We explore the behavior of interacting bosonic atoms in an optical lattice subject to a large artificial magnetic field. We extend earlier investigations of this system where the number of magnetic flux quanta per unit cell alpha is close to a simple rational number [Phys. Rev. Lett. 96, 180407 (2006)]. Interesting topological states such as the Laughlin and Read-Rezayi states can occur even if the atoms experience a weak trapping potential in one direction. An explicit numerical calculation near alpha = 1/2 shows that the system exhibits a striped vortex lattice phase of one species, which is analogous to the behavior of a two-species system for small alpha. We also investigate methods to probe the encountered states. These include spatial correlation functions and the measurement of noise correlations in time of flight expanded atomic clouds. Characteristic differences arise which allow for an identification of the respective quantum Hall states. We furthermore discuss that a counterintuitive flow of the Hall current occurs for certain values of alpha.
Chiral topological superconductors are expected to appear as intermediate states when a quantum anomalous Hall system is proximity coupled to an s-wave superconductor and the magnetization direction is reversed. In this paper we address the edge state properties of ordinary quantum Hall systems proximity coupled to s-wave superconductors, accounting explicitly for Landau quantization. We find that the appearance of topological superconducting phases with an odd number of Majorana edge modes is dependent on the structure of the system's vortex lattice. More precisely, vortex lattices containing…
Parity anomaly is a quantum mechanical effect that the parity symmetry in a two-dimensional classical action is failed to be restored in any regularization of the full quantum theory and is characterized by a half-quantized Hall conductivity. Here we propose a scheme to explore the experimental signature from parity anomaly in the measurement of optical Hall conductivity, in which the optical Hall conductivity is nearly half quantized for a proper range of frequency. The behaviors of optical Hall conductivity are studied for several models, which reveal the appearance of half-quantized Hall co…
When passing an optical medium in the presence of a magnetic field, the polarization of light can be rotated either when reflected at the surface (Kerr effect) or when transmitted through the material (Faraday rotation). This phenomenon is a direct consequence of the optical Hall effect arising from the light-charge carrier interaction in solid state systems subjected to an external magnetic field, in analogy with the conventional Hall effect. The optical Hall effect has been explored in many thin films and also more recently in 2D layered materials. Here, an alternative approach based on stra…
Spin-Hall-Like Magnon Transport in a Synthetic Antiferromagnetic Skyrmion Lattice
Dongguan Institute of Materials Science and Technology, Chinese Academy of Sciences（中国科学院东莞材料基因高等理工研究院）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Shenzhen Technology University（深圳技术大学）；Hunan University（湖南大学）；Central South University（中南大学）
Quantum Hall effect in three-dimensional lattice induced by Wannier-Stark-Landau localization
Donostia International Physics Center（多诺斯蒂亚国际物理中心）；Advanced Polymers and Materials: Physics, Chemistry and Technology, Chemistry Faculty (UPV/EHU)（巴斯克大学化学学院先进聚合物与材料：物理、化学与技术）
The proposals for realizing exotic particles through coupling of quantum Hall effect to superconductivity involve spatially non-uniform magnetic fields. As a step toward that goal, we study, both theoretically and experimentally, a system of Dirac electrons exposed to an Abrikosov flux lattice. We theoretically find that non-uniform magnetic field causes a carrier-density dependent reduction of the Hall conductivity. Our studies show that this reduction originates from a rather subtle effect: a levitation of the Berry curvature within Landau levels broadened by the non-uniform magnetic field. …
We study nonlinear optical response of graphene in the quantum Hall regime to an intense laser pulse. In particular, we consider harmonic generation process. We demonstrate that the generalized magneto-optical conductivity of graphene on the harmonics of a strong pump laser radiation has a characteristic Hall plateaus feature. The plateaus heights depend on the laser intensity and broadening of Landau levels, so that are not quantized exactly. This nonlinear effect remains robust against the significant broadening of Landau levels. We predict realization of an experiment through the observatio…
We study the time evolution of the Optical Spin Hall Effect (OSHE), which occurs when exciton-polaritons undergo resonant Rayleigh scattering. The resulting spin pattern in momentum space is quantified by calculating the degree of circular polarization of the momentum space image for each point in time. We find the degree of circular polarization performing oscillations, which can be described within the framework of the pseudospin model by Kavokin et al. (Ref. 1).
Gaussian-Bond Hall Viscosity and Nonlocal Hall Response of a Sampled Landau Level
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学理论物理研究所）；Institute of Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Department of Physics, Nagoya University（名古屋大学物理学系）；Center for Spintronics Research Network, Keio University（庆应义塾大学自旋电子学研究网络中心）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能研究开发机构先进科学研究中心）
We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a many-Dirac-points system. We find that the quantum Hall effects present different features as change as relative strengths of several perturbations. Namely, a gauge-field-dressed next-nearest-neighbor hopping can induce the quantum spin Hall effect and a Zeeman field can induce a so-called quantum anomalous valley Hall effect which includes two copies of quantum Hall states with opposite Chern numbers and counter-propagating edge states. Our study extends the borders of the field of quantum Hall eff…
In a quantum Hall system, the finite-wavevector Hall conductivity displays an intriguing dependence on the Hall viscosity, a coefficient that describes the non-dissipative response of the fluid to a velocity gradient. In this paper, we pursue this connection in detail for quantum Hall systems on a lattice, noting that the neat continuum relation breaks down and develops corrections due to the broken rotational symmetry. In the process, we introduce a new, quantum mechanical derivation of the finite-wavevector Hall conductivity for the integer quantum Hall effect, which allows terms to arbitrar…
Geometrically frustrated materials, such as spin ice or kagome lattice, are known to exhibit exotic Hall effect phenomena due to spin chirality. We explore Hall effect mechanism in an artificial honeycomb spin ice of Nd--Sn element using Hall probe and polarized neutron reflectivity measurements. In an interesting observation, a strong enhancement in Hall signal at relatively higher temperature of $T$ $\sim$ 20 K is detected. The effect is attributed to the planar Hall effect due to magnetic moment configuration in spin ice state in low field application. In the antiferromagnetic state of neod…
The quest to realize novel phases of matter with topological order is an important pursuit with implications for strongly correlated physics and quantum information. Utilizing ideas from state-of-the-art coherent control of artificial quantum systems such as superconducting circuits, we present a proposal to realize bosonic fractional quantum Hall physics on small lattices by creating nearly flat topological bands using staggered flux patterns. Fingerprints of fractionalization through charge pumping can be observed with nearly perfect quantization using as few as 24 lattice sites (two photons…
Materials with designed properties arises in a synergy between theoretical and experimental approaches. In this study we explore the set of Archimedean lattices forming a guidance to its electronic properties and topological phases. Within these lattices, rich electronic structure emerge forming type-I and II Dirac fermions, topological flat bands and high-degeneracy points with linear and flat dispersions. Employing a tight-binding model, with spin-orbit coupling, we characterize a quantum spin Hall (QSH) phase in all Archimedean lattices. Our discussion is validated within density functional…
Valley-related multiple Hall effect in 2D lattice is a fundamental transport phenomenon in the fields of condensed-matter physics and material science. So far, most proposals for its realization are limited to toy models or extrinsic effects. Here, based on tight-binding model and first-principles calculations, we report the discovery of intrinsic valley-related multiple Hall effect in 2D organometallic lattice of NbTa-benzene. Protected by the breaking of both time-reversal and inversion symmetry, NbTa-benzene exhibits large valley polarization spontaneously in both the conduction and valence…
Topological insulators (TIs) are characterized by the quantum anomalous Hall effect (QAHE) on the topological surface states under time-reversal symmetry breaking. Motivated by recent experiments on the magneto-optical effects induced by the QAHE, we develop a theory for the dynamical Hall conductivity for subgap optical frequency and intense optical fields using the Keldysh-Floquet Green's function formalism. Our theory reveals a nonlinear regime in which the Hall conductivity remains close to $e^2/2h$ at low frequencies. At higher optical fields, we find that the subsequent collapse of the h…
