Related papers: Interaction effects on quantum Hall transitions: d…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
We summarize the main ingredients of a unifying theory for abelian quantum Hall states. This theory combines the Finkelstein approach to localization and interaction effects with the topological concept of an instanton vacuum as well as…
Recent developments in the scaling theory of the integer quantum Hall effect are discussed. In particular, the influence of electron-electron interactions on the critical behavior are studied. It is further argued that recent experiments on…
Conductivity of Integer Quantum Hall Effect (IQHE) may be expressed as the topological invariant composed of the two - point Green function. Such a topological invariant is known both for the case of homogeneous systems with intrinsic…
We consider dephasing by interactions in a one-dimensional chiral fermion system (e.g. a Quantum Hall edge state). For finite-range interactions, we calculate the spatial decay of the Green's function at fixed energy, which sets the…
Let $m$ denote the number of quasielectrons (QEs) in a quantum Hall system containing $N$ particles altogether. We show in several general cases that for systems containing $m$ QEs in a single angular momentum shell above $N-m$ Fermions in…
In this work we investigate the phenomena associated with the new thresholds in the spectrum of excitations arising when different one-dimensional strongly interacting systems are voltage biased and weakly coupled by tunneling. We develop…
The normal-state behavior of the temperature-dependent Hall coefficient in cuprate superconductors is investigated using linear response theory. The Hall conductivity is of paramount importance in that its sign and magnitude directly…
Using a fermionic renormalization group approach we analyse a model where the electrons diffusing on a quantum dot interact via Fermi-liquid interactions. Describing the single-particle states by Random Matrix Theory, we find that…
The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The unique combination of spin, valley, and orbital degeneracies in bilayer graphene is…
We investigate integer and fractional quantum Hall states in quantum point contacts (QPCs) of different geometries, defined in AlGaAs/GaAs heterostructures employing different doping and screening techniques. We find that, even in the…
Motivated by the recent experimental breakthrough on the observation of the fractional quantum anomalous Hall (FQAH) effects in semiconductor and graphene moir\'{e} materials, we explore the rich physics associated with the coexistence of…
We have presented a quantum mechanical toy model for the study of Coulomb interactions in Quantum Hall (QH) system. Inclusion of Coulomb interaction is essential for the study of {\it{bilayer}} QH system and our model can simulate it, in…
It is demonstrated that an understanding of the 5/2 fractional quantum Hall effect can be achieved within the composite fermion theory without appealing to the Pfaffian wave function. The residual interaction between composite fermions…
I present a brief survey of important recent developments in the quantum Hall effect. The review covers both fractional and integer regimes, from an experimentalist's perspective. The topics include direct measurement of fractional charge,…
We show the explicit connection between two distinct and complementary approaches to the fractional quantum Hall system (FQHS): the quantum wires formalism and the topological low-energy effective description given in terms of an Abelian…
Taking into account the transverse gauge field fluctuations, which interact with composite fermions, we examine the finite temperature compressibility of the fermions as a function of an effective magnetic field $\Delta B = B - 2 n_e hc/e$…
We study quantum Ising spins placed on small-world networks. A simple model is considered in which the coupling between any given pair of spins is a nonzero constant if they are linked in the small-world network and zero otherwise. By…
We report on numerical studies of the energy spectrum and the localization properties in the double-layer quantum Hall system at $\nu = 1$. The Coulomb interaction is treated by the Hartree-Fock approximation, and the localization…
We study a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest-neighbor bonds of different signs. We discuss the influence of quantum fluctuations on the nature of the zero-temperature phase…