Quantized Hall Conductance Research Articles

Quantum Transport by Spin‐Polarized Edge States in Graphene Nanoribbons in the Quantum Spin Hall and Quantum Anomalous Hall Regimes

Using the non‐equilibrium Green's function method and the Keldysh formalism, we study the effects of spin–orbit interactions and time‐reversal symmetry breaking exchange fields on non‐equilibrium quantum transport in graphene armchair nanoribbons. We identify signatures of the quantum spin Hall (QSH) and the quantum anomalous Hall (QAH) phases in non‐equilibrium edge transport by calculating the spin‐resolved real space charge density and local currents at the nanoribbon edges. We find that the QSH phase, which is realized in a system with intrinsic spin–orbit coupling, is characterized by chiral counter‐propagating local spin currents summing up to a net charge flow with opposite spin polarization at the edges. In the QAH phase, emerging in the presence of Rashba spin–orbit coupling and a ferromagnetic exchange field, two chiral edge channels with opposite spins propagate in the same direction at each edge, generating an unpolarized charge current and a quantized Hall conductance G = 2e2/h. Increasing the intrinsic spin–orbit coupling causes a transition from the QAH to the QSH phase, evinced by characteristic changes in the non‐equilibrium edge transport. In contrast, an antiferromagnetic exchange field can coexist with a QSH phase, but can never induce a QAH phase due to a symmetry that combines time‐reversal and sublattice translational symmetry.

Theory of Disorder-Induced Half-Integer Thermal Hall Conductance.

The thermal Hall conductance in the half-filled first Landau level was recently measured to take the quantized noninteger value κ_{xy}=5/2 (in units of temperature times π^{2}k_{B}^{2}/3h), which indicates a non-Abelian phase of matter. Such exotic states have long been predicted to arise at this filling factor, but the measured value disagrees with numerical studies, which predict κ_{xy}=3/2 or 7/2. We resolve this contradiction by invoking the disorder-induced formation of mesoscopic puddles with locally κ_{xy}=3/2 or 7/2. Interactions between these puddles generate a coherent macroscopic state that exhibits a plateau with quantized κ_{xy}=5/2. The non-Abelian quasiparticles characterizing this phase are distinct from those of the microscopic puddles and, by the same mechanism, could even emerge from a system comprised of microscopic Abelian puddles.

Perfect Circular Dichroism in the Haldane Model

We theoretically show that perfect circular dichroism (CD) occurs in the Haldane model in which the two-dimensional (2D) material absorbs only either left-handed or right-handed circularly polarized light. Perfect CD occurs in the phase diagram of the Haldane model when the zero-field quantum Hall conductivity has a nonzero value. The coincidence of the occurrence of perfect CD and zero-field quantum Hall effect is attributed to the fact that the effect of broken time-reversal symmetry is larger than the effect of broken inversion symmetry. On the other hand, valley polarization and perfect CD occur exclusively in the phase diagram. Further, for the four regions of the phase diagram, pseudospin polarization occurs at the K and K′ points in the hexagonal Brillouin zone with either the same sign or opposite sign for the K and K′ points and for the valence and conduction bands. This theoretical prediction may have an impact on search for a new optical device that selects circularly polarized light controlled by the electric field.

Theory of the disordered ν=52 quantum thermal Hall state: Emergent symmetry and phase diagram

Fractional quantum Hall (FQH) system at Landau level filling fraction $\nu=5/2$ has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance $\sigma_{xy}=5e^2/2h$. Thermal Hall conductances of the Pf and APf states are quantized at $\kappa_{xy}=7/2$ and $\kappa_{xy}=3/2$ respectively in a proper unit. However, a recent experiment shows the thermal Hall conductance of $\nu=5/2$ FQH state is $\kappa_{xy}=5/2$. It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a $\kappa_{xy}=5/2$ phase. In this work, we do perturbative and non-perturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold $\Lambda_1$, which is lowered to an emergent U(1)$\times$U(1) symmetry at energy scales between $\Lambda_1$ and a higher value $\Lambda_2$, and is finally lowered to the composite fermion parity symmetry $\mathbb{Z}_2^F$ above $\Lambda_2$. Based on the emergent symmetries, we propose a phase diagram of the disordered $\nu=5/2$ FQH system, and show that a $\kappa_{xy}=5/2$ phase arises at disorder energy scales $\Lambda>\Lambda_1$. Furthermore, we show the gapped double-semion sector of $N_D$ compact domain walls contributes non-local topological degeneracy $2^{N_D-1}$, causing a low-temperature peak in the heat capacity. We implement a non-perturbative method to bootstrap generic topological 1+1D domain walls (2-surface defects) applicable to any 2+1D non-Abelian topological order. We identify potentially relevant spin TQFTs for various $\nu = 5/2$ FQH states in terms of fermionic version of U(1)$_{\pm 8}$ Chern-Simons theory $\times \mathbb{Z}_8$-class TQFTs.

Multiterminal conductance at the surface of a Weyl semimetal

Weyl semimetals are a new paradigmatic topological phase of matter featuring a gapless spectrum. One of its most distinctive features is the presence of Fermi arc surface states. Here, we report on atomistic simulations of the dc conductance and quantum Hall response of a minimal Weyl semimetal. By using scattering theory we show that a quantized Hall conductance with a non-vanishing longitudinal conductance emerges associated to the Fermi arc surface states with a remarkable robustness to high concentrations of defects in the system. Additionally, we predict that a slab of a Weyl semimetal with broken time-reversal symmetry bears persistent currents fully determined by the system size and the lattice parameters.

Universal Relation among the Many-Body Chern Number, Rotation Symmetry, and Filling.

Understanding the interplay between the topological nature and the symmetry property of interacting systems has been a central matter of condensed matter physics in recent years. In this Letter, we establish nonperturbative constraints on the quantized Hall conductance of many-body systems with arbitrary interactions. Our results allow one to readily determine the many-body Chern number modulo a certain integer without performing any integrations, solely based on the rotation eigenvalues and the average particle density of the many-body ground state.

Quantum Hall effect in graphene with interface-induced spin-orbit coupling

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.

Magnetothermoelectric transport properties in phosphorene

We numerically study the electrical and thermoelectric transport properties in phosphorene in the presence of both a magnetic field and disorder. The quantized Hall conductivity is similar to that of a conventional two-dimensional electron gas, but the positions of all the Hall plateaus shift to the left due to the spectral asymmetry, in agreement with the experimental observations. The thermoelectric conductivity and Nernst signal exhibit remarkable anisotropy, and the thermopower is nearly isotropic. When a bias voltage is applied between top and bottom layers of phosphorene, both thermopower and Nernst signal are enhanced and their peak values become large.

Symmetry breaking and the fermionic fractional Chern insulator in topologically trivial bands

We describe a mechanism by which fermions in topologically trivial bands can form correlated states exhibiting a fractional quantum Hall (FQH) effect upon introduction of strong repulsive interactions. These states are solid-liquid composites, in which a FQH liquid is induced by the formation of charge order (CO), following a recently proposed paradigm of symmetry-breaking topological (SBT) order [Phys. Rev. Lett. 113, 216404 (2014)]. We devise a spinless fermion model on a triangular lattice, featuring a topologically trivial phase when interactions are omitted. Adding strong short-range repulsion, we first establish a repulsion-driven CO phase at density $\rho_{\mathrm{CO}}=2/3$ particles per site, then dope the model to higher densities $\rho = \rho_{\mathrm{CO}} + \nu/6$. At $\nu=1/3,2/5$ ($\rho=13/18,11/15$), we observe definitive signatures of both CO and the FQH effect --- sharply peaked static structure factor, gapped and degenerate energy spectrum and fractionally quantized Hall conductivity $\sigma_{\mathrm{H}}=1/3,2/5$ in units of $e^2/h$ --- over a range of all model parameters. We thus obtain direct evidence for fermionic SBT order of FQH type in topologically trivial bands.

Intrinsic quantum anomalous hall effect in a two-dimensional anilato-based lattice.

Using first-principles calculations, we predict an intrinsic quantum anomalous Hall (QAH) state in a monolayer anilato-based metal-organic framework M2(C6O4X2)3 (M = Mn and Tc, X = F, Cl, Br and I). The spin-orbit coupling of M d orbitals opens a nontrivial band gap up to 18 meV at the Dirac point. The electron counting rule is used to explain the intrinsic nature of the QAH state. The calculated nonzero Chern number, gapless edge states and quantized Hall conductance all confirm the nontrivial topological properties in the anilato-based lattice. Our findings provide an organic materials platform for the realization of the QAH effect without the need for magnetic and charge doping, which are highly desirable for the development of low-energy-consumption spintronic devices.

Conductance oscillations in Chern insulator junctions: Valley-isospin dependence and Aharonov-Bohm effects

The transport properties of Chern insulator junctions generated by bipolar junctions in quantum Hall graphene are theoretically studied in the coherent regime. Coherent transport across the junction exhibits two mesoscopic features: valley-isospin dependence of the quantum Hall conductance, and the Aharonov-Bohm (AB) effects with the interface channels. We demonstrate that the valley-isospin dependence can be measured in a graphene sample with perfect edge terminations, resulting in conductance oscillation for the smallest Chern number case. On the other hand, while conductance plateaus are found to be unclear for larger Chern numbers, the conductance exhibits an oscillatory behavior of which period is relatively longer than the valley-isospin dependent oscillation. This conductance oscillation is ascribed to the AB effect, which is implicitly created by the split metallic channels near the junction interface. We point out that a possible origin of the unclear plateaus previously speculated to be incompleteness in realistic devices is the low-visibility conductance oscillation due to unequal beam splitting.

Integer quantum Hall effect and topological phase transitions in silicene

We numerically investigate the effects of disorder on the quantum Hall effect (QHE) and the quantum phase transitions in silicene based on a lattice model. It is shown that for a clean sample, silicene exhibits an unconventional QHE near the band center, with plateaus developing at $\nu=0,\pm2,\pm6,\ldots,$ and a conventional QHE near the band edges. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center, in which higher plateaus disappear first. However, the center $\nu=0$ Hall plateau is more sensitive to disorder and disappears at a relatively weak disorder strength. Moreover, the combination of an electric field and the intrinsic spin-orbit interaction (SOI) can lead to quantum phase transitions from a topological insulator to a band insulator at the charge neutrality point (CNP), accompanied by additional quantum Hall conductivity plateaus.

Computational study of the two-terminal transport of Floquet quantum Hall insulators

Periodic driving fields can induce topological phase transitions, resulting in Floquet topological phases with intriguing properties such as very large Chern numbers and unusual edge states. Whether such Floquet topological phases could generate robust edge state conductance much larger than their static counterparts is an interesting question. In this paper, working under the Keldysh formalism, we study two-lead transport via the edge states of irradiated quantum Hall insulators using the method of recursive Floquet-Green's functions. Focusing on a harmonically-driven Hofstadter model, we show that quantized Hall conductance as large as $8e^2/h$ can be realized, but only after applying the so-called Floquet sum rule. To assess the robustness of edge state transport, we analyze the DC conductance, time-averaged current profile and local density of states. It is found that co-propagating chiral edge modes are more robust against disorder and defects as compared with the remarkable counter-propagating edge modes, as well as certain symmetry-restricted Floquet edge modes. Furthermore, we go beyond the wide-band limit, which is often assumed for the leads, to study how the conductance quantization (after applying the Floquet sum rule) of Floquet edge states can be affected if the leads have finite bandwidths. These results may be useful for the design of transport devices based on Floquet topological matter.

Giant quantized Goos-Hänchen effect on the surface of graphene in the quantum Hall regime

We theoretically predict a giant quantized Goos-H\"{a}nchen (GH) effect on the surface of graphene in quantum Hall regime. The giant quantized GH effect manifests itself as an angular shift whose quantized step reaches the order of mrad for light beams impinging on a graphene-on-substrate system. The quantized GH effect can be attributed to quantized Hall conductivity, which corresponds to the discrete Landau levels in quantum Hall regime. We find that the quantized step can be greatly enhanced for incident angles near the Brewster angle. Moreover, the Brewster angle is sensitive to the Hall conductivity, and therefore the quantized GH effect can be modulated by the Fermi energy and the external magnetic field. The giant quantized GH effect offers a convenient way to determine the quantized Hall conductivity and the discrete Landau levels by a direct optical measurement.

Quantum Hall effect in monolayer and bilayer black phosphorus

We numerically study the quantum Hall effect in both monolayer and bilayer black phosphorus (BP) under an external electric field in the presence of both disorder and a strong perpendicular magnetic field based on the tight-binding model. In the monolayer BP case, the quantized Hall conductivity is similar to that of a two-dimensional electron gas (2DEG), but the positions of all the Hall plateaus shift to the left due to the spectral asymmetry, in agreement with the experimental observations. The width of Hall plateau can be increased by applying a bias voltage to the top and bottom layers of the monolayer BP. The longitudinal conductivity exhibits a strong anisotropy that is large along the armchair direction. In the bilayer BP case, the Hall conductivity remains the same quantization rule as in the case of monolayer BP. Under a certain bias voltage, the plateau is markedly absent, and the LLs spectrum shows the appearance of doubly degenerate branches with a zero-energy level. Eventually, the system undergoes a phase transition from 2DEG to Dirac semimetal, which indicates a biased-induced closure of the bulk energy gap. The two central plateaus with are the most robust against disorder scattering. The longitudinal conductivity remains almost constant around zero energy in the presence of moderate disorder strength.

Topological insulators based on the semi-metallic HgCdTe

The review of peculiarity of growth and experimental results of the magneto-transport measurements (longitudinal magneto-resistance Rxx and the Hall resistance Rxy) over a wide interval of temperatures for several samples of Hg1−xCdxTe (x ≈ 0.13–0.15) grown by MBE is presented in this paper. An amazing temperature stability of the SdH-oscillation period and amplitude is observed in the entire temperature interval of measurements up to 50 K. Moreover, the quantum Hall effect (QHE) behaviour of the Hall resistance was shown in the same temperature interval. These peculiarities of the Rxx and Rxy for strained thin layers are interpreted using quantum Hall conductivity (QHC) on topologically protected surface states (TPSS). In the case of not strained layers it is assumed that the QHC on the TPSS contributes also to the conductance of the bulk samples. The experimental results on magneto-transport (QHC and SdH) obtained for the strained 100 nm thickness Hg1−xCdxTe layer are interpreted on the basis of the 8 × 8 kp model and an advantage of the Hg1−xCdxTe as topological insulators is shown. This article is an expanded version of the scientific reports presented at the International Conference on Semiconductor Nanostructures for Optoelectronics and Biosensors 2016 ICSeNOB2016, May 22–25, 2016, Rzeszow, Poland.

Ballistic edge states in Bismuth nanowires revealed by SQUID interferometry

The protection against backscattering provided by topology is a striking property. In two-dimensional insulators, a consequence of this topological protection is the ballistic nature of the one-dimensional helical edge states. One demonstration of ballisticity is the quantized Hall conductance. Here we provide another demonstration of ballistic transport, in the way the edge states carry a supercurrent. The system we have investigated is a micrometre-long monocrystalline bismuth nanowire with topological surfaces, that we connect to two superconducting electrodes. We have measured the relation between the Josephson current flowing through the nanowire and the superconducting phase difference at its ends, the current–phase relation. The sharp sawtooth-shaped phase-modulated current–phase relation we find demonstrates that transport occurs selectively along two ballistic edges of the nanowire. In addition, we show that a magnetic field induces 0–π transitions and ϕ0-junction behaviour, providing a way to manipulate the phase of the supercurrent-carrying edge states and generate spin supercurrents.

Quantum spin Hall state in monolayer 1T'-WTe2

A quantum spin Hall (QSH) insulator is a novel two-dimensional quantum state of matter that features quantized Hall conductance in the absence of magnetic field, resulting from topologically protected dissipationless edge states that bridge the energy gap opened by band inversion and strong spin-orbit coupling. By investigating electronic structure of epitaxially grown monolayer 1T'-WTe2 using angle-resolved photoemission (ARPES) and first principle calculations, we observe clear signatures of the topological band inversion and the band gap opening, which are the hallmarks of a QSH state. Scanning tunneling microscopy measurements further confirm the correct crystal structure and the existence of a bulk band gap, and provide evidence for a modified electronic structure near the edge that is consistent with the expectations for a QSH insulator. Our results establish monolayer 1T'-WTe2 as a new class of QSH insulator with large band gap in a robust two-dimensional materials family of transition metal dichalcogenides (TMDCs).

Discovery of intrinsic quantum anomalous Hall effect in organic Mn-DCA lattice

The quantum anomalous Hall (QAH) phase is a topological state of matter characterized by a nonzero quantized Hall conductivity without an external magnetic field. The realizations of the QAH effect, however, are experimentally challengeable. Based on ab initio calculations, here, we propose an intrinsic QAH phase in the Mn–dicyanoanthracene (DCA) Kagome lattice. The nontrivial topology in Kagome bands is confirmed by the nonzero Chern number, quantized Hall conductivity, and gapless chiral edge states of the Mn-DCA lattice. A tight-binding model is further constructed to clarify the origin of the QAH effect. Furthermore, its Curie temperature, estimated to be ∼253 K using the Monte-Carlo simulation, is comparable with room temperature and higher than that of most of the two-dimensional ferromagnetic thin films. Our findings present a reliable material platform for the observation of the QAH effect in covalent-organic frameworks.

Mechanism for Hall conductance of two-band systems against decoherence

The Kubo formula expresses a linear response of the quantum system to weak classical fields. Previous studies showed that the environment degrades the quantum Hall conductance. By studying the dynamics of dissipative two-band systems, in this paper we find that the formation of system-environment bound states is responsible for the Hall conductance immune to the effect of the environment. The bound states can form only when the system-environment couplings are below a threshold. Our results may be of both theoretical and experimental interest in exploring dissipative topological insulators in realistic situations, and may open new perspectives for designing active quantum Hall devices working in realistic environments.