Variable range hopping as the mechanism of the conductivity peak broadening in the quantum Hall regime

We argue that it is the hopping transport that is responsible for broadening of the ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$ peaks. An explicit expression for the width Δν of the peak as a function of the temperature T is found. A close relation between the characteristic temperature in the dependence Δν on T and that in the variable-range-hopping exponent at an integer ν is established. Broadening of the peak with increasing current is also explained. The current J is shown to act like the effective temperature ${\mathit{T}}_{\mathit{e}\mathit{f}\mathit{f}}$∝${\mathit{J}}^{1/2}$ if ${\mathit{T}}_{\mathit{e}\mathit{f}\mathit{f}}$≫T. The anomalous behavior of two peaks which are close to each other (spin split, e.g.) is considered.