Cl. Kane et Mpa. Fisher, CONTACTS AND EDGE-STATE EQUILIBRATION IN THE FRACTIONAL QUANTUM HALL-EFFECT, Physical review. B, Condensed matter, 52(24), 1995, pp. 17393-17405
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.