Multivalley electron gas in a strong magnetic field

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Abstract
We discuss the nonuniform high-field collective states of a multivalley electron gas. We consider specifically a model where there are two different orientations for the principal axes of the effective-mass tensor in the various valleys, and the magnetic field is applied along a direction that is symmetric with respect to these orientations. The onset of various instabilities is found within the Hartree-Fock approximation for the electron-hole correlations, as a function of the carrier density and magnetic field strength, the effective-mass anisotropy, the electronic g factor, and the number of degenerate valleys. Depending on the parameters, we find that the ground state may contain spin-density waves or valley-density waves—i.e., a state in which there are out-of-phase charge-density waves in various valleys. We discuss how the disorder that is present in most experimentally relevant systems may affect various collective transitions.