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 quantum.
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…
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.
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.
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 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…
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.
We study a nonadiabatic effect on the conductances in the quantum Hall effect of two-dimensional electrons with a periodic potential. We found that the Hall and longitudinal conductances oscillate in time with a very large frequencies due to quantum fluctuation.
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…
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…
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…
The charge and spin Hall conductance of the two-dimensional hole gas within the Luttinger model with and without inversion symmetry breaking terms in a perpendicular magnetic field are studied, and two key phenomena are predicted. The sign of the spin Hall conductance is modulated periodically by the external magnetic field, which means a possible application in the future. Furthermore, a resonant spin Hall conductance in the two-dimensional hole gas with a certain hole density at a typical magnetic field is indicated, which implies a likely way to firmly establish the intrinsic spin Hall effe…
Measurement and theory of the two-terminal conductance of monolayer and bilayer graphene in the quantum Hall regime are compared. We examine features of conductance as a function of gate voltage that allow monolayer, bilayer, and gapped samples to be distinguished, including N-shaped distortions of quantum Hall plateaus and conductance peaks and dips at the charge neutrality point. Generally good agreement is found between measurement and theory. Possible origins of discrepancies are discussed.
We study the energy spectrum and the quantized Hall conductance of electrons in a two-dimensional periodic potential with perpendicular magnetic field WITHOUT neglecting the coupling of the Landau bands. Remarkably, even for weak Landau band coupling significant changes in the Hall conductance compared to the one-band approximation of Hofstadter's butterfly are found. The principal deviations are the rearrangement of subbands and unexpected subband contributions to the Hall conductance.
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 propose a scheme where transport measurements of charge current and its noise can be used to determine the spin Hall conductance in a four-terminal setup. Starting from the scattering formalism we express the spin current and spin Hall conductance in terms of spin-dependent transmission coefficients. These coefficients are then expressed in terms of charge current and noise. We use the scheme to characterize the spin injection efficiency of a ferromagnetic/semiconductor interface.
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）
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 …
We evaluate the distribution of Hall conductances in magnetic subbands of two-dimensional electron gas with Rashba spin-orbit (SO) coupling placed in a periodic potential and perpendicular magnetic field. In this semiconductor structure the spin-orbit coupling mixes the states of different magnetic subbands and changes the distribution of their Hall conductances in comparison with the case of spinless particles. The calculations were made for semiconductor structures with a weak ($AlGaAs/GaAs$) and relatively strong ($GaAs/InGaAs$) SO and Zeeman interactions. The Hall conductances of fully occ…
Following a previous work [Shen, Ma, Xie and Zhang, Phys. Rev. Lett. 92, 256603 (2004)] on the resonant spin Hall effect, we present detailed calculations of the spin Hall conductance in two-dimensional quantum wells in a strong perpendicular magnetic field. The Rashba coupling, generated by spin-orbit interaction in wells lacking bulk inversion symmetry, introduces a degeneracy of Zeeman-split Landau levels at certain magnetic fields. This degeneracy, if occuring at the Fermi energy, will induce a resonance in the spin Hall conductance below a characteristic temperature of order of the Zeeman…
Topological states of matter are characterized by topological invariant, which are physical quantities whose values are quantized and do not depend on details of the measured system. Of these, the easiest to probe in experiments is the electrical Hall conductance, which is expressed in units of $e^2/h$ ($e$ the electron charge, $h$ the Planck's constant). In the fractional quantum Hall effect (FQHE), fractional quantized values of the electrical Hall conductance attest to topologically ordered states, which are states that carry quasi particles with fractional charge and anyonic statistics. An…
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…
We study experimentally the reproducible conductance fluctuations between the quantum Hall plateaus in the conductance of two-terminal submicron silicon MOSFETs. For the dramatic fluctuations at the insulator-to-first-plateau transition we find a conductance distribution that is approximately uniform between zero and $e^2/h$. We point out that this is consistent with the prediction of random $S$-matrix theory for a conductor with single-channel leads in a magnetic field.
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 investigate the Hall conductance of a two-dimensional Chern insulator coupled to an environment causing gain and loss. Introducing a biorthogonal linear response theory, we show that sufficiently strong gain and loss lead to a characteristic non-analytical contribution to the Hall conductance. Near its onset, this contribution exhibits a universal power-law with a power 3/2 as a function of Dirac mass, chemical potential and gain strength. Our results pave the way for the study of non-Hermitian topology in electronic transport experiments.
We analyze the conductance fluctuations observed in the quantum Hall regime for a bulk two-dimensional electron system in a Corbino geometry. We find that characteristics like the power spectral density and the temperature dependence agree well with simple expectations for universal conductance fluctuations in metals, while the observed amplitude is reduced. In addition, the dephasing length $L_Φ\propto T^{-1/2}$, which governs the temperature dependence of the fluctuations, is surprisingly different from the scaling length $L_{sc}\propto T^{-1}$ governing the width of the quantum Hall plateau…
We consider the network model of the integer quantum Hall effect transition. By generalizing the real--space renormalization group procedure for the classical percolation to the case of quantum percolation, we derive a closed renormalization group (RG) equation for the universal distribution of conductance of the quantum Hall sample at the transition. We find an approximate solution of the RG equation and use it to calculate the critical exponent of the localization length and the central moments of the conductance distribution. The results obtained are compared with the results of recent nume…
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 …
It is widely accepted that topological quantities are useful to describe quantum liquids in low dimensions. The (spin) Hall conductances are typical examples. They are expressed by the Chern numbers, which are topological invariants given by the Berry connections of the ground states. We present a topological description for the (spin) Hall conductances on a discretized Brillouin Zone. At the same time, it is quite efficient in practical numerical calculations for concrete models. We demonstrate its validity in a model with quantum phase transitions. Topological changes supplemented with the t…
The chiral surface electrons in the bulk quantum Hall effect probably form the first extended system in which conductance fluctuations can be calculated non-perturbatively in the presence of disorder. By use of the Kubo formula with appropriate boundary conditions, we calculate exactly the variance of conductance with non-perturbative methods. We find that the conductance fluctuations of this system are ``nonuniversal'' and the variance of the conductance scales in a very peculiar way. This result can be checked with exact computation using the Landauer-Buttiker formula and both methods show t…
Clean topological insulators exposed to a magnetic field develop Landau levels accompanied by a nonzero Hall conductivity for the infinite slab geometry. In this work we consider the case of disordered topological insulator nanowires and find, in contrast, that a zero Hall plateau emerges within a broad energy window close to the Dirac point. We numerically calculate the conductance and its distribution for a statistical ensemble of disordered nanowires, and use the conductance fluctuations to study the dependence of the insulating phase on system parameters, such as the nanowire length, disor…
We study the charge and spin transport in a two terminal graphene nanoribbon (GNR) decorated with random Gold (Au) adatoms using a Kane-Mele model. Two commonly used GNRs, that is, the armchair graphene nanoribbon (AGNR) and the zigzag graphene nanoribbon (ZGNR) are compared and contrasted, which shows that in presence of Au adatoms, a somewhat robust $2e^2/h$ conductance plateau occurs in the case of AGNR around the zero of the Fermi energy, while in ZGNR this plateau is fragile. We show that this flat plateau, having a conductance value $2e^2/h$, is not a hallmark signature of a topologicall…
We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy bandgap and Landau level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size and magnetic length, we elu…
We present an analytical scaling theory for localization in a two-dimensional hierarchical network model that is designed to represent phase-coherent electron transport in the quantum-Hall regime. Scaling expressions for both the longitudinal and Hall resistivities are derived. In agreement with recent numerical studies, we find that the Hall resistivity is quantized in the metallic phase but diverges in the insulating phase. This suggests that the characteristics of a quantized Hall insulator can occur only in the presence of a strong dephasing mechanism.
The magnetic-induced orbital motion of quasiparticles affects the conductance properties of a hybrid strip of a quantum-anomalous-Hall topological material with induced superconductivity. We elucidate the scenario of topological NSN ideal junctions in presence of orbital magnetic motion, showing how it leads to a halved quantized conductance $0.5e^2/h$ even in absence of Majorana modes. The magnetic orbital effect favours Fermionic charged modes with finite wave numbers, in contradistinction to Majorana zero modes which are chargeless zero-energy modes with vanishing wave number. The bias sens…
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…
