Quantum Hall Phases Research Articles

Landau-Ginzburg theories of non-Abelian quantum Hall states from non-Abelian bosonization

It is an important open problem to understand the landscape of non-Abelian fractional quantum Hall phases which can be obtained starting from physically motivated theories of Abelian composite particles. We show that progress on this problem can be made using recently proposed non-Abelian bosonization dualities in 2+1 dimensions, which morally relate $U(N)_k$ and $SU(k)_{-N}$ Chern-Simons-matter theories. The advantage of these dualities is that regions of the phase diagram which may be obscure on one side of the duality can be accessed by condensing local operators on the other side. Starting from parent Abelian states, we use this approach to construct Landau-Ginzburg theories of non-Abelian states through a pairing mechanism. In particular, we obtain the bosonic Read-Rezayi sequence at fillings $\nu=k/(kM+2)$ by starting from $k$ layers of bosons at $\nu=1/2$ with $M$ Abelian fluxes attached. The Read-Rezayi states arise when $k$-clusters of the dual non-Abelian bosons condense. We extend this construction by showing that $N_f$-component generalizations of the Halperin $(2,2,1)$ bosonic states have dual descriptions in terms of $SU(N_f+1)_1$ Chern-Simons-matter theories, revealing an emergent global symmetry in the process. Clustering $k$ layers of these theories yields a non-Abelian $SU(N_f)$-singlet state at filling $\nu = kN_f / (N_f + 1 + kMN_f)$.

Quasihole Tunneling in Disordered Fractional Quantum Hall Systems**Supported by the National Natural Science Foundation of China under Grant No 11674282, the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No XDB28000000, and the National Basic Research Program of China under Grant No 2015CB921101.

Fractional quantum Hall systems are often described by model wave functions, which are the ground states of pure systems with short-range interaction. A primary example is the Laughlin wave function, which supports Abelian quasiparticles with fractionalized charge. In the presence of disorder, the wave function of the ground state is expected to deviate from the Laughlin form. We study the disorder-driven collapse of the quantum Hall state by analyzing the evolution of the ground state and the single-quasihole state. In particular, we demonstrate that the quasihole tunneling amplitude can signal the fractional quantum Hall phase to insulator transition.

Observation of Helical Edge Transport in a Screened Graphene

Helical quantum Hall phase in graphene on SrTiO3 Authors: Louis Veyrat, Corentin Déprez, Alexis Coissard, Xiaoxi Li, Frédéric Gay, Kenji Watanabe, Takashi Taniguchi, Zheng Han, Benjamin A. Piot, Hermann Sellier, and Benjamin Sacépé arXiv:1907.02299 Recommended with a commentary by Leonid I. Glazman, Yale University |View Commentary (pdf)| DOI: 10.36471/JCCM_July_2019_03https://doi.org/10.36471/JCCM_July_2019_03

Anisotropic magnetoelectronic structures and magneto-transport properties of topological Dirac semimetal nanowires

Abstract The magnetoelectronic structures, and the charge and spin conductance spectra of topological Dirac semimetal (TDS) nanowires are calculated by adopting the tight-binding Hamiltonian model in combination with the Green’s-function-based Landauer-Buttiker formula. Anisotropic electronic structures and magneto-transport properties are found in TDS nanowires with different confinement and magnetic field directions. With respect to in-plane-confinement TDS nanowires, trivial surface/corner states are observed and they are split into two spin-polarized states with oppositive signs when a weak out-of-plane magnetic field is applied. Moreover, the spin-polarized surface states will be transformed into bulk and corner states as the magnetic field strength is increased. Therefore, quantized spin conductance energy windows and fully-spin-polarized conductance can be achieved in the normal/out-of-plane-magnetic-field-modulated/normal TDS system in the case of the weak and strong fields, respectively. However, chiral surface states are generated when an in-plane magnetic field is applied, resulting in the perfect charge conductance steps of the normal/in-plane-magnetic-field-modulated/normal TDS system. With respect to the TDS nanowire with both the in-plane and out-of-plane confinements, nontrivial spin-momentum-locked helical surface states are observed. However, the helical character of the surface states will be destroyed and nontrivial-trivial topological phase transition happens as a high in-plane magnetic field is applied. In addition, the energy position of the surface subband inside the bulk energy gap is shifted so that the surface state transport can be switched on or off by tuning the magnetic field strength. Interestingly, the surface subband situated inside the bulk energy gap is split into two subbands with opposite spin signs as an out-of-plane magnetic field is added. Therefore, the topological phase transition between the quantum spin Hall and spin-polarized quantum Hall phases in the TDS nanowire, and the spin-polarized transport in the normal/out-of-plane-magnetic-field-modulated/normal TDS system, can be controlled by varying the magnetic field strength. These effects may benefit both the fundamental understanding of the magneto-electronic characters of the TDS nanostructures and the design of low-dissipation (spin) electronic devices.

Topological crystalline insulators from stacked graphene layers

In principle the stacking of different two-dimensional (2D) materials allows the construction of 3D systems with entirely new electronic properties. Here we propose to realize topological crystalline insulators (TCI) protected by mirror symmetry in heterostructures consisting of graphene monolayers separated by two-dimensional polar spacers. The polar spacers are arranged such that they can induce an alternating doping and/or spin-orbit coupling in the adjacent graphene sheets. When spin-orbit coupling dominates, the non-trivial phase arises due to the fact that each graphene sheet enters a quantum spin-Hall phase. Instead, when the graphene layers are electron and hole doped in an alternating fashion, a uniform magnetic field leads to the formation of quantum Hall phases with opposite Chern numbers. It thus has the remarkable property that unlike previously proposed and observed TCIs, the non-trivial topology is generated by an external time-reversal breaking perturbation.

Non-Abelian bosonization and modular transformation approach to superuniversality

Quantum Hall inter-plateaux transitions are physical exemplars of quantum phase transitions. Near each of these transitions, the measured electrical conductivity scales with the same correlation length and dynamical critical exponents, i.e., the critical points are superuniversal. In apparent contradiction to these experiments, prior theoretical studies of quantum Hall phase transitions within the framework of Abelian Chern-Simons theory coupled to matter found correlation length exponents that depend on the value of the quantum critical Hall conductivity. Here, we use non-Abelian bosonization and modular transformations to theoretically study the phenomenon of superuniversality. Specifically, we introduce a new effective theory that has an emergent $U(N)$ gauge symmetry with any $N > 1$ for a quantum phase transition between an integer quantum Hall state and an insulator. We then use modular transformations to generate from this theory effective descriptions for transitions between a large class of fractional quantum Hall states whose quasiparticle excitations have Abelian statistics. We find the correlation length and dynamical critical exponents are independent of the particular transition within a controlled 't Hooft large $N$ expansion, i.e., superuniversal! We argue that this superuniversality could survive away from this controlled large $N$ limit using recent duality conjectures.

Transition to the quantum hall regime in InAs nanowire cross-junctions

We present a low-temperature electrical transport study on four-terminal ballistic InAs nanowire cross-junctions in magnetic fields aligned perpendicular to the cross-plane. Two-terminal longitudinal conductance measurements between opposing contact terminals reveal typical 1D conductance quantization at zero magnetic field. As the magnetic field is applied, the 1D bands evolve into hybrid magneto-electric sub-levels that eventually transform into Landau levels for the widest nanowire devices investigated (width = 100 nm). Hall measurements in a four-terminal configuration on these devices show plateaus in the transverse Hall resistance at high magnetic fields that scale with (ve2/h)−1. e is the elementary charge, h denotes Planck’s constant and v is an integer that coincides with the Landau level index determined from the longitudinal conductance measurements. While the 1D conductance quantization in zero magnetic field is fragile against disorder at the NW surface, the plateaus in the Hall resistance at high fields remain robust as expected for a topologically protected Quantum Hall phase.

Interacting multi-channel topological boundary modes in a quantum Hall valley system

Symmetry and topology are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties1,2. Domain walls between distinct broken-symmetry QHFM phases are predicted to host gapless one-dimensional modes-that is, quantum channels that emerge because of a topological change in the underlying electronic wavefunctions at such interfaces. Although various QHFMs have been identified in different materials3-8, interacting electronic modes at these domain walls have not been probed. Here we use a scanning tunnelling microscope to directly visualize the spontaneous formation of boundary modes at domain walls between QHFM phases with different valley polarization (that is, the occupation of equal-energy but quantum mechanically distinct valleys in the electronic structure) on the surface of bismuth. Spectroscopy shows that these modes occur within a topological energy gap, which closes and reopens as the valley polarization switches across the domain wall. By changing the valley flavour and the number of modes at the domain wall, we can realize different regimes in which the valley-polarized channels are either metallic or develop a spectroscopic gap. This behaviour is a consequence of Coulomb interactions constrained by the valley flavour, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting one-dimensional quantum wires.QHFM domain walls can be realized in different classes of two-dimensional materials, providing the opportunity to explore a rich phase space of interactions in these quantum wires.

Bulk pumping in two-dimensional topological phases

The notion of topological (Thouless) pumping in topological phases is traditionally associated with Laughlin's pump argument for the quantization of the Hall conductance in two-dimensional (2D) quantum Hall systems. It relies on magnetic flux variations that thread the system of interest without penetrating its bulk, in the spirit of Aharonov-Bohm effects. Here we explore a different paradigm for topological pumping induced, instead, by magnetic flux variations $\delta\chi$ inserted through the bulk of topological phases. We show that $\delta\chi$ generically controls the analog of a topological pump, accompanied by robust physical phenomena. We demonstrate this concept of bulk pumping in two paradigmatic types of 2D topological phases: integer and fractional quantum Hall systems and topological superconductors. We show, in particular, that bulk pumping provides a unifying connection between seemingly distinct physical effects such as density variations described by Streda's formula in quantum Hall phases, and fractional Josephson currents in topological superconductors. We discuss the generalization of bulk pumping to other types of topological phases.

Competing Fractional Quantum Hall and Electron Solid Phases in Graphene.

We report experimental observation of the reentrant integer quantum Hall effect in graphene, appearing in the N=2 Landau level. Similar to high-mobility GaAs/AlGaAs heterostructures, the effect is due to a competition between incompressible fractional quantum Hall states, and electron solid phases. The tunability of graphene allows us to measure the B-T phase diagram of the electron solid phase. The hierarchy of reentrant states suggests spin and valley degrees of freedom play a role in determining the ground state energy. We find that the melting temperature scales with magnetic field, and construct a phase diagram of the electron liquid-solid transition.

Gate-Tunable Topological Flat Bands in Trilayer Graphene Boron-Nitride Moiré Superlattices.

We investigate the electronic structure of the flat bands induced by moiré superlattices and electric fields in nearly aligned ABC trilayer graphene (TLG) boron-nitride (BN) interfaces where Coulomb effects can lead to correlated gapped phases. Our calculations indicate that valley-spin resolved isolated superlattice flat bands that carry a finite Chern number C=3 proportional to the layer number can appear near charge neutrality for appropriate perpendicular electric fields and twist angles. When the degeneracy of the bands is lifted by Coulomb interactions, these topological bands can lead to anomalous quantum Hall phases that embody orbital and spin magnetism. Narrow bandwidths of ∼10 meV achievable for a continuous range of twist angles θ≲0.6° with moderate interlayer potential differences of ∼50 meV make the TLG-BN systems a promising platform for the study of electric-field tunable Coulomb-interaction-driven spontaneous Hall phases.

Fractional Quantum Hall Phases of Bosons with Tunable Interactions: From the Laughlin Liquid to a Fractional Wigner Crystal.

Highly tunable platforms for realizing topological phases of matter are emerging from atomic and photonic systems and offer the prospect of designing interactions between particles. The shape of the potential, besides playing an important role in the competition between different fractional quantum Hall phases, can also trigger the transition to symmetry-broken phases, or even to phases where topological and symmetry-breaking order coexist. Here, we explore the phase diagram of an interacting bosonic model in the lowest Landau level at half filling as two-body interactions are tuned. Apart from the well-known Laughlin liquid, Wigner crystal, stripe, and bubble phases, we also find evidence of a phase that exhibits crystalline order at fractional filling per crystal site. The Laughlin liquid transits into this phase when pairs of bosons strongly repel each other at relative angular momentum 4ℏ. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.

Recombination dynamics of Landau levels in an InGaAs/InP quantum well

The dynamics of differently spin-polarized carriers photoexcited in a system of Landau levels is investigated in an InGaAs/InP quantum well. Shake-up emission from Landau levels above the Fermi level is observed, and it is shown to significantly affect the recombination dynamics of Landau levels. The shake-up effect is found to occur due to the inter-Landau-level scattering, which manifests itself in a rapid decay of the emission from Landau levels. In addition, the inter-Landau-level scattering is shown to determine the time delay of photoluminescence response due to the relaxation of photoexcited electrons among Landau levels. The sharp minimum of the recombination time is observed between the quantum Hall phases with the filling factors $\ensuremath{\nu}=1$ and 2, and it is attributed to the formation of the metallic intermediate phase, which causes increasing overlap between the electron and hole wave functions.

Chiral topological phases from artificial neural networks

Motivated by recent progress in applying techniques from the field of artificial neural networks (ANNs) to quantum many-body physics, we investigate as to what extent the flexibility of ANNs can be used to efficiently study systems that host chiral topological phases such as fractional quantum Hall (FQH) phases. With benchmark examples, we demonstrate that training ANNs of restricted Boltzmann machine type in the framework of variational Monte Carlo can numerically solve FQH problems to good approximation. Furthermore, we show by explicit construction how n-body correlations can be kept at an exact level with ANN wave-functions exhibiting polynomial scaling with power n in system size. Using this construction, we analytically represent the paradigmatic Laughlin wave-function as an ANN state.

Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference

States with spontaneously broken symmetry can form due to Coulomb interactions in electronic systems with multiple internal degrees of freedom. Materials with several degenerate regions in the Brillouin zone—called valleys—offer a rich setting for the emergence of such states, which have potential electronic and optical applications1–4. To date, identification of these broken-symmetry phases has mostly relied on macroscopic transport or optical properties. Here we demonstrate a direct approach by visualizing the wavefunctions of bismuth surface states with a scanning tunnelling microscope. Strong spin–orbit coupling on the surface of bismuth leads to six degenerate, teardrop-shaped, hole valleys5. Our spectroscopic measurements reveal that exchange interactions fully lift this degeneracy at high magnetic field, and we are able to determine the nature of the valley ordering by imaging the broken-symmetry Landau level wavefunctions. The spatial features of singly degenerate Landau level wavefunctions near isolated defects contain unique signatures of interference between spin-textured valleys, which identify the electronic ground state as a quantum Hall ferroelectric. Our observations confirm the recent prediction6 that interactions in strongly anisotropic valley systems favour the occupation of a single valley, giving rise to emergent ferroelectricity in the surface state of bismuth. A phase of strongly interacting electrons that has a spontaneous dipole moment is seen for the first time using an approach that images the electron's wavefunction through interference at an impurity.

Quasi-one-dimensional Hall physics in the Harper–Hofstadter–Mott model

We study the ground-state phase diagram of the strongly interacting Harper–Hofstadter–Mott model at quarter flux on a quasi-one-dimensional lattice consisting of a single magnetic flux quantum in y-direction. In addition to superfluid phases with various density patterns, the ground-state phase diagram features quasi-one-dimensional analogs of fractional quantum Hall phases at fillings ν = 1/2 and 3/2, where the latter is only found thanks to the hopping anisotropy and the quasi-one-dimensional geometry. At integer fillings—where in the full two-dimensional system the ground-state is expected to be gapless—we observe gapped non-degenerate ground-states: at ν = 1 it shows an odd ‘fermionic’ Hall conductance, while the Hall response at ν = 2 consists of the transverse transport of a single particle–hole pair, resulting in a net zero Hall conductance. The results are obtained by exact diagonalization and in the reciprocal mean-field approximation.

Imaging Anyons with Scanning Tunneling Microscopy

Anyons are exotic quasi-particles with fractional charge that can emerge as fundamental excitations of strongly interacting topological quantum phases of matter. Unlike ordinary fermions and bosons, they may obey non-abelian statistics--a property that would help realize fault tolerant quantum computation. Non-abelian anyons have long been predicted to occur in the fractional quantum Hall (FQH) phases that form in two-dimensional electron gases (2DEG) in the presence of a large magnetic field, su ch as the $\nu=\tfrac{5}{2}$ FQH state. However, direct experimental evidence of anyons and tests that can distinguish between abelian and non-abelian quantum ground states with such excitations have remained elusive. Here we propose a new experimental approach to directly visualize the structure of interacting electronic states of FQH states with the scanning tunneling microscope (STM). Our theoretical calculations show how spectroscopy mapping with the STM near individual impurity defects can be used to image fractional statistics in FQH states, identifying unique signatures in such measurements that can distinguish different proposed ground states. The presence of locally trapped anyons should leave distinct signatures in STM spectroscopic maps, and enables a new approach to directly detect - and perhaps ultimately manipulate - these exotic quasi-particles.

Emergent phases of fractonic matter

Fractons are emergent particles which are immobile in isolation, but which can move together in dipolar pairs or other small clusters. These exotic excitations naturally occur in certain quantum phases of matter described by tensor gauge theories. Previous research has focused on the properties of small numbers of fractons and their interactions, effectively mapping out the "Standard Model" of fractons. In the present work, however, we consider systems with a finite density of either fractons or their dipolar bound states, with a focus on the $U(1)$ fracton models. We study some of the phases in which emergent fractonic matter can exist, thereby initiating the study of the "condensed matter" of fractons. We begin by considering a system with a finite density of fractons, which we show can exhibit microemulsion physics, in which fractons form small-scale clusters emulsed in a phase dominated by long-range repulsion. We then move on to study systems with a finite density of mobile dipoles, which have phases analogous to many conventional condensed matter phases. We focus on two major examples: Fermi liquids and quantum Hall phases. A finite density of fermionic dipoles will form a Fermi surface and enter a Fermi liquid phase. Interestingly, this dipolar Fermi liquid exhibits a finite-temperature phase transition, corresponding to an unbinding transition of fractons. Finally, we study chiral two-dimensional phases corresponding to dipoles in "quantum Hall" states of their emergent magnetic field. We study numerous aspects of these generalized quantum Hall systems, such as their edge theories and ground state degeneracies.

Polaron Polaritons in the Integer and Fractional Quantum Hall Regimes

Elementary quasiparticles in a two-dimensional electron system can be described as exciton polarons since electron-exciton interactions ensures dressing of excitons by Fermi-sea electron-hole pair excitations. A relevant open question is the modification of this description when the electrons occupy flat bands and electron-electron interactions become prominent. Here, we perform cavity spectroscopy of a two-dimensional electron system in the strong coupling regime, where polariton resonances carry signatures of strongly correlated quantum Hall phases. By measuring the evolution of the polariton splitting under an external magnetic field, we demonstrate the modification of polaron dressing that we associate with filling factor dependent electron-exciton interactions.

Light-Induced Fractional Quantum Hall Phases in Graphene.

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at nonzero relative angular momentum can become dominant, resembling a hollow-core pseudopotential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν=1/2 and ν=2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.