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We present a quantum Hall effect of magnons in two-dimensional clean insulating magnets at finite temperature. Through the Aharonov-Casher effect, a magnon moving in an electric field acquires a geometric phase and forms Landau levels in an…
The quantum Hall effect hosts quantum phase transitions in which the localization length, that is the size of disorder-induced bulk localized states, is governed by universal scaling from percolation theory. However, this universal…
The quantum anomalous Hall effect (QAHE) in magnetic topological insulators offers great potential to revolutionize quantum electrical metrology by establishing primary resistance standards operating at zero external magnetic field and…
We theoretically investigate a quasi-one-dimensional quantum wire, where the lowest two subbands are populated, in the presence of a helical magnetic field. We uncover a backscattering mechanism involving the helical magnetic field and…
Transport measurements on two dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally-ordered, compressible liquid state. We develop and analyze a microscopic theory of such a…
The response of particle density to a dilation of a periodic potential in an insulator, with or without a fixed background potential or a magnetic field, is shown to be quantized. A similar phenomenon occurs in a quantum Hall system, where…
There is considerable experimental evidence for the existence in Quantum Hall systems of an approximate emergent discrete symmetry, $\Gamma_0(2) \subset SL(2,Z)$. The evidence consists of the robustness of the tests of a suite a predictions…
It is well known that noncommutative geometry naturally emerges in the quantum Hall states due to the presence of strong and constant magnetic fields. Here, we discuss the underlying noncommutative geometry of quantum Hall fluids in which…
The discovery of the anomalous Hall effect (AHE) in bulk metallic antiferromagnets (AFMs) motivates the search of the same phenomenon in two-dimensional (2D) systems, where a quantized anomalous Hall conductance can in principle be…
We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, based on the theory of conformal restriction. This is a mathematical theory that was recently…
We report simultaneous transport and scanning microwave impedance microscopy to examine the correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime in gated graphene devices. Surprisingly,…
We theoretically consider disorder and temperature effects on the integer quantum Hall effect (IQHE) using a variety of distinct and complementary analytical and numerical techniques. In particular, we address simple, physical, and…
It is widely held that disorder is essential to the existence of a finite interval of magnetic field in which the Hall conductance is quantized, i.e. for the existence of `plateaus' in the quantum Hall effect. Here, we show that the…
The magneto-transport properties of planar and layered strongly inhomogeneous two-phase systems are investigated, using the explicit expressions for the effective conductivities and resistivities obtained by the exact dual transformation,…
We consider a two-dimensional gas of interacting fermions in presence of an external constant magnetic field: the system is extended and homogeneous, and thus assumed to be invariant under magnetic translations. Working within the…
Quantum corrections to transport through a chaotic ballistic cavity are known to be universal. The universality not only applies to the magnitude of quantum corrections, but also to their dependence on external parameters, such as the Fermi…
A recent theory has provided a possible explanation for the ``non-universal scaling'' of the low-temperature conductance (and conductivity) peak-heights of two-dimensional electron systems in the integer and fractional quantum Hall regimes.…
Quantum Hall effect (QHE), the ground to construct modern conceptual electronic systems with emerging physics, is often much influenced by the interplay between the host two-dimensional electron gases and the substrate, sometimes predicted…
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 start the paper with a brief presentation of the main characteristics of graphene, and of the Dirac theory of massless fermions in 2+1 dimensions obtained as the associated low-momentum effective theory, in the absence of external…