Related papers: Intrinsic nonlinear Hall effect beyond Bloch geome…
We prove the bulk-edge correspondence in $K$-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk…
The spin Hall effect is a phenomenon of inducing spin current by an external electric field. We recently proposed that this effect can occur in p-type semiconductors without relying upon any disorder scattering [S. Murakami et al., Science…
In this work we report experiments on defined by shallow etching narrow Hall bars. The magneto-transport properties of intermediate mobility two-dimensional electron systems are investigated and analyzed within the screening theory of the…
We propose that a nonlinear Hall response can be observed in Bloch oscillations of ultracold atoms in optical lattices under the condition of preserved time-reversal symmetry. In the short-time limit of Bloch oscillations driven by a direct…
A square lattice model which exhibits a nonzero quantized Hall conductance in a zero net magnetic field at certain values of the parameters is presented. The quantization is due to the existence of a topological winding number that…
We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system…
A numerical analysis is made of the breakdown of the quantum Hall effect caused by the Hall electric field in competition with disorder. It turns out that in the regime of dense impurities, in particular, the number of localized states…
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external…
We develop the quantum hydrodynamics of inner waves in the bulk of fractional quantum Hall states. We show that the inelastic light scattering by inner waves is a sole effect of the gravitational anomaly. We obtain the formula for the…
We present a general formula for the topological part of the effective action for quantum Hall systems in higher dimensions, including fluctuations of the gauge field and metric around background fields of a specified topological class. The…
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully…
I give a brief review of higher dimensional quantum Hall effect (QHE) and how one can use a general framework to describe the lowest Landau level dynamics as a noncommutative field theory whose semiclassical limit leads to anomaly free…
The Hall effect, ever intriguing since its discovery, has spurred the exploration of its phenomena, intensified by advances in topology and novel materials. Differentiating the ordinary Hall effect from extraordinary properties like the…
A generalized definition of intrinsic and extrinsic transport coefficients is introduced. We show that transport coefficients from the intrinsic origin are solely determined by local electronic structure, and thus the intrinsic spin Hall…
Free planar electrons in a uniform magnetic field are shown to possess the symmetry of area-preserving diffeomorphisms ($W$-infinity algebra). Intuitively, this is a consequence of gauge invariance, which forces dynamics to depend only on…
We investigate spontaneous interlayer phase coherence and the occurrence of the quantum Hall effect in triple-layer electron systems. Our work is based on a simple tight-binding model that greatly facilitates calculations and whose accuracy…
Nonlinear Hall responses are a direct electrical probe of quantum geometry, but they are symmetry-forbidden in many pristine two-dimensional metals. We show that layer-selective magnetic proximity unlocks intrinsic linear and nonlinear Hall…
We consider the ground state of an electron gas embedded in a quantum gyrotropic cavity. We show that the light-matter interaction leads to a nontrivial topology of the many-body electron-photon wave function characterized by a nonzero…
The classical Hall effect, the traditional means of determining charge-carrier sign and density in a conductor, requires a magnetic field to produce transverse voltages across a current-carrying wire. We show that along curved paths --…