Contacts and edge-state equilibration in the fractional quantum Hall effect.

Abstract

We develop a simple kinetic equation description of edge-state dynamics in the fractional quantum Hall effect (FQHE), which allows us to examine in detail equilibration processes between multiple edge modes. As in the integer quantum Hall effect, intermode equilibration is a prerequisite for quantization of the Hall conductance. Two sources for such equilibration are considered: edge-impurity scattering and equilibration by the electrical contacts. Several specific models for electrical contacts are introduced and analyzed. For FQHE states in which edge channels move in both directions, such as \ensuremath{\nu}=2/3, these models for the elecrical contacts do not equilibrate the edge modes, resulting in a nonquantized Hall conductance, even in a four-terminal measurement. Inclusion of edge-impurity scattering, which directly transfers charge between channels, is shown to restore the four-terminal quantized conductance. For specific filling factors, notably \ensuremath{\nu}=4/5 and \ensuremath{\nu}=4/3, the equilibration length due to impurity scattering diverges in the zero-temperature limit, which should lead to a breakdown of quantization for small samples at low temperatures. Experimental implications are discussed.