Tight-binding model for strongly modulated two-dimensional superlattices

Common models describing magnetotransport properties of periodically modulated two–dimensional systems often either directly start from a semiclassical approach or give results well conceivable within the semiclassical framework. Recently, magnetoresistance oscillations have been found on samples with strong unilateral modulation and short period (d = 15 nm) which cannot be explained on a semiclassical level (magnetic breakdown [1]). We use a simple fully quantum mechanical model which gives us both magnetoresistance data nicely comparing to the experiments and a good intuitive insight into the effects taking place in the system. Beginning with the pioneering work of Weiss et al.[2] much effort was dedicated to magnetotransport properties of periodically modulated two dimensional systems (2DES). A wide palette of structures has been studied both experimentally and theoretically: with periodic modulation in one direction or in both directions, with modulation by either or both electric and magnetic field, with various modulation strengths and concentrations of electrons (see [3] and references therein). Despite the complexity of many such systems, the experimental data can usually be interpreted within a semiclassical (SC) picture, based on constructing classical trajectories of charge carrier and (if necessary) imposing a quantization condition which reflects the formation of Landau levels in the one–electron spectrum. In this paper, we refer to a system where the SC prediction contradicts the experimental finding. It is a strongly unilaterally modulated 2DES with modulation period as short as 15 nm (see Section 2 for criterion of short period); it may thus be conceived as an array of weakly coupled quantum wires, see sketch in Fig. 1. Experimentally, these conditions were achieved in a GaAlAs/GaAs superlattice fabricated by cleaved edge overgrowth technique first reported by Deutschmann et al. [1], see also more detailed description in [4, 5]. § To whom correspondence should be addressed ([email protected]) Tight-binding model for strongly modulated two-dimensional superlattices 2