The four-terminal Hall conductance

The four-terminal Hall conductance GH has the same value, because each edge is in local equilibrium. In the presence of disorder this edge channel formulation of the fractional QHE is generalized in an analogous way as in the integer QHE by including localized states in the bulk. In a smoothly varying disorder potential, these localized states take the form of circulating edge channels, as in Figs. 78 and 79. In this way the filling factor of the bulk can locally deviate from νP without a change in the Hall conductance, leading to the formation of a plateau in the magnetic field dependence of GH. In a narrow channel, localized states are not required for a finite plateau width because the edge channels make it possible for the chemical potential to lie in an energy gap for a finite-magnetic-field interval. The Hall conductance then remains quantized at νP (e2/h) as long as μ − V in the bulk lies between du+P /dn and du−P /dn.