Hall Plateaus Research Articles

Superuniversality of dimerized SU(N+M) spin chains

We explore the physics of the quantum Hall effect using the Haldane mapping of dimerised $SU(N+M)$ spin chains, the large $N$ expansion and the density matrix renormalization group technique. We show that while the transition is first order for $N+M >2$, the system at zero temperature nevertheless displays a continuously diverging length scale $\xi$ (correlation length). The numerical results for $(M, N) = (1,3), ~ (2, 2),~(1, 5)$ and $(1, 7)$ indicate that $\xi$ is a directly observable physical quantity, namely the spatial width of the edge states. We relate the physical observables of the quantum spin chain to those of the quantum Hall system (and, hence, the $\vartheta$ vacuum concept in quantum field theory). Our numerical investigations provide strong evidence for the conjecture of super universality which says the dimerised spin chain quite generally displays all the basic features of the quantum Hall effect, independent of the specific values of $M$ and $N$. For the cases at hand we show that the singularity structure of the quantum Hall plateau transitions involves a universal function with two scale parameters that may in general depend on $M$ and $N$. This includes not only the Hall conductance but also the ground state energy as well as the correlation length $\xi$ with varying values of $\vartheta \sim \pi$.

Experimental evidence for dissipationless transport of the chiral edge state of the high-field Chern insulator in MnBi2Te4 nanodevices

We demonstrate the dissipationless transport of the chiral edge state (CES) in the nanodevices of quantum anomalous Hall insulator candidate MnBi2Te4. The device presents a near-zero longitudinal resistance together with a quantized Hall plateau in excess of 0.97 h/e2 over a range of temperatures from very low up to the Neel temperature of 22 K. Each of four-probe nonlocal measurements gives near-zero resistance and two-probe measurements exhibit a plateau of +1 h/e2, while the results of three-probe nonlocal measurements depend on the magnetic field. This indicates non-dissipation as well as the chirality of the edge state. The CES shows three regimes of temperature dependence, i.e., well-preserved dissipationless transport below 6 K, variable range hopping while increasing the temperature and thermal activation at higher than 22 K. Even at the lowest temperature, a current of over 1.4 {\mu}A breaks the dissipationless transport. These form a complete set of evidences of the Chern insulator state in the MnBi2Te4 systems.

Quantum magneto-transport property of two-dimensional semi-Dirac electron system

We theoretically investigate the quantum magneto-transport property of a two-dimensional semi-Dirac system under a perpendicular magnetic field. Based on the low-energy k⋅p Hamiltonian within the framework of linear response theory, we find that the Landau levels (LLs) are proportional to the two-thirds (2/3) power law of the magnetic field and level index. There is a gap in the LL spectrum and the LL spacing decreases with the increase of the level index. Further, the Hall conductance is strictly quantized with the sequential integer plateaus (in unit of 2e2/h ) at 0, ±1, ±2, ⋯ as the Fermi energy increases. The Shubnikov–de Haas (SdH) oscillation shows some pronounced peaks when the Fermi energy coincides with the LLs. The width of the Hall plateau and the interval of the SdH peak decrease with the increase of Fermi energy due to the decreasing LL spacings. Moreover, the Hall resistance is dependent linearly on the magnetic field in the low field regime but quantized in the high field regime. The longitudinal resistance is nearly a constant and shows distinct peaks in the low and high magnetic field regimes, respectively. Those magneto-transport spectra reflect the structure of LLs well. Our results provide further understanding on the electron states of semi-Dirac electron systems and may be useful in explaining the result of magneto-transport experiment.

Selective enhancement of Kane Mele-type spin-orbit interaction in graphene

In order to enhance the spin orbit interaction (SOI) in graphene for seeking the dissipationless quantum spin Hall devices, unique Kane-Mele-type SOI and high mobility samples are desired. However, the common external modification of graphene often introduces “extrinsic” Rashba-type SOI, which will destroy the possible topological state, bring a certain degree of impurity scattering and reduce the sample mobility. Here we show that by the EDTA-Dy molecule dressing, the carrier mobility is even improved, and the quantum Hall plateaus are observed more clearly. The Kane-Mele type SOI is mimicked after dressing, which is evidenced by the suppressed weak localization at equal carrier densities and simultaneous Elliot-Yafet spin relaxation. This is attributed to the spin-flexural phonon coupling induced by the enhanced graphene ripples, as revealed by the in-plane magnetotransport measurement.

Reprint of: Marginal CFT perturbations at the integer quantum Hall transition

According to recent arguments by the author, the conformal field theory (CFT) describing the scaling limit of the integer quantum Hall plateau transition is a deformed level-4 Wess–Zumino–Novikov–Witten model with Riemannian target space inside a complex Lie supergroup GL. After a summary of that proposal and some of its predictions, the leading irrelevant and relevant perturbations of the proposed CFT are discussed. Argued to be marginal, these result in a non-standard renormalization group (RG) flow near criticality, which calls for modified finite-size scaling analysis and may explain the long-standing inability of numerical work to reach agreement on the values of critical exponents. The technique of operator product expansion is used to compute the RG-beta functions up to cubic order in the couplings. The mean value of the dissipative conductance at the RG-fixed point is calculated for a cylinder geometry with any aspect ratio.

Competing Zero-Field Chern Insulators in Superconducting Twisted Bilayer Graphene.

The discovery of magic angle twisted bilayer graphene has unveiled a rich variety of superconducting, magnetic, and topologically nontrivial phases. Here, we show that the zero-field states at odd integer filling factors in h-BN nonaligned devices are consistent with symmetry broken Chern insulators, as is evidenced by the observation of the anomalous Hall effect near moiré cell filling factor ν=+1. The corresponding Chern insulator has a Chern number C=±1 and a relatively high Curie temperature of T_{c}≈4.5 K. In a perpendicular magnetic field above B>0.5 T we observe a transition of the ν=+1 Chern insulator from Chern number C=±1 to C=3, characterized by a quantized Hall plateau with R_{yx}=h/3e^{2}. These observations demonstrate that interaction-induced symmetry breaking leads to zero-field ground states that include almost degenerate and closely competing Chern insulators, and that states with larger Chern numbers couple most strongly to the B field. In addition, the device reveals strong superconducting phases with critical temperatures of up to T_{c}≈3.5 K. By providing the first demonstration of a system that allows gate-induced transitions between magnetic and superconducting phases, our observations mark a major milestone in the creation of a new generation of quantum electronics.

Composite fermion nonlinear sigma models

We study the integer quantum Hall plateau transition using composite fermion mean-field theory. We show that the topological $\theta = \pi$ term in the associated nonlinear sigma model [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] is stable against a certain particle-hole symmetry violating perturbation, parameterized by the composite fermion effective mass. This result, which applies to both the Halperin, Lee, and Read and Dirac composite fermion theories, represents an emergent particle-hole symmetry. For a disorder ensemble without particle-hole symmetry, we find that $\theta$ can vary continuously within the diffusive regime. Our results call for further study of the universality of the plateau transition.

Thermal dissipation in the quantum Hall regime in graphene

It is widely accepted that both backscattering and dissipation cannot occur in topological systems because of the topological protection. Here we show that the thermal dissipation can occur in the quantum Hall (QH) regime in graphene in the presence of dissipation sources, although the Hall plateaus and the zero longitudinal resistance still survive. Dissipation appears along the downstream chiral flow direction of the constriction in the Hall plateau regime, but it occurs mainly in the bulk in the Hall plateau transition regime. In addition, dissipation processes are accompanied with the evolution of the energy distribution from non-equilibrium to equilibrium. This indicates that topology neither prohibits the appearance of dissipation nor prohibits entropy increasing, which opens a new topic on the dissipation in topological systems.

Routes to realize the axion-insulator phase in MnBi2Te4(Bi2Te3)n family

Axion, first postulated as a hypothetical particle in high-energy physics, is now extended to describe a novel topological magnetoelectric effect derived from the Chern–Simons theory in condensed matter systems. The recent discovered intrinsic magnetic topological insulators (MTIs) MnBi2Te4 and its derivatives have attracted great attention because of their potential as a material platform to realize such a quantized axion field. Since the magnetic exchange gap can bring the “half-quantized” anomalous Hall effect at the surface, an axion insulator manifests as quantum anomalous Hall and zero Hall plateau effects in the thin films. However, many puzzles about this material family remain elusive yet, such as the gapless surface state and the direct experimental evidence of the axion insulator. In this Perspective, we discuss the preconditions, manifestations, and signatures of the axion-insulator phase, in the context of the development of the natural magnetic topological heterostructure MnBi2Te4(Bi2Te3)n family with various intriguing quantum phenomena. Recent theoretical and experimental efforts regarding the intrinsic magnetic topological insulators are summarized here to pave the way for this phenomenally developing field.

Magnetic-field-induced robust zero Hall plateau state in MnBi2Te4 Chern insulator

The intrinsic antiferromagnetic topological insulator MnBi2Te4 provides an ideal platform for exploring exotic topological quantum phenomena. Recently, the Chern insulator and axion insulator phases have been realized in few-layer MnBi2Te4 devices at low magnetic field regime. However, the fate of MnBi2Te4 in high magnetic field has never been explored in experiment. In this work, we report transport studies of exfoliated MnBi2Te4 flakes in pulsed magnetic fields up to 61.5 T. In the high-field limit, the Chern insulator phase with Chern number C = −1 evolves into a robust zero Hall resistance plateau state. Nonlocal transport measurements and theoretical calculations demonstrate that the charge transport in the zero Hall plateau state is conducted by two counter-propagating edge states that arise from the combined effects of Landau levels and large Zeeman effect in strong magnetic fields. Our result demonstrates the intricate interplay among intrinsic magnetic order, external magnetic field, and nontrivial band topology in MnBi2Te4.

Marginal CFT perturbations at the integer quantum Hall transition

According to recent arguments by the author, the conformal field theory (CFT) describing the scaling limit of the integer quantum Hall plateau transition is a deformed level-4 Wess–Zumino–Novikov–Witten model with Riemannian target space inside a complex Lie supergroup GL. After a summary of that proposal and some of its predictions, the leading irrelevant and relevant perturbations of the proposed CFT are discussed. Argued to be marginal, these result in a non-standard renormalization group (RG) flow near criticality, which calls for modified finite-size scaling analysis and may explain the long-standing inability of numerical work to reach agreement on the values of critical exponents. The technique of operator product expansion is used to compute the RG-beta functions up to cubic order in the couplings. The mean value of the dissipative conductance at the RG-fixed point is calculated for a cylinder geometry with any aspect ratio.

Any axion insulator must be a bulk three-dimensional topological insulator

This study demonstrates that, contrary to earlier claims in the field involving analyses of a so-called ``zero Hall plateau'', it is more intricate than expected to unambiguously reveal the existence of an axion insulator. In particular, the authors find from their scaling analysis of transport experiments on V-doped (Bi,Sb)${}_{2}$Te${}_{3}$ films of varying thickness that the truly three-dimensional bulk character is a necessary condition for axion insulators, a condition that is likely not satisfied for the materials exhibiting a zero Hall plateau.

Theoretical study of 3D quantum Hall effect in periodic electron system

The exsitance of three-dimensional Hall effect (3DQHE) due to spontaneous Fermi surface instabilities in magnetic field was proposed decades ago, and has stimulated recent progress in experiments. The reports in recent experiments show that the Hall plateaus and vanishing transverse magneto-resistivities (TMRs) (which are two main signatures of 3DQHE) are not easy to be observed in natural materials. And two main different explanations of the slow varying slope like Hall plateaus and non-vanishing TMRs (which can be called as quasi-quantized Hall effect (QQHE)) have been proposed. By studying the magneto-transport with a simple effective periodic 3D system, we show how 3DQHE can be achieved in certain parameter regimes at first. We find two new mechanisms that may give rise to QQHE. One mechanism is the low Fermi energy effect, and the other is the strong impurity effect. Our studies also proved that the artificial superlattice is an ideal platform for realizing 3DQHE with high layer barrier periodic potential.

Doping the chiral spin liquid: Topological superconductor or chiral metal

We point out that there are two different chiral spin liquid states on the triangular lattice and discuss the conducting states that are expected on doping them. These states labeled CS1 and CS2 are associated with two distinct topological orders with different edge states, although they both spontaneously break time reversal symmetry and exhibit the same quantized spin Hall conductance. While CSL1 is related to the Kalmeyer-Laughlin state, CSL2 is the $\nu =4$ member of Kitaev's 16 fold way classification. Both states are described within the Abrikosov fermion representation of spins, and the effect of doping can be accessed by introducing charged holons. On doping CSL2, condensation of charged holons leads to a topological d+id superconductor. However on doping CSL1 , in sharp contrast , two different scenarios can arise: first, if holons condense, a chiral metal with doubled unit cell and finite Hall conductivity is obtained. However, in a second novel scenario, the internal magnetic flux adjusts with doping and holons form a bosonic integer quantum Hall (BIQH) state. Remarkably, the latter phase is identical to a $d+id$ superconductor. In this case the Mott insulator to superconductor transition is associated with a bosonic variant of the integer quantum Hall plateau transition for the holon. We connect the above two scenarios to two recent numerical studies of doped chiral spin liquids on triangular lattice. Our work clarifies the complex relation between topological superconductors, chiral spin liquids and quantum criticality .

A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/25/2. We consider the FQHE at another even denominator fraction, namely \nu=2+3/8ν=2+3/8, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the ``\bar{3}\bar{2}^{2}1^{4}3‾2‾214" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8ν=2+3/8. We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4}3‾2‾214 state that can reveal its underlying topological structure.

Critical Behavior and Universal Signature of an Axion Insulator State.

Recently, the search for an axion insulator state in the ferromagnetic-3D topological insulator (TI) heterostructure and MnBi_{2}Te_{4} has attracted intense interest. However, its detection remains difficult in experiments. We systematically investigate the disorder-induced phase transition of the axion insulator state in a 3D TI with antiparallel magnetization alignment surfaces. It is found that there exists a 2D disorder-induced phase transition on the surfaces of the 3D TI which shares the same universality class with the quantum Hall plateau to plateau transition. Then, we provide a phenomenological theory which maps the random mass Dirac Hamiltonian of the axion insulator state into the Chalker-Coddington network model. Therefore, we propose probing the axion insulator state by investigating the universal signature of such a phase transition in the ferromagnetic-3D TI heterostructure and MnBi_{2}Te_{4}. Our findings not only show a global phase diagram of the axion insulator state, but also stimulate further experiments to probe it.

Abelian parton state for the ν=4/11 fractional quantum Hall effect

We consider the fractional quantum Hall effect at the filling factor $\ensuremath{\nu}=4/11$, where two independent experiments have observed a well-developed and quantized Hall plateau. We examine the Abelian state described by the ``$4\overline{2}{1}^{3}$'' parton wave function and numerically demonstrate it to be a plausible candidate for the ground state at $\ensuremath{\nu}=4/11$. We work out the low-energy effective theory of the $4\overline{2}{1}^{3}$ edge and make predictions for experimentally measurable properties of the state.

How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down

We review recent numerical studies of two-dimensional (2D) Dirac fermion theories that exhibit an unusual mechanism of topological protection against Anderson localization. These describe surface-state quasiparticles of time-reversal invariant, three-dimensional (3D) topological superconductors (TSCs), subject to the effects of quenched disorder. Numerics reveal a surprising connection between 3D TSCs in classes AIII, CI, and DIII, and 2D quantum Hall effects in classes A, C, and D. Conventional arguments derived from the non-linear σ-model picture imply that most TSC surface states should Anderson localize for arbitrarily weak disorder (CI, AIII), or exhibit weak antilocalizing behavior (DIII). The numerical studies reviewed here instead indicate spectrum-wide surface quantum criticality, characterized by robust eigenstate multifractality throughout the surface-state energy spectrum. In other words, there is an “energy stack” of critical wave functions. For class AIII, multifractal eigenstate and conductance analysis reveals identical statistics for states throughout the stack, consistent with the class A integer quantum-Hall plateau transition (QHPT). Class CI TSCs exhibit surface stacks of class C spin QHPT states. Critical stacking of a third kind, possibly associated to the class D thermal QHPT, is identified for nematic velocity disorder of a single Majorana cone in class DIII. The Dirac theories studied here can be represented as perturbed 2D Wess–Zumino–Novikov–Witten sigma models; the numerical results link these to Pruisken models with the topological angle ϑ=π. Beyond applications to TSCs, all three stacked Dirac theories (CI, AIII, DIII) naturally arise in the effective description of dirty d-wave quasiparticles, relevant to the high-Tc cuprates.

Geometry of random potentials: Induction of two-dimensional gravity in quantum Hall plateau transitions

In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points uniquely define a discrete surface $S$ and its dual $S^*$ made of quadrangular and $n-$gonal faces, respectively, thereby linking the geometry of the potential with the geometry of discrete surfaces. The map is parameter-dependent on the Fermi level. Edge states of Fermi lakes moving along equipotential contours between neighbour saddle points form a network of scatterings, which define the geometric basis, in the fermionic model, for the plateau transitions. The replacement probability characterizing the network model with geometric disorder recently proposed by Gruzberg, Kl\"umper, Nuding and Sedrakyan, is physically interpreted within the current framework as a parameter connected with the Fermi level.

Detection of hidden localized states by the quantum Hall effect in graphene

We fabricated a monolayer graphene transistor device in the shape of the Hall-bar structure, which produced an exactly symmetric signal following the sample geometry. During electrical characterization, the device showed the standard integer quantum Hall effect of monolayer graphene except for a broader range of several quantum Hall plateaus corresponding to small filling factors in the electron region. We investigated this anomaly on the basis of localized states owing to the presence of possible electron traps, whose energy levels were estimated to be near the Dirac point. In particular, the inequality between the filling of electrons and holes was ascribed to the requirement of excess electrons to fill the trap levels. The relations between the quantum Hall plateau, Landau level, and filling factor were carefully analyzed to reveal the details of the localized states in this graphene device.