Exchange-enhanced spin splitting in a two-dimensional electron system with lateral modulation.

Abstract

The effective spin splitting of the Landau bands produced by an external unidirectional periodic-modulation potential is studied in the thermodynamic Hartree-Fock (HF) approximation. The HF energies, which depend on three quantum numbers, the center coordinates of the wave functions, and the discrete Landau and spin quantum numbers, and also the thermodynamic density of states (TDOS), which is experimentally accessible by magnetocapacitance measurements, are calculated numerically for representative values of wavelength and strength of the modulation potential. For GaAs at low temperatures, the exchange enhancement can yield an effective spin gap comparable with the cyclotron energy. The spin gaps occur in strips, in which the center coordinates correspond to HF energies near the Fermi energy. The width of these strips depends on the steepness of the modulation potential and, in an intricate manner, on temperature and screening effects. Screening effects may lead to broad peaks in the TDOS, while van Hove singularities due to the one-dimensional Landau bands lead to sharp peaks in the TDOS. The conditions, under which such structures should be resolved in experiments, are discussed.