Related papers: Edge state critical behavior of the integer quantu…
We review recent results obtained within the framework of the integer quantum Hall effect in the spirit of the work of Germinet, Klein, Schenker in \cite{GKS}. Landau Hamiltonians perturbed by random electric or magnetic perturbations are…
In this work, we exploit the findings of the screening theory of the integer quantized Hall effect (QHE) based on the formation of the incompressible strips and its essential influence on the global resistances and propose certain…
We review some elementary aspects of the critical properties of the series of metal-insulator transitions that constitute the integer quantum Hall effect. Numerical work has proven essential in charting out this phenomenon. Without being…
We study equilibration of quantum Hall edge states at integer filling factors, motivated by experiments involving point contacts at finite bias. Idealising the experimental situation and extending the notion of a quantum quench, we consider…
By studying the quantum Hall effect of stationary states with high values of injected current using a von Neumann lattice representation, we found that broadening of extended state bands due to a Hall electric field occurs and causes the…
The quantum Hall effect is one of the most extensively studied topological effects in solid state physics. The transitions between different quantum Hall states exhibit critical phenomena described by universal critical exponents. Numerous…
The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, non-unitary conformal field theories with logarithmic correlations. The nature and the physical…
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 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…
Using an innovative combination of a quasi-Corbino sample geometry and the cross-gate technique, we have developed a method that enables us to separately contact single edge channels in the quantum Hall regime and investigate equilibration…
Edge states in the integral quantum Hall effect on a lattice are reviewed from a topological point of view. For a system with edges which is realized inevitably in an experimental situation, the Hall conductance $\sigma_{xy}$ is given by a…
Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically…
We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and…
The fate of integer quantum Hall effect (IQHE) at weak magnetic field is studied numerically in the presence of {\it correlated} disorders. We find a systematic {\it float-up} and {\it merging} picture for extended levels on the low-energy…
Quantum Hall states can be characterized by their chiral edge modes. Upon softening the edge potential, the edge has long been known to undergo spontaneous reconstruction driven by charging effects. In this paper we demonstrate a…
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…
The edge states in the fractional quantum Hall systems at filling factor $\nu=1/3$ are studied by the density matrix renormalization group method. It is shown that the density oscillation induced by the local boundary condition at the edge…
We have introduced a controllable nano-scale incursion into a potential barrier imposed across a two-dimensional electron gas, and report on the phenomena that we observe as the incursion develops. In the quantum Hall regime, the…
Under hydrostatic pressure, the ground state of a two-dimensional electron gas at $\nu=5/2$ changes from a fractional quantum Hall state to the stripe phase. By measuring the energy gap of the fractional quantum Hall state and of the onset…
Quantum Hall states are characterized by a topological invariant, the many-body Chern number, which determines their quantized Hall conductivity. This invariant also emerges in circular dichroic responses, namely, by applying a circular…