Interaction-driven dimensional crossover for a superlattice in a strong magnetic field: Hartree-Fock theory

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Abstract
We study, within the Hartree-Fock approximation, uniform and layered electronic systems in a magnetic field which is sufficiently strong that only the lowest Landau level is occupied. The formulation is based on an expression for the density matrix which allows exchange to be treated exactly. The crossover from the three-dimensional limit to the two-dimensional limit as the barriers between layers are strengthened is studied. We find that, for the layered systems, interactions favor a state with filled subbands and hence drive a transition from three-dimensional to two-dimensional behavior as the electron density is increased.