Hofstadter spectra in two-dimensional superlattice potentials with arbitrary modulation strength

The electronic structure of lateral superlattices in the presence of a perpendicular magnetic field has been a subject of great interest in the past few years. The evolution of these electronic spectra has been mostly analyzed using weak or strong potential modulation limits. In this work we develop a model, within the tight-binding approximation, that handles potential modulations of arbitrary strength. We show the evolution of Hofstadter-like spectra from weak potential modulation up to the strong modulation case, where the lower bands are characteristic of weakly coupled quantum dots. The crossover from weak to strong potential modulation is clarified.