Composite Fermions, Edge Currents and the Fractional Quantum Hall Effect

TL;DR

This paper develops a comprehensive theory of composite fermion edge states in quantum Hall systems, explaining experimental observations and revealing new types of edge states with distinct transport properties.

Contribution

It introduces a novel classification of composite fermion edge states, including three types with unique properties, expanding understanding beyond previous theories.

Findings

Edge state effective potentials differ from electrons

Three types of composite fermion edge states identified

Theory matches observed quantized Hall conductances

Abstract

We present a theory of composite fermion edge states and their transport properties in the fractional and integer quantum Hall regimes. We show that the effective electro-chemical potentials of composite fermions at the edges of a Hall bar differ, in general, from those of electrons. An expression for the difference is given. Composite fermion edge states of three different types are identified. Two of the three types have no analog in previous theories of the integer or fractional quantum Hall effect. The third type includes the usual integer edge states. The direction of propagation of the edge states agrees with experiment. The present theory yields the observed quantized Hall conductances at Landau level filling fractions p/(mp+-1), for m=0,2,4, p= 1,2,3,... It explains the results of experiments that involve conduction across smooth potential barriers and through adiabatic constrictions, and of experiments that involve selective population and detection of fractional edge channels. The relationship between the present work and Hartree theories of composite fermion edge structure is discussed.