Session F54: Advances in the Integer Quantum Hall Effect

Chalker-Coddington network model as a Floquet topological insulator

We re-examine the Chalker-Coddington network model, which was originally introduced to model integer quantum Hall plateau transitions. We point out that the dynamics of this model actually describe a periodically-driven (Floquet) system whose bands have vanishing Chern number throughout the phase diagram. Instead, the topological phase of the network model arises from a non-trivial dynamical Floquet invariant, i.e. the network model describes transitions between trivial and chiral Floquet phases of a distinct topological class from the integer quantum Hall effect. In view of this observation, we re-evaluate the standard arguments given in the past that the quantum Hall plateau transition and the transition in the Chalker-Coddington network model belong to the same universality class.   

Quantum Hall Effect in Quasi-One-Dimensional Weak Topological Insulator

Prototypical weak topological insulators (WTI) have been theoretically predicted to be realized in quasi-one-dimensional materials Bi₄X₄ (X = Br, I) [PRL 116, 066801 (2016)] and then experimentally confirmed in ARPES [Nature (London) 566, 518 (2019)]. The unique surface states of such a WTI have two entangled Dirac cones with strong anisotropy. We study theoretically the integer quantum Hall effect of such WTI surface states and show the important roles played by the special geometry, symmetry, topology, and their interplay in Bi₄X₄. We also predict prominent signatures in transport experiments.   

Non-interacting and interacting Graphene in a strong uniform magnetic field

We study monolayer graphene in a uniform magnetic field in the absence and presence of interactions. In the non-interacting limit for p/q flux quanta per unit cell, the central two bands have 2q Dirac points in the Brillouin zone in the nearest-neighbor model. These touchings and their locations are guaranteed by chiral symmetry and the lattice symmetries of the honeycomb structure. If we add a staggered potential and a next nearest neighbor hopping we find their competition leads to a topological phase transition. We also study the stability of the Dirac touchings to one-body perturbations that explicitly lowers the symmetry.

In the interacting case, we study the phases in the strong magnetic field limit. We consider on-site Hubbard and nearest-neighbor Heisenberg interactions. In the continuum limit, the theory has been studied before [1]. It has been found that there are four competing phases namely, ferromagnetic, antiferromagnetic, charge density wave, and Kekulé distorted phases. We find phase diagrams for q=3,4,5,6,9,12 where some of the phases found in the continuum limit are co-existent in the lattice limit with some phases not present in the continuum limit.

[1] M. Kharitonov PRB 85, 155439 (2012)   

Quantum Hall Effect in Chirality-induced Weyl Semiconductor n-type Tellurene

Very recently a new mechanism of generating Weyl nodes were proposed in chiral crystals with strong spin-orbit coupling, which, in sharp contrast to conventional band-inversion-induced Weyl semimetals, can exist in semiconductor systems. Tellurium (Te) is predicted to have these Weyl nodes located at the edge of the conduction band, originated from its DNA-like chiral chain crystal structure. However Te is naturally p-type doped and its conduction band has rarely been studied through transport measurement. In this work we report the first quantum Hall experiment in ALD doped n-type 2D tellurium (dubbed as tellurene) samples with mobility 6,000 cm²/Vs. The chirality-induced Weyl nodes give rise to radial spin texture, and topologically non-trivial π Berry phase was detected in quantum Hall sequences. Additionally, the doping profile forms a wide quantum well with symmetric-antisymmetric energy states leading to an approximate SU(8) isospin symmetry. Our work expands the spectrum of Weyl matters into semiconductor regime for the first time.   

Chiral quasiparticle tunneling between quantum Hall edges in proximity with a superconductor

We study a two-terminal graphene Josephson junction with contacts shaped to form a narrow constriction,
less than 100 nm in length. The contacts are made from type-II superconducting contacts and able to withstand
magnetic fields high enough to reach the quantum Hall regime in graphene. In this regime, the device
conductance is determined by edge states, plus the contribution from the constricted region. In particular,
the constriction area can support supercurrents up to fields of ∼2.5 T. Additionally, enhanced conductance
is observed through a wide range of magnetic fields and gate voltages. This additional conductance and the
appearance of supercurrent is attributed to the tunneling between counterpropagating quantum Hall edge states
along opposite superconducting contacts.
Published in: M.T. Wei, et.al. PHYSICAL REVIEW B 100, 121403(R) (2019)
  

Hall and dissipative viscosity and conductivity in a disordered 2D electron gas

Hydrodynamic charge transport is at the center of recent research efforts. Of particular interest is the nondissipative Hall viscosity, which conveys topological information in clean gapped systems. The prevalence of disorder in the real world calls for a study of its effect on viscosity, as well as on its relation with the nonlocal conductivity, the main venue to its experimental measurement. Here we address this question for disordered noninteracting 2D electrons. Analytically, we employ the self-consistent Born approximation, accounting for the modification of the single-particle density of states and the elastic transport time by the Landau quantization. Our results interpolate smoothly between the limiting cases of weak (strong) magnetic field and strong (weak) disorder. In the regime of weak magnetic field we describe the quantum (Shubnikov-de Haas type) oscillations of the viscosity, nonlocal conductivity, and Wen-Zee response. For strong magnetic fields we characterize the effects of the disorder-induced broadening of the Landau levels on the transport coefficients. This is supplemented by numerical calculations for a few filled Landau levels. Our results show that the Hall viscosity and its relation with conductivity are surprisingly robust to disorder.   

Geometric entanglement in integer quantum Hall states

We study the structure of entanglement in integer quantum Hall states using the entanglement entropy (EE) as well as the reduced density matrix, through its spectrum and eigenstates. We focus on an important class of spatial regions that have a sharp corner, which leads to an angle-dependent contribution to the EE. We unravel surprising relations by comparing this corner term at different fillings. We further find that the corner term, when properly normalized, has nearly the same angle dependence as conformal theories in 2 spatial dimensions. We also reveal that the low-lying entanglement spectrum and corresponding eigenfunctions describe edge excitations localized at the corner. Finally, we present an outlook for fractional quantum Hall states.   

Strong-disorder renormalization group approach to the integer quantum Hall effect

The critical behavior of the integer quantum Hall transition has recently reattracted considerable attention [1]. We propose an alternative numerical approach, namely a modified strong-disorder renormalization group (SDRG) method, in order to investigate this transition. The SDRG method is a recursive decimation process which is known to yield exact results for electronic tight-binding models, provided one keeps all links generated under renormalization. In practical applications, the number of kept links is limited. Nonetheless, in a recent study of the Anderson localization transition, it has been shown that one can get reasonable results for the critical exponents by keeping only a relatively small maximum number of links per site [2]. We generalize this method to the integer quantum Hall problem and apply it to both square lattice and long strip geometries.

[1] PUSCHMANN, M. et al. Integer quantum hall transition on a tight-binding lattice. Phys. Rev. B, American Physical Society, v. 99, p. 121301, 2019.
[2] MARD, H. J. et al. Strong-disorder approach for the anderson localization transition. Phys. Rev. B, American Physical Society, v. 96, p. 045143, 2017.   

Non-local induced pairing in chiral edge states

A superconductor in contact with a quantum Hall material will induce fundamentally non-local superconducting correlations in the quantum Hall edge state through the proximity effect. Such correlations are often put into models by hand in local approximations, but by building a model without assumed locality we are able predict the strength and non-local spatio-temporal behaviour of the correlation. Accurately modelling this correlation allows us to treat geometries of experimental interest and predict the behavior of interesting effects such as crossed Andreev reflection. This is relevant for several recent experiments, and the treated hybridized state has been proposed as part of a system hosting non-Abelian anyonic zero modes.   

Reconstruction near the interface of a ν=4 and ν=3 QH systems

We study the Hartree-Fock ground state near the interface between the ν=4 and ν=3 quantum Hall systems. In this problem we have two tuning parameters, w which is the width of interface in units of l (magnetic length), and Ec which is the strength of coulomb interaction in units of the cyclotron energy. In the bulk, for 2.52 < Ec <2.94, the ν=3 state is fully polarised but ν=4 state is a singlet. We have found that in this regime there are two edge phases. Phase 1 has 3 chiral modes, 2 downstream and 1 upstream. In this phase spin is a good quantum number. In Phase 2 we only found 1 chiral mode which is downstream. This phase has a spin rotation and can have a pair of counter propagating neutral modes. We use the time dependent Hartree-Fock method to calculate the collective excitations of these phases.   

Spin-1 Photonic Skyrmion in Viscous Quantum Hall Fluids

We present the fundamental model of a topological electromagnetic phase of matter: viscous Maxwell-Chern-Simons theory. We demonstrate that this is the minimal (exactly solvable) gauge theory with a nontrivial photonic Chern number. The interplay of symmetry and topology is also captured in the Chern number, which is determined by the spin-1 representations of a photonic skyrmion at high-symmetry points in the Brillouin zone. Physically, our predicted electromagnetic phases are connected to a dynamical photonic mass in a viscous quantum Hall fluid. The electromagnetic phase is topologically nontrivial when the Hall viscosity inhibits the total bulk Hall response. Our work bridges the gap between electromagnetic and condensed matter topological physics while also demonstrating the central role of spin-1 quantization in nontrivial photonic phases.   

Excited quantum Hall effect: enantiomorphic flat bands in a Yin-Yang Kagome lattice

Quantum Hall effect (QHE) is one of the most fruitful research topics in condensed-matter physics. Ordinarily, the QHE manifests in a ground state with time-reversal symmetry broken by magnetization to carry a quantized chiral edge conductivity around a two-dimensional insulating bulk. We propose a theoretical concept and model of non-equilibrium excited-state QHE (EQHE) without intrinsic magnetization. It arises from circularly polarized photoexcitation between two enantiomorphic flat bands of opposite chirality, each supporting originally a helical topological insulating state hosted in a Yin-Yang Kagome lattice. The chirality of its edge state can be reversed by the handedness of light, instead of the direction of magnetization as in the conventional quantum (anomalous) Hall effect, offering a simple switching mechanism for quantum devices. Implications and realization of EQHE in real materials are discussed.   

ferromagnetic transition in chiral metal

This letter studies a spinful 1D chiral electron model with contact interaction and nonlinear dispersion, where an itinerant ferromagnetic phase transition happens at repulsive interaction and an Amperean pairing at attractive interaction, the two phases are symmetrical and connected by a particle-hole transformation. We use bosonization and relate it with the fermion model to study the phase transition criticality and find the spin and charge modes have different dynamical exponent, which leads to a fractional-power time correlation, unlike the Luttinger liquid theory. We also find a similar transition in the quantum Hall edge states, the nonlinear dispersion is replaced with the presence of interaction form factor after projecting to the Landau levels.   

van der Waals Heterostructures of 3D Topological Insulators and 2D Magnetic Materials

Three dimensional (3D) topological insulator (TI) based van der Waals heterostructures form an excellent platform to study the proximity effect between a TI surface and another layered material, such as a two-dimensional (2D) ferromagnet. Previously we have observed both massless relativistic Dirac fermions and massive (gapped) Dirac fermions in this way for the topological surface state of BiSbTeSe₂¹ and have reported quantum Hall data for these surfaces. However, typical ferromagnets get oxidized easily during the fabrication process. Thus, the induced magnetization in the TI interface is not clean under ambient conditions. To minimize the influence of oxidation, we explore this fabrication inside a glovebox. We will report the performance of such TI based devices in comparison to those built-in ambient conditions and further study the proximity effect in TI-based van der Waals heterostructures.


¹ Chong S et al 2018 Nano Lett. 18 8047   

Phase transition and anomalous scaling in the quantum Hall transport of topological-insulator Sn-Bi1.1Sb0.9Te2S devices

The scaling physics of quantum Hall transport in optimized topological insulators with a plateau precision of ∼1/1000 e²/h is considered. Two exponential scaling regimes are observed in temperature-dependent transport dissipation, one of which accords with thermal-activation behavior with a gap of 2.8 meV (>20 K), the other being attributed to variable-range hopping (1–20 K). Magnetic-field-driven plateau-to-plateau transition gives scaling relations of (dR_xy/dB)^max ∝ T ^−κ and △B⁻¹ ∝ T ^−κ with a onsistent exponent of κ ∼ 0.2, which is half the universal value for a conventional two-dimensional electron gas. This is evidence of percolation assisted by quantum tunneling and reveals the dominance of electron-electron interaction of the topological surface states.