Conductivity-peak broadening in the quantum Hall regime

We argue that hopping conductivity dominates on both sides of ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$ peaks in low-mobility samples and use a theory of hopping of interacting electrons to estimate a width Δν of the peaks. Explicit expressions for Δν as a function of the temperature T, current J, and frequency ω are found. It is shown that Δν grows with T as (T/${\mathit{T}}_1$ ${)}^{\mathrm{\kappa }}$, where κ 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)∝${\mathit{J}}^{1/2}$ if ${\mathit{T}}_{\mathrm{eff}}$(J)≫T. The broadening of the Ohmic ac-conductivity peaks with frequency ω is found to be determined by the effective temperature ${\mathit{T}}_{\mathrm{eff}}$(ω)∼ħω/${\mathit{k}}_{\mathit{B}}$.