CONTACTS AND EDGE-STATE EQUILIBRATION IN THE FRACTIONAL QUANTUM HALL-EFFECT

We develop a simple kinetic equation description of edge-state dynamic s in the fractional quantum Hall effect (FQHE), which allows us to exa mine in detail equilibration processes between multiple edge modes. As in the integer quantum Hall effect, intermode equilibration is a prer equisite for quantization of the Hall conductance. Two sources for suc h equilibration are considered: edge-impurity scattering and equilibra tion by the electrical contacts. Several specific models for electrica l contacts are introduced and analyzed. For FQHE states in which edge channels move in both directions; such as nu = 2/3, these models for t he electrical 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 charg e between channels, is shown to restore the four-terminal quantized co nductance. For specific filling factors, notably nu = 4/5 and nu = 4/3 , the equilibrium length due to impurity scattering diverges in the ze ro-temperature limit, which should lead to a breakdown of quantization for small samples at low temperatures. Experimental implications are discussed.