Resonant scattering on impurities in the quantum Hall effect

We develop an alternative approach to carrier transport between the edge states via resonant scattering on impurities, which is applicable both for short- and long-range impurities. A detailed analysis of resonant scattering on a single impurity is performed. The results are used for study on the interedge transport by multiple resonant hopping via different impurity sites. It is shown that the total conductance can be found from an effective Schrödinger equation with constant diagonal matrix elements in the Hamiltonian, where the complex nondiagonal matrix elements are the amplitudes of a carrier hopping between different impurities. It is explicitly demonstrated how the complex phase leads to Aharonov-Bohm oscillations in the total conductance. Neglecting the contribution of self-crossing resonant-percolation trajectories, one finds that the interedge carrier transport is similar to propagation in a one-dimensional system with off-diagonal disorder. We demonstrate that each Landau band has an extended state E${\mathrm{¯}}_{\mathit{N}}$, while the other states are localized. The localization length behaves as ${\mathit{L}}_{\mathit{N}}^{\mathrm{-}1}$(E)∼(E-E${\mathrm{¯}}_{\mathit{N}}$${)}^2$.