Related papers: Duality and the Modular Group in the Quantum Hall …
An analytic form for the crossover of the conductivity tensor between two Hall plateaux, as a function of the external magnetic field, is proposed. The form of the crossover is obtained from the action of a symmetry group, a particular…
An analytic form for the conductivity tensor in crossover between two quantum Hall plateaux is derived, which appears to be in good agreement with existing experimental data. The derivation relies on an assumed symmetry between quantum Hall…
We discuss the possible origin of the duality observed in the quantum Hall current-voltage characteristics. We clarify the difference between "particle-vortex" (complex modular) duality, which acts on the full transport tensor, and…
We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers…
We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…
We construct a family of holomorphic $\beta$-functions whose RG flow preserves the $\Gamma(2)$ modular symmetry and reproduces the observed stability of the Hall plateaus. The semi-circle law relating the longitudinal and Hall…
An integer Quantum Hall effect transition is studied in a modulation doped p-SiGe sample. In contrast to most examples of such transitions the longitudinal and Hall conductivities at the critical point are close to 0.5 and 1.5 (e^2/h), the…
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…
By using Renormalization Group methods we analyze the description of the Quantum Hall Fluid in terms of a dual plasma with dyons as effective degrees of freedom. The physical interpretation of the parameters of the model as the longitudinal…
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…
We show that any critical transition region between two adjacent Hall plateaus in either integer or fractional quantum Hall effect is characterized by a universal semi-circle relationship between the longitudinal and transverse…
The quantum Hall effect is studied numerically in modulated two-dimensional electron systems in the presence of disorder. Based on the scaling property of the Hall conductivity as well as the localization length, the critical energies where…
At low temperatures the phase diagram for the quantum Hall effect has a powerful symmetry arising from the Law of Corresponding States. This symmetry gives rise to an infinite order discrete group which is a generalisation of…
We examine the longitudinal, non-linear, current-voltage characteristics near the quantum Hall liquid to insulator transition and show that a simple mapping exists between the characteristics on the quantum Hall side and those on the…
We consider the network model of the integer quantum Hall effect transition. By generalizing the real--space renormalization group procedure for the classical percolation to the case of quantum percolation, we derive a closed…
As a unified theory of integer and fractional quantum Hall plateau transitions, a nonperturbative theory of the two-parameter scaling renormalization group function is presented. By imposing global symmetries known as ``the law of…
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 consider the action of the modular group $\Gamma (2)$ on the set of positive rational fractions. From this, we derive a model for a classification of fractional (as well as integer) Hall states which can be visualized on two…
We study numerically conductance fluctuations near the integer quantum Hall effect plateau transition. The system is presumed to be in a mesoscopic regime, with phase coherence length comparable to the system size. We focus on a…
A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron-electron interactions. We assume that there exists a non-zero excitation gap above the ground…