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

TL;DR

This paper develops an analytical theory for the conductivity oscillations in 2D conductors with localized states, revealing how these oscillations evolve with magnetic field and temperature, including thermal activation and variable-range hopping behaviors.

Contribution

It introduces a new analytical model accounting for localized states in Landau levels, explaining conductivity oscillations and temperature-dependent regimes in 2D conductors.

Findings

Oscillations in conductivity are described by the theory, showing sharp peaks at high magnetic fields.

Temperature affects the peaks, transitioning from thermal activation to variable-range hopping regimes.

Between peaks, conductivity approaches zero, indicating localization effects.

Abstract

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