Conductivity-peak broadening in the quantum Hall regime.

Abstract

We argue that hopping conductivity dominates on both sides of ${\mathrm{\ensuremath{\sigma}}}_{\mathit{x}\mathit{x}}$ peaks in low-mobility samples and use a theory of hopping of interacting electrons to estimate a width \ensuremath{\Delta}\ensuremath{\nu} of the peaks. Explicit expressions for \ensuremath{\Delta}\ensuremath{\nu} as a function of the temperature T, current J, and frequency \ensuremath{\omega} are found. It is shown that \ensuremath{\Delta}\ensuremath{\nu} grows with T as (T/${\mathit{T}}_{1}$${)}^{\mathrm{\ensuremath{\kappa}}}$, where \ensuremath{\kappa} is the inverse-localization-length exponent. The current J is shown to affect the peak width like the effective temperature ${\mathit{T}}_{\mathrm{eff}}$(J)\ensuremath{\propto}${\mathit{J}}^{1/2}$ if ${\mathit{T}}_{\mathrm{eff}}$(J)\ensuremath{\gg}T. The broadening of the Ohmic ac-conductivity peaks with frequency \ensuremath{\omega} is found to be determined by the effective temperature ${\mathit{T}}_{\mathrm{eff}}$(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\Elzxh}\ensuremath{\omega}/${\mathit{k}}_{\mathit{B}}$.