Chaos and anomalous diffusion of ballistic electrons in lateral surface superlattices

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Abstract
We study the classical dynamics of a charged particle in a two-dimensional (2D) lattice-periodic potential with a perpendicular magnetic field. Due to chaotic scattering the particle shows diffusion in 1D and 2D, as well as anomalous diffusion associated with 1/f noise. The onset of diffusion is explained by heteroclinic intersections and stochastic layers, and the transition from 1D to 2D diffusion is caused by the destruction of a separating Kolmogorov-Arnold-Moser torus. As a simplification we introduce a discrete-time model based on a separatrix map, which facilitates the analysis of free-path distributions related to the occurrence of anomalous diffusion. These results represent classical approximations for the dynamics of electron wave packets in lateral surface superlattices on semiconductor heterojunctions.