Shubnikov—de Haas oscillations, peaks and different temperature regimes of the diagonal conductivity in the integer quantum Hall conductor

Abstract

A theory for the Shubnikov—de Haas oscillations in the diagonal conductivity σxx of a 2D conductor is developed for the case when electron states within the broaden Landau levels are localized except the narrow stripe in the center. The standard Shubnikov—de Haas oscillations take place only in the low-field region which at higher magnetic fields crosses over into peaks. In the limit Ωτ >> 1 peaks in the σxx became sharp and between them σxx → 0 (Ω is the cyclotron frequency, τ is the electron scattering time). The conductivity peaks display different temperature behavior with the decrease of temperature, T: a thermal activation regime, σxx exp(-Δ/T), which holds at higher temperatures, crosses over into the variable-range-hopping regime at lower temperatures with σxx 1/T exp(-√(Т₀/Т) (the prefactor 1/T is absent in the conductance).