Composite Fermions, Edge Currents and the Fractional Quantum Hall Effect
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.
Keywords
Cite
@article{arxiv.cond-mat/9502058,
title = {Composite Fermions, Edge Currents and the Fractional Quantum Hall Effect},
author = {George Kirczenow and Brad L. Johnson},
journal= {arXiv preprint arXiv:cond-mat/9502058},
year = {2009}
}
Comments
19 pages + 6 figures. Self-unpacking uuencoded postscript. To appear in Physical Review B. Revised version has more details in the Appendix and a discussion of one more experiment in Section 6