Transport via classical percolation at quantum Hall plateau transitions
Résumé
We consider transport properties of disordered two-dimensional electron gases under high perpendicular magnetic field, focusing in particular on the peak longitudinal conductivity $\sigma_{xx}^\mathrm{peak}$ at the quantum Hall plateau transition. We use a local conductivity model, valid at temperatures high enough such that quantum tunneling is suppressed, taking into account the random drift motion of the electrons in the disordered potential landscape and inelastic processes provided by electron-phonon scattering. A diagrammatic solution of this problem is proposed, which leads to a rich interplay of conduction mechanisms, where classical percolation effects play a prominent role. The scaling function for $\sigma_{xx}^\mathrm{peak}$ is derived in the high temperature limit, which can be used to extract universal critical exponents of classical percolation from experimental data.