Magnetic Quantum Oscillations of the Conductivity in Two-dimensional Conductors with Localization

Abstract

An analytic theory is developed for the diagonal conductivity $σ_{xx}$ of a 2D conductor which takes account of the localized states in the broaden Landau levels. In the low-field region $σ_{xx}$ display the Shubnikov-de Haas oscillations which in the limit $Ωτ\gg 1$ transforms into the sharp peaks ($Ω$ is the cyclotron frequency, $τ$ is the electron scattering time). Between the peaks $σ_{xx}\to 0$. With the decrease of temperature, $T$, the peaks in $σ_{xx}$ display first a thermal activation behavior $σ_{xx}\propto \exp(-Δ/T)$, which then crosses over into the variable-range-hopping regime at lower temperatures with $σ_{xx}\propto 1/T \exp(-\sqrt{T_{0}/T})$ (the prefactor 1/T is absent in the conductance).