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

A theory for the Shubnikov–de Haas oscillations in the diagonal conductivity σ xx of a 2D conductor is developed for the case when electron states within the broadened Landau levels are localized except for a 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 σ xx became sharp and between them σ xx →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, σ xx ∝ exp (−Δ/T), which holds at higher temperatures, crosses over into the variable-range-hopping regime at lower temperatures with σ xx ∝1/T exp (− T 0 /T ) (the prefactor 1/T is absent in the conductance).