Abstract
A study is made of the quantum states and spin polarization of a two-dimensional electron gas with spin-orbit coupling in an external period potential and in magnetic field. The influence of Rashba and Dresselhaus spin-orbit coupling on the band structure, wave functions, and spin-density distribution is studied for a two-dimensional electron gas in the field of a one-dimensional lateral superlattice. The calculations take into account the modulation of the Rashba parameter by the periodic potential of the superlattice. The Harper-Hofstadter problem is solved for a two-dimensional electron gas with spin-orbit coupling in the field of a periodic two-dimensional potential and in a perpendicular magnetic field. The band spectrum, wave functions, and spin-density distribution of the electron gas are found. The dispersion relations in the magnetic subbands, the spin densities, and the mean values of the spins are calculated for different values of the number of magnetic flux quanta through the unit cell of the superlattice, with Rashba spin-orbit coupling and the Zeeman splitting taken into account.
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