Monte Carlo Simulation of Lateral Surface Superlattices in a Magnetic Field

Abstract

In a two-dimensional (2D) electron gas in a 2D periodic lattice potential with a magnetic field applied perpendicular to the electron gas plane, the energy spectrum is fractal. If the field is a weak perturbation, the spectrum becomes a periodic function of the field, with a period of one flux quanta per lattice cell (Hofstadter, 1978). A single period of this spectrum takes the form of a “butterfly.” There are well-defined energy gaps, but the energy bands are extremely sensitive, non-analytic functions of the field. In real crystals, the lattice constants are so small that the magnetic fields corresponding to the condition r _c ≃ a are unachievably large — on the order of 10⁸ G. However, this condition can now be achieved in quasi-2D electron gases with artificially engineered lattices. In these lateral surface superlattices (LSSL’s), quasi-2D electron dynamics is realized in FET channels, and superlattice potentials are created by mesh-gate electrodes. With typical superlattice potential periods on the order of 0.1 μm, the required magnetic fields are reduced by a factor of 10⁵ and practical experiments become possible.