Behavior of Electrons at Soft Edges in the Fractional Quantum Hall and WignerCrystal States

摘要

Over the past year, there has been a great deal of interest in the possibility ofedge channels existing in systems exhibiting the fractional quantum Hall effect (FQHE) 1-51. In this work, we analyze a model of a two-dimensional electron gas in a strong magnetic field whose electrochemical potential falls off slowly on the scale of the magnetic length ( soft edge ). This model is probably appropriate for edges created by gated geometries. It has been shown recently by Beenakker that if one assumes that transport at the edges in this model is ballistic, then one may understand the unusual quantizations seen in the experiments 4,5, and indeed understand transport in the FQHE in terms of sample edges.