Related papers: The Quantum Hall Effect in the Absence of Disorder
We numerically study the quantum Hall effect in biased bilayer graphene based on a tight-binding model in the presence of disorder. Integer quantum Hall plateaus with quantized conductivity $\sigma_{xy}=\nu e^2/h$ (where $\nu$ is any…
The quantum Hall conductance of a disordered two-dimensional gas of non-interacting electrons is re-examined for its integrity against disorder in the limit of no mixing between different Landau levels. The exact one-electron eigenstates of…
We numerically study the quantum Hall effect (QHE) in bilayer graphene based on tight-binding model in the presence of disorder. Two distinct QHE regimes are identified in the full energy band separated by a critical region with…
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…
We study effects of disorder on the integer quantized Hall effect within the screening theory, systematically. The disorder potential is analyzed considering the range of the potential fluctuations. Short range part of the single impurity…
As a model for the transitions between plateaus in the fractional Quantum Hall effect we study the critical behavior of non-interacting charged particles in a static random magnetic field with finite mean value. We argue that this model…
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…
I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic…
We numerically investigate the effects of disorder on the quantum Hall effect (QHE) and the quantum phase transitions in silicene based on a lattice model. It is shown that for a clean sample, silicene exhibits an unconventional QHE near…
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 both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we…
The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field and was later generalized to Chern insulators without net magnetization. Here,…
We derive an empirical formula for the width of quantum Hall effect plateaus which is free of adjustable parameters. It describes the integer, fractional and $\nu = 0$ (Wigner insulator) quantum Hall effect in single heterojunctions. The…
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative…
We consider Coulomb drag between two layers of two-dimensional electron gases subject to a strong magnetic field, with the Landau level filling factor in each layer being 1/2. We find $\rho_D$ to be very large, as compared to the zero…
Quantum transport properties in quantum Hall wires in the presence of spatially correlated disordered magnetic fields are investigated numerically. It is found that the correlation drastically changes the transport properties associated…
The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and…
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…
We report results of numerical studies of the integer quantum Hall effect in a tight binding model on a two-dimensional square lattice with non-interacting electrons, in the presence of a random potential as well as a uniform magnetic field…
The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of…