A unified transport theory for the integral and fractional quantum hall effects: Phase boundaries, edge currents, and transmission/reflection probabilities

Abstract

We propose a unified transport theory for the fractional (FQHE) and integral quantum Hall effect (IQHE) of the Buttiker-Landauer type in the presence of smooth confinement and impurity potentials, where resistances are expressed in terms of transmission and reflection probabilities of edge channels in the incompressible fluid states. Electron-electron interaction is taken into account in the FQHE by writing down a Laughlin type wave function for a pure phase, and in the compressible fluids at non-special filling factors by a self-consistent screening of the background potential. Our theory is able to explain recent experimental observations.