Transport properties between quantum Hall plateaus

We propose a unified transport theory for the two-dimensional electron gas in the dissipative quantum Hall regime in the presence of a long-range disorder. We find that the evolution of the longitudinal conductivity peaks as a function of the disorder can be described by a single parameter ${\mathrm{\beta }}^{\mathrm{-}1}$ which is determined by the typical gradient of the electron-density fluctuations. In the case of a relatively strong disorder we utilize the edge-states-network model to describe transport in a half-filled Landau level. In the fractional quantum Hall regime we apply the network model to the system of composite fermions, finding the universal values of the resistivity at even-denominator filling fractions. The breakdown of the network model takes place at weak disorder because the edge channels develop into wide compressible strips and at strong disorder because of the destruction of the incompressible strips, isolating the edge channels. We find the limits of the applicability of the network model in terms of β. In the limit of very weak disorder the system is effectively a Fermi liquid of composite fermions. We calculate the conductivity in this regime by considering the motion of noninteracting fermions in a spatially varying magnetic field arising from the density fluctuations. The resistivity is found to scale linearly with the magnetic field with the slope given by ${\mathrm{\beta }}^{\mathrm{-}1}$. Although the presence of nonlocal transport makes measurements of the resistivity difficult, we find qualitative and, in some cases, quantitative agreement with experiment.