Related papers: Integers and Fractions
We give a brief introduction to the phenomenon of the Fractional Quantum Hall effect, whose discovery was awarded the Nobel prize in 1998. We also explain the composite fermion picture which describes the fractional quantum Hall effect as…
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…
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…
Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be…
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,…
Integer and fractional quantum Hall effects were studied with different physics models and explained by different physical mechanisms. In this paper, the common physical mechanism for integer and fractional quantum Hall effects is studied,…
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…
In this contribution, we present an introduction to the physical principles underlying the quantum Hall effect. The field theoretic approach to the integral and fractional effect is sketched, with some emphasis on the mechanism of…
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…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave…
It is shown, that a spectrum generating algebras and wave functions for the integral and fractional quantum Hall effect are related by the non-unitary similarity transformation. This transformation corresponds to the introduction of the…
The quantum Hall effects, discovered about thirty years ago have remained one of the most spectacular discoveries in condensed matter physics in the past century. Those discoveries triggered huge expansion in the field of low-dimensional…
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.
This paper intends to provide a theoretical basis for the unification of the integer and the fractional quantum Hall effects. Guided by concepts and theories of quantum mechanics and with the solution of the Pauli equation in a magnetic…
In certain backgrounds string theory exhibits quantum Hall-like behavior. These backgrounds provide an explicit realization of the effective non-commutative gauge theory description of the fractional quantum Hall effect (FQHE), and of the…
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…
There are compelling reasons to seek a new coherent description of the Quantum Hall Effects (QHE). The theories of the `Integer' (IQHE) and the `Fractional' (FQHE) quantum Hall effects are very different at present, despite their remarkable…
The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall…
The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of…
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…