Related papers: The Quantized Hall Effect. (Lab Tutorial. In Germa…
The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may…
The quantum valley Hall effect (QVHE) has been observed in a variety of experimental setups, both quantum and classical. While extremely promising for applications, one should be reminded that QVHE is not an exact topological phenomenon and…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
In view of the progress achieved in the field of the ac quantum Hall effect, the Working Group of the Comite Consultatif d'Electricite et Magnetisme (CCEM) on the AC Quantum Hall Effect asked the authors of this paper to write a compendium…
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.
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…
A theory of integer quantum Hall effect(QHE) in realistic systems based on von Neumann lattice is presented. We show that the momentum representation is quite useful and that the quantum Hall regime(QHR), which is defined by the propagator…
A short review paper for the quantum anomalous Hall effect. A substantially extended one is published as Adv. Phys. 64, 227 (2015).
We analysis the quantum Hall effect exhibited by a system of particles moving in a higher dimensional space. This can be done by considering particles on the Bergman ball {\bb{B}_{\rho}^d} of radius \rho in the presence of an external…
We investigated the Integer Quantum Hall Effect (IQHE) using an inductive method. The following conclusions can be derived from our study: (i) when the Fermi energy is located between Landau levels the only extended states at the Fermi…
In this paper, we revisit some quantum mechanical aspects related to the Quantum Hall Effect. We consider a Landau type model, paying a special attention to the experimental and geometrical features of Quantum Hall experiments. The…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
We study theoretically the parallel quantum wires of the experiment by Auslaender et al. [Science 308, 88 (2005)] at low electron density. It is shown that a Hall effect as observed in two- or three-dimensional electron systems develops as…
In the Hall effect, a voltage drop develops perpendicularly to the current flow in the presence of a magnetic field, leading to a transverse Hall resistance. Recent developments with quantum simulators have unveiled strongly correlated and…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
A two-dimensional array of quantum dots in a magnetic field is considered. The electrons in the quantum dots are described as unitary random matrix ensembles. The strength of the magnetic field is such that there is half a flux quantum per…
Based on very general arguments we show that for any geometry of the experiment, in the regime when the measurement leads to a quantized Hall conductivity, almost the entire current injected into the sample is carried by the bulk states.…
We consider the quantum Hall effect in quantum electrodynamics and find a deviation from the quantum mechanical prediction for the Hall conductivity due to radiative antiscreening of electric charge in an external magnetic field. A weak…
We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective of the interaction strength the Hall conductivity is given by the filling fraction of Landau levels averaged over…