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Magnetoresistance measurements and theoretical calculations for two-dimensional electron systems under a perpendicular magnetic field are presented which illuminate transport effects due to a periodic electrostatic potential modulation. We focus on features arising from the resolution of the magnetic miniband structure which are beyond the perturbative regime governed by the dispersion of Landau bands. Our non-perturbative quantum-mechanical calculations reveal that the dispersion of individual minibands is responsible for the complicated behaviour of the magnetoresistance in the regime of intermediate modulation strength. In particular, the interplay between miniband and scattering contributions to the conductivity leads to an almost structureless magnetoresistance in this regime followed by the formation of antidot peaks due to the miniband conductivity.
We study the energy-level statistics for electrons in a lateral two-dimensional superlattice in dependence on the strength of the modulation potential at a given perpendicular magnetic field. The interminiband statistics at some selected point in the magnetic Brillouin zone shows a transition from degenerate Landau levels to universal spectral correlations while the corresponding classical dynamics displays a crossover from regular cyclotron orbits to chaotic motion. In terms of the nearest-neighbor spacing distribution, we observe the occurrence of level repulsion for all nonzero modulation amplitudes, which indicates a discontinuous transition to universal fluctuations for the smallest level spacings when the rotational invariance of the system is broken by a finite superlattice potential. In order to test the universality of the transition on larger scales, we propose a random matrix model with one transition parameter for comparison. Confirmed by two different types of potential shapes, we detect an explicit influence of the potential shape on the level spacing distributions, which hence cannot be described by the one-parameter model. Using the spectral rigidity, however, universal long-range fluctuations in the regime of negligible Landau-level mixing are found, in agreement with our random matrix model.
Magnetotransport in lateral superlattices covers a variety of apparently different physics dependent on the amplitude of the modulation potential relative to the Fermi energy ranging from the weakly modulated 2DEG to the antidot lattice. Here we investigate the transition between weak modulation and antidots within the quantum-mechanical theory by studying (i) the single-particle spectrum with respect to quantum signatures of classical chaos and (ii) the change of characteristic features in the magnetoresistance starting from the Kubo formula.
