Quantum Hall Systems Research Articles

Fermionic Chern insulator from twisted light with linear polarization

The breaking of time-reversal symmetry is a crucial ingredient to topological bands. It can occur intrisically in materials with magnetic order, or be induced by external fields, such as magnetic fields in quantum Hall systems, or circularly polarized light fields in Floquet Chern insulators. Apart from polarization, photons can carry another degree of freedom, orbital angular momentum, through which time-reversal symmetry can be broken. In this Letter, we pose the question whether this property allows for inducing topological bands via a linearly polarized but twisted light beam. To this end, we study a graphene-like model of electrons on a honeycomb lattice interacting with a twisted light field. To identify topological behavior of the electrons, we calculate their local markers of Chern number, and monitor the presence of in-gap edge states. Our results are shown to be fully analogous to the behavior found in paradigmatic models for static and driven Chern insulators, and realizing the state is experimentally straightforward. With this, our work establishes a new mechanism for generating Fermionic topological phases of matter that can harness the central phase singularity of an optical vortex beam.

Domain-wall dynamics in Bose-Einstein condensates with synthetic gauge fields.

Interactions in many-body physical systems, from condensed matter to high-energy physics, lead to the emergence of exotic particles. Examples are mesons in quantum chromodynamics and composite fermions in fractional quantum Hall systems, which arise from the dynamical coupling between matter and gauge fields1,2. The challenge of understanding the complexity of matter-gauge interaction can be aided by quantumsimulations, for which ultracold atoms offer a versatile platform via the creation of artificial gauge fields. An important step towards simulating the physics of exotic emergent particles is the synthesis of artificial gauge fields whose state depends dynamically on the presence of matter. Here we demonstrate deterministic formation of domain walls in a stable Bose-Einstein condensate with a gauge field that is determined by the atomic density. The density-dependent gauge field is created by simultaneous modulations of an optical lattice potential and interatomic interactions, and results in domains of atoms condensed into two different momenta. Modelling the domain walls as elementary excitations, we find that the domain walls respond to synthetic electric field with a charge-to-mass ratio larger than and opposite to that of the bare atoms. Our work offers promising prospects to simulate the dynamics and interactions of previously undescribed excitations in quantum systems with dynamical gauge fields.

Generalized model for the charge transport properties of dressed quantum Hall systems

We present a generalized mathematical model for predicting the transport properties of a quantum system exposed to a stationary magnetic field and a high-intensity electromagnetic field. The new formulation, which applies to two-dimensional (2D) dressed quantum Hall systems, is based on Landau quantization theory and the Floquet-Drude conductivity approach. We model our system as a two-dimensional electron gas (2DEG) that interacts with two external fields. To analyze the strong light coupling with the 2DEG, we employ the Floquet theory as a nonperturbative procedure. Moreover, the Floquet-Fermi golden rule is adopted to explore the impurity scattering effects on charge transport in disordered quantum Hall systems. We derive fully analytical expressions to describe longitudinal components in the conductivity tensor in dressed quantum Hall systems. Subsequently, we demonstrate that the conductivity characteristics of quantum Hall systems can be manipulated using strong external light. Our results align with well-established and experimentally verified theoretical descriptions for undressed systems while providing a more generalized analysis of the conductivity characteristics in quantum Hall systems. Thus our model can be applied to accurately interpret the usage of strong external radiation as a tool in nanoscale quantum devices.

Intrinsic and Extrinsic Anomalous Hall Effects in Disordered Magnetic Weyl Semimetal

We study the intrinsic and extrinsic Hall effects in disordered magnetic Weyl semimetals numerically. We show that in Weyl metals, where the Fermi energy deviates from the Weyl point, the Hall and longitudinal conductances exhibit a specific relation, which is distinguished from the well-known relation in integer quantum Hall systems. Around the Weyl point, the Hall conductance increases with increasing longitudinal conductance. This increasing behavior indicates the existence of additional contributions to the Hall conductance from the subbands of Weyl cones besides that from the bulk Berry curvature. We also show that the extrinsic anomalous Hall effect due to the spin scatterers (skew scattering) is significantly suppressed in Weyl metals.

Nonequilibrium Charge Dynamics of Tomonaga–Luttinger Liquids in Quantum Hall Edge Channels

AbstractTomonaga–Luttinger liquids exhibit unique features that cannot be seen in ordinary Fermi liquids. Recent advancement in measurement techniques on 1D quantum Hall edge channels allows to reveal unique characteristics, such as spin‐charge separation and nonthermal metastable states. In this review, an overview of nonequilibrium dynamics in quantum‐Hall Tomonaga–Luttinger liquids is presented. After the introduction of a circuit model for collective excitations (bosons) in the system, transport eigenmodes in interaction‐ and disorder‐dominated regimes are discussed with time‐resolved charge measurements for the integer and fractional quantum Hall systems. Moreover, nonthermal steady states associated with the integrable model are studied with energy distribution functions obtained with a quantum dot spectrometer. These nontrivial dynamics can be extended to other 1D systems, including 2D topological insulators.

Machine learning study for disorder effect at a half-filled high Landau level

The robustness against disorder scattering is crucial for experimentally observing the predicted charge density waves (CDWs) in a fractional quantum Hall (FQH) system with partially-filled topmost Landau level (LL). Here, we applied two types of machine learning (ML) methods to study the influence of the disorder on an example system with half-filled N = 2 LL. Through the unsupervised principal component analysis (PCA) method, we recognize that a CDW stripe phase is represented by two principal components, which alternatively dominate in weak scattering case and coherently collapse at strong scattering. A combination of these two PCA components enables us to fully describe the evolution of the stripe phase and to determine its critical transition point towards a random disorder phase. A practice with the supervised neural network (NN) method also provides us with the numerically same boundary for the two separated phases. These ML approaches have proved to be effective tools for our system as their results are well compatible with previous numerical works. Moreover, the nonnecessity to the explicit knowledge of the states extends their potential to study other unfamiliar disordered systems.

Principal component analysis for fractional quantum Hall states in bilayer systems

We initiate an unsupervised machine learning (ML) study with the principal component analysis (PCA) for two example bilayer fractional quantum Hall (FQH) systems at filling factors ν=4/5 and 2/3 where the interlayer tunneling effect and Coulomb interaction are considered. Some common features in PCA are exploited to recognize the transition and boundary between two competing ground state (GS) phases even without a complete softening in the spectrum. We also provide the numerical evidence to confirm a bilayer system as an analogy to its single-layer counterpart at large interlayer tunneling limit. The general approaches with PCA have been applied to determine the collapsing boundaries for phases at the strongly-correlated bilayer limit, the decoupled bilayer limit, and the strong interlayer tunneling limit, which lead to the qualitatively similar phase diagrams as previous numerical studies but do not rely on explicit knowledge of the states. Thus, our PCA study is extendable for other unfamiliar bilayer systems.

Research progress of integrated photonic quantum simulation

Quantum simulation is to use a controllable quantum system to simulate other complicated or hard-to-control quantum system, and to deal with some complex unknown quantum systems that cannot be simulated on classical computers due to the exponential explosion of the Hilbert space. Among different kinds of physical realizations of quantum simulation, integrated optical systems have emerged as an appropriate platform in recent years due to the advantages of flexible control, weak decoherence, and no interaction in optical systems. In this review, we attempt to introduce some of the basic models used for quantum simulation in integrated photonic systems. This review article is organized as follows. In Section 2, we introduce the commonly used material platforms for integrated quantum simulation, including the silicon-based, lithium niobate-based integrated circuits, and the femtosecond laser direct writing optical waveguides. Several integrated optical platforms such as the coupled waveguide arrays, photonic crystals, coupled resonator arrays, and multiport interferometers are also introduced. In Section 3, we focus on the analog quantum simulations in the integrated photonic platform, including Anderson localization of light in disordered systems, various kinds of topological insulators, nonlinear and non-Hermitian systems. More specifically, in Subsection 3.1, we present the integrated photonic realizations of disordered and quasi-periodic systems. In Subsection 3.2, we review the integrated photonic realizations of the topological insulators with and without time-reversal symmetry, including Floquet topological insulators, quantum spin hall system, anomalous quantum hall system, valley hall system, Su-Schrieffer-Heeger (SSH) model, and photonic topological Anderson insulators. Besides, topological insulator lasers and topologically protected quantum photon sources are briefly reviewed. In Subsection 3.3, we review the nonlinear and non-Hermitian integrated optical systems. In Section 4 we present the integrated digital quantum simulations based on the multiport interferometers, including the discrete-time quantum random walk, Boson sampling, and molecular simulation. In Section 5, we summarize the content of the article and present the outlook on the future perspectives of the integrated photonic quantum simulation. We believe that the integrated photonic platforms will continue to provide an excellent platform for quantum simulation. More practical applications will be found based on this system through combining the fields of topological photonics, laser technologies, quantum information, nonlinear and non-Hermitian physics.

Cobordism invariance of topological edge-following states

We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore, the gap-filling spectra contribute to quantised current channels, which follow and are localised at the possibly complicated boundary. This index obstruction is shown to be insensitive to deformations of the domain boundary, so the phenomenon is generic for magnetic Laplacians modelling quantum Hall systems and Chern topological insulators. A key construction is a quasi-equivariant version of Roe's algebra of locally compact finite propagation operators.

Distinguishing between non-abelian topological orders in a quantum Hall system.

Quantum Hall states can harbor exotic quantum phases. The nature of these states is reflected in the gapless edge modes owing to “bulk-edge” correspondence. The most studied putative non-abelian state is the spin-polarized filling factor (ν) = 5/2, which permits different topological orders that can be abelian or non-abelian. We developed a method that interfaces the studied quantum state with another state and used it to identify the topological order of ν = 5/2 state. The interface between two half-planes, one hosting the ν = 5/2 state and the other an integer ν = 3 state, supports a fractional ν = 1/2 charge mode and a neutral Majorana mode. The counterpropagating chirality of the Majorana mode, probed by measuring partition noise, is consistent with the particle-hole Pfaffian (PH-Pf) topological order and rules out the anti-Pfaffian order.

Exact Landau Level Description of Geometry and Interaction in a Flatband.

Flatbands appear in many condensed matter systems, including the two-dimensional electron gas in a high magnetic field, correlated materials, and moiré heterostructures. They are characterized by intrinsic geometric properties such as the Berry curvature and Fubini-Study metric. The influence of the band geometry on electron-electron interaction is difficult to understand analytically because the geometry is in general nonuniform in momentum space. In this work, we study the topological flatband of Chern number C=1 with a momentum-dependent but positive definite Berry curvature that fluctuates in sync with Fubini-Study metric. We derive an exact correspondence between such ideal flatbands and Landau levels and show that the band geometry fluctuation gives rise to a new type of interaction in the corresponding Landau levels that depends on the center of mass of two particles. We characterize such interactions by generalizing the usual Haldane pseudopotentials. This mapping gives exact zero-energy ground states for short-ranged repulsive generalized pseudopotentials in flatbands, in analogy to fractional quantum Hall systems. Driving the center-of-mass interactions beyond the repulsive regime leads to a dramatic reconstruction of the ground states towards gapless phases. The generalized pseudopotential could be a useful basis for future numerical studies.

Homemade-HEMT-based transimpedance amplifier for high-resolution shot-noise measurements.

We report a cryogenic transimpedance amplifier (TA) suitable for cross-correlation current-noise measurements. The TA comprises homemade high-electron-mobility transistors with high transconductance and low noise characteristics, fabricated in an AlGaAs/GaAs heterostructure. The low input-referred noise and wide frequency band of the TA lead to a high resolution in current-noise measurements. The TA's low input impedance suppresses unwanted crosstalk between two distinct currents from a sample, justifying the advantage of the TA for cross-correlation measurements. We demonstrate the high resolution of a TA-based experimental setup by measuring the shot noise generated at a quantum pointcontact in a quantum Hall system.

Robustness of chiral edge modes in fractal-like lattices below two dimensions: A case study

One of the most prominent characteristics of two-dimensional Quantum Hall systems are chiral edge modes. Their existence is a consequence of the bulk-boundary correspondence and their stability guarantees the quantization of the transverse conductance. In this work, we study two microscopic models, the Hofstadter lattice model and an extended version of Haldane's Chern insulator. Both models host Quantum Hall phases in two dimensions. We transfer them to lattice implementations of fractals with a dimension between one and two and study the existence and robustness of their edge states. Our main observation is that, contrary to their two-dimensional counterpart, there is no universal behavior of the edge modes in fractals. Instead, their presence and stability critically depends on details of the models and the lattice realization of the fractal.

Biasing topological charge injection in topological matter

We explore the interplay between topologies in the momentum and real spaces to formulate a thermodynamic description of nonequilibrium injection of topological charges under external bias. We show that the edge modes engendered by the momentum-space topology can play a functional role of connecting the external reservoirs to the bulk transport of topological charges in the real space. We illustrate our general results with two examples: the spin-torque injection of skyrmions in an electrically-biased integer quantum Hall system, and the vortex injection in a topological $p\,+\,i\,p$ superconductor coupled to heat reservoirs. Based on the universal fractional entropy of the Majorana zero modes bound to the vortices, their controllable injection proposed in this work could provide a route for creating and manipulating Majorana fermions.

Stochastization of Long Living Spin-Cyclotron Excitations in a Spin-Unpolarised Quantum Hall System

In the present study we address the kinetics of long-lived excitations at zero temperature in an electronic quantum Hall system with filling factor $\nu=2$. The initial coherent state of spin-cyclotron magnetoexitons with two-dimensional wave vector ${\bf q}=0$ resulting from laser pumping is stochastized over time due to emission of acoustic phonons. The elementary emission process requires participation of two magnetoexitons, so the effective rate of phonon emission is proportional to the excitation density squared, and the stochastization process occurs nonexponentially with time. The final distribution of magnetoexitons over 2D momenta, established as a result of stochastization, is compared with equilibrium distribution at finite temperature.

Cavity-mediated electron hopping in disordered quantum Hall systems

We investigate the emergence of long-range electron hopping mediated by cavity vacuum fields in disordered quantum Hall systems. We show that the counter-rotating (anti-resonant) light-matter interaction produces an effective hopping between disordered eigenstates within the last occupied Landau band. The process involves a number of intermediate states equal to the Landau degeneracy: each of these states consists of a virtual cavity photon and an electron excited in the next Landau band with the same spin. We study such a cavity-mediated hopping mechanism in the dual presence of a random disordered potential and a wall potential near the edges, accounting for both paramagnetic coupling and diamagnetic renormalization. We determine the cavity-mediated scattering rates, showing the impact on both bulk and edge states. The effect for edge states is shown to increase when their energy approaches the disordered bulk band, while for higher energy the edge states become asymptotically free. We determine the scaling properties while increasing the Landau band degeneracy. Consequences on the quantum Hall physics and future perspectives are discussed.

Z4 parafermion ±π/2 modes in an interacting periodically driven superconducting chain

We theoretically report the emergence of ${Z}_{4}$ parafermion edge modes in a periodically driven spinful superconducting chain with a modest fermionic Hubbard interaction. These parafermion edge modes represent $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/(2T)$ quasienergy excitations ($T$ being the driving period), which have no static counterpart and arise from the interplay between an interaction effect and periodic driving. At special parameter values, these exotic quasiparticles can be analytically and exactly derived. Strong numerical evidence of their robustness against variations in parameter values and spatial disorder is further presented. Our proposal offers a route toward realizing parafermions without fractional quantum Hall systems or complicated interactions.

Spontaneous fractional Chern insulators in transition metal dichalcogenide moiré superlattices

Moir{\'e} superlattice realized in two-dimensional heterostructures offers an exciting platform to access strongly-correlated electronic states. In this work, we study transition metal dichalcogenides (TMD) Moir{\'e} superlattices with time-reversal-symmetry and nontrivial spin{/valley}-Chern numbers. Utilizing realistic material parameters and the method of exact diagonalization, we find that at a certain twisting angle and fractional filling, gapped fractional topological states, i.e., fractional Chern insulators, are naturally {stabilized} by simply introducing the Coulomb repulsion. In contrast to fractional quantum Hall systems, where the time-reversal symmetry has to be broken explicitly, these fractional states break the time-reversal symmetry spontaneously. {We show that the Chern number contrasting in the opposite valleys imposes a strong constraint on the nature of fractional Chern insulator and the associated low energy excitations.} We also propose to realize the non-abelian Moore-Read state in TMD Moir{\'e} superlattice sandwiched between nonlinear dielectric media.

Double nuclear spin relaxation in hybrid quantum Hall systems

Recent advances in quantum engineering have given us the ability to design hybrid systems with novel properties normally not present in the regime they operate in. The coupling of spin ensembles and magnons to microwave resonators has for instance lead to a much richer understanding of collective effects in these systems and their potential quantum applications. We can also hybridize electron and nuclear spin ensembles together in the solid-state regime to investigate collective effects normally only observed in the atomic, molecular, and optical world. Here we explore in the solid state regime the dynamics of a double domain nuclear spin ensemble coupled to the Nambu-Goldstone boson in GaAs semiconductors and show it exhibits both collective and individual relaxation (thermalization) on very different time scales. Further the collective relaxation of the nuclear spin ensemble is what one would expect from superradiant decay. This opens up the possibility for the exploration of novel collective behavior in solid state systems where the natural energies associated with those spins are much less than the thermal energy.

Dynamics of quantum Hall interfaces

A quantum Hall (QH) interface is different from an ordinary QH edge, as the latter has its location determined by the confining potential, while the former can be unpinned and behave like a free string. In this paper, we demonstrate this difference by studying three different interfaces formed by (i) the Laughlin state and the vacuum, (ii) the Pfaffian state and the vacuum, and (iii) the Pfaffian and the anti-Pfaffian states. We find that string-like interfaces propagating freely in the QH system lead to very different dynamical properties from edges. This qualitative difference gives rise to fascinating new physics and suggests a new direction in future research on QH physics. We also discuss briefly possible analogies between QH interfaces and concepts in string theory.