two plateau regions in the phase space. Despite the presence …
We investigate spin-dependent transport in three--terminal mesoscopic cavities with spin--orbit coupling. Focusing on the inverse spin Hall effect, we show how injecting a pure spin current or a polarized current from one terminal generates additional charge current and/or voltage across the two output terminals. This allows to extract the spin conductance of the cavity from two purely electrical measurements on the output. We use random matrix theory to show that the spin conductance of chaotic ballistic cavities fluctuates universally about zero mesoscopic average and describe experimental i…
The energy spectrum of massless Dirac fermions in graphene under two dimensional periodic magnetic modulation having square lattice symmetry is calculated. We show that the translation symmetry of the problem is similar to that of the Hofstadter or TKNN problem and in the weak field limit the tight binding energy eigenvalue equation is indeed given by Harper Hofstadter hamiltonian. We show that due to its magnetic translational symmetry the Hall conductivity can be identified as a topological invariant and hence quantized. We thus extend the idea of Quantum Hall Effect to magnetically modulate…
The universal quantization of thermal conductance provides information on the topological order of a state beyond electrical conductance. Such measurements have become possible only recently, and have discovered, in particular, that the value of the observed thermal conductance of the 5/2 state is not consistent with either the Pfaffian or the anti-Pfaffian model, motivating several theoretical articles. The analysis of the experiments has been made complicated by the presence of counter-propagating edge channels arising from edge reconstruction, an inevitable consequence of separating the dop…
In a GaAs/AlGaAs two-dimensional electron system with two occupied subbands, the experimentally determined phase diagram in the density-magnetic field plane exhibits rich topological features. Ring-like structures are observed at even integer filling factors, in the phase diagram. Even with the identical quantized Hall resistance values as those given rise by the ordinary integer quantum Hall effect due to the Landau level quantization; the activation energies of these states within the rings are much smaller. These ring structures cannot account for by the simple single particle picture. We a…
Half-quantized anomalous Hall conductance in topological insulator/ferromagnet van der Waals heterostructures
Linnaeus University（林奈大学）；Nordita, KTH Royal Institute of Technology and Stockholm University（北欧原子理论中心，皇家理工学院和斯德哥尔摩大学）；University of Connecticut（康涅狄格大学）；University of Texas at El Paso（德克萨斯大学埃尔帕索分校）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
The evolution of the structure and conductance of an Al nanowire subject to a tensile stress has been studied by first-principles total-energy simulations. Our calculations show the correlation between discontinuous changes in the force (associated to changes in the bonding structure of the nanowire) and abrupt modifications of the conductance as the nanowire develops a thinner neck, in agreement with the experiments. We reproduce the characteristic increase of the conductance in the last plateau, reaching a value close to the conductance quantum $G_0 = 2 e^2 / h$ before the breaking of the na…
We study the electronic transport of heterojunctions made of chiral topological superconductors (TSCs) with $N$ chiral Majorana fermion modes and quantum Hall insulators (QHIs) with integer Chern number $C$. In the weak disorder regime, we show the two-terminal conductance $σ_{12}$ of a QHI-TSC-QHI junction is generically non-quantized, but obeys a certain distribution determined by $C$ and $N$, which is induced by random SO($N$) rotations of chiral Majorana fermion mode basis on the TSC edges. Oppositely, in the strong disorder regime, $σ_{12}$ tends to be a quantized value. We conclude with …
Using scanning tunneling microscopy (STM), we investigated the evolution of electrical conductance between a Pb tip and Pb(111) surface from tunneling to atomic point contact at a site that was defined with atomic precision. We found that the conductance evolution depended on the contact site, for instance, on-top, bridge, or hollow (hcp and fcc) sites in the Pb lattice. In the transition from tunneling to contact regimes, the conductance measured at the on-top site was enhanced. In the point contact regime, the hollow sites had conductances larger than those of the other sites, and between th…
We report a theoretical investigation of quantized spin-Hall conductance fluctuation of graphene devices in the diffusive regime. Two graphene models that exhibit quantized spin-Hall effect (QSHE) are analyzed. Model-I is with unitary symmetry under an external magnetic field $B\ne 0$ but with zero spin-orbit interaction, $t_{SO}=0$. Model-II is with symplectic symmetry where B=0 but $t_{SO} \ne 0$. Extensive numerical calculations indicate that the two models have exactly the same universal QSHE conductance fluctuation value $0.285 e/4π$ regardless of the symmetry. Qualitatively different fro…
Controllable quantized conductance states of TiN/Ti/HfO$_x$/TiN memristors are realized with great precision through a pulse-mode reset procedure, assisted with analytical differentiation of the condition of the set procedure, which involves critical monitoring of the measured bias voltage. An intriguing training effect that leads to faster switching of the states is also observed during the operation. Detailed analyses on the low- and high-resistance states under different compliance currents reveal a complete picture of the structural evolution and dynamic behaviors of the conductive filamen…
Quantized conductance in a CVD-grown nanoribbon with hidden Rashba effect
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Hefei National Laboratory（合肥国家实验室）
We calculate the quantized conductance of nanosize point contacts between two ferromagnets for different mutual orientations of the magnetic moments. It is found that the magnetoresistance MR is a multivalued function of the quantized conductance at the parallel alignment of the magnetizations sigma^F. This leads us to the conclusion that experimentally observed large fluctuations of MR versus sigma^F are rather due to the conductance quantization than to measurement errors or a poor reproducibility of the results. Using the results of the calculations we are able to understand experimental da…
Due to a strong spin-orbit interaction and a large Landé g-factor, InSb plays an important role in research on Majorana fermions. To further explore novel properties of Majorana fermions, hybrid devices based on quantum wells are conceived as an alternative approach to nanowires. In this work, we report a pronounced conductance quantization of quantum point contact devices in InSb/InAlSb quantum wells. Using a rotating magnetic field, we observe a large in-plane (|g1|=26) and out-of-plane (|g1|=52) g-factor anisotropy. Additionally, we investigate crossings of subbands with opposite spins and …
The ballistic motion of carriers of graphene in an orthogonal electromagnetic field is investigated to explain Hall conductance of graphene under experimental conditions. With the electrical field, all electronic eigen-states have the same expectation value of the velocity operator, or classically, all carriers move in cycloids with the same average velocity. The magnitude of this velocity is just appropriate to generate the quantized Hall conductance which is in turn exactly independent of the external field. Electrical field changes each Landau level into a bundle of energies, whose overlap …
We study the quantization of Dirac fermions in lithographically defined graphene nanoconstrictions. We observe quantized conductance in single nanoconstrictions fabricated on top of a thin hexamethyldisilazane layer over a Si/SiO_2 wafer. This nanofabrication method allows us to obtain well defined edges in the nanoconstrictions, thus reducing the effects of edge roughness on the conductance. We prove the occurrence of ballistic transport and identify several size quantization plateaus in the conductance at low temperature. Experimental data and numerical simulations show good agreement, demon…
To develop next-generation electronics and high efficiency energy-harvesting devices, it is crucial to understand how charge and heat are transported at the nanoscale. Metallic atomic-size contacts are ideal systems to probe the quantum limits of transport. The thermal and electrical conductance of gold atomic contacts has been recently proven to be quantized at room temperature. However, a big experimental challenge in such measurements is represented by the fast breaking dynamics of metallic junctions at room temperature, which can exceed the typical response time of the thermal measurement.…
Silicene (a monolayer of silicon atoms) is a quantum spin-Hall insulator, which undergoes a topological phase transition into other insulators by applying external field such as electric field, photo-irradiation and antiferromagnetic order. We investigate the electronic and transport properties of silicene nanoribbons based on the Landauer formalism. We propose to determine topological phase transitions by measuring the density of states and conductance. The conductance is quantized and changes its value when the system transforms into different phases. We show that a silicene nanoribbon near …
Provided the electrical properties of electro-burnt graphene junctions can be understood and controlled, they have the potential to underpin the development of a wide range of future sub-10nm electrical devices. We examine both theoretically and experimentally the electrical conductance of electro-burnt graphene junctions at the last stages of nanogap formation. We account for the appearance of a counterintuitive increase in electrical conductance just before the gap forms. This is a manifestation of room-temperature quantum interference and arises from a combination of the semi-metallic band …
We analyze transport of magnetization in insulating systems described by a spin Hamiltonian. The magnetization current through a quasi one-dimensional magnetic wire of finite length suspended between two bulk magnets is determined by the spin conductance which remains finite in the ballistic limit due to contact resistance. For ferromagnetic systems, magnetization transport can be viewed as transmission of magnons and the spin conductance depends on the temperature T. For antiferromagnetic isotropic spin-1/2 chains, the spin conductance is quantized in units of order $(g μ_B)^2/h$ at T=0. Magn…
A scanning tunnelling microscope has been used to determine the conductance of single molecular wires with the configuration X-bridge-X, X-bridge-Y and Y-bridge-Y (X = thiol terminus and Y = COOH). We find that for molecular wires with mixed functional groups (X-bridge-Y) the single molecule conductance decreases with respect to the comparable symmetric molecules. These differences are confirmed by theoretical computations based on a combination of density functional theory and the non-equilibrium Green functions formalism. This study demonstrates that the apparent contact resistance, as well …
We present the results of million atom electronic quantum transport calculations for graphene nanoconstrictions with edges that are smooth apart from atomic scale steps. We find conductances quantized in integer multiples of 2e2/h and a plateau at ~0.5*2e2/h as in recent experiments [Tombros et al., Nature Physics 7, 697 (2011)]. We demonstrate that, surprisingly, conductances quantized in integer multiples of 2e2/h occur even for strongly non-adiabatic electron backscattering at the stepped edges that lowers the conductance by one or more conductance quanta below the adiabatic value. We also …
Crystals with symmetry-protected topological order, such as topological insulators, promise coherent spin and charge transport phenomena even in the presence of disorder at room temperature. Still, a major obstacle towards an application of topological surface states in integrated circuits is a clear, reliable, and straightforward read-out independent of a prevailing charge carrier density in the bulk. Here, we demonstrate how to image and read-out the local conductance of helical surface modes in the prototypical topological insulators Bi2Se3 and BiSbTe3. We apply the so-called Shockley-Ramo …
We investigated the effect due to perpendicular magnetic field on quantum wires where spin-orbit interaction (SOI) of electrons is not neglected. Based on the calculated energy dispersion, the nonlinear ballistic conductance ($G$) and electron-diffusion thermoelectric power ($S_d$) are calculated as functions of electron density, temperature and applied bias voltage. A low-temperature half-step feature in $G$, which was observed experimentally by Quay et al. [see Nature Physics {\bf 6}, 336 (2010)], as well as a new peak in $S_d$ are reproduced here in the low density regime. These phenomena a…
We report a precise experimental study on the shot noise of a quantum point contact (QPC) fabricated in a GaAs/AlGaAs based high-mobility two-dimensional electron gas (2DEG). The combination of unprecedented cleanliness and very high measurement accuracy has enabled us to discuss the Fano factor to characterize the shot noise with a precision of 1 %. We observed that the shot noise at zero magnetic field exhibits a slight enhancement exceeding the single particle theoretical prediction, and that it gradually decreases as a perpendicular magnetic field is applied. We also confirmed that this ad…
In this letter we study the Hall conductance for a non-Hermitian Chern insulator and quantitatively describe how the Hall conductance deviates from a quantized value. We show the effects of the non-Hermitian terms on the Hall conductance are two folds. On one hand, it broadens the density-of-state of each band, because of which there always exists a non-universal bulk contribution. On the other hand, it adds decay term to the edge state, because of which the topological contribution also deviates from the quantized Chern number. We provides a simple formula for the topological contribution for…
Kubo formula gives a linear response of a quantum system to external fields, which are classical and weak with respect to the energy of the system. In this work, we take the quantum nature of the external field into account, and define a Hall conductance to characterize the linear response of a two-band system to the quantized field. The theory is then applied to topological insulators. Comparisons with the traditional Hall conductance are presented and discussed.
We study longitudinal transport in Weyl semimetal nanowires, both in the absence and in the presence of a magnetic flux threading the nanowires. We identify two qualitatively different regimes of transport with respect to the chemical potential in the nanowires. In the "surface regime", for low doping, most of the conductance occurs through the Fermi-arc surface states, and it rises in steps of one quantum of conductance as a function of the chemical potential; furthermore, with varying flux the conductance changes in steps of one quantum of conductance with characteristic Fabry-Pérot interfer…
