Landau quantization of two-dimensional heavy holes, energy spectrum of magnetoexcitons, and optical quantum transitions

Abstract

The Landau quantization of the two-dimensional (2D) heavy holes, its influence on the energy spectrum of 2D magnetoexcitons, and their optical orientation are studied. The Hamiltonian of the heavy holes is written in a two-band model taking into account the Rashba spin-orbit coupling (RSOC) with two spin projections, but with nonparabolic dispersion law and third order chirality terms. The most Landau levels, except three with m = 0, 1, 2, are characterized by two quantum numbers m - 3 and m for m > 3 for two spin projections, respectively. The difference between them is determined by the third order chirality. Four lowest Landau levels (LLLs) for heavy holes were combined with two LLLs for conduction electron, which were taken the same as they were deduced by Rashba in his theory of spin-orbit coupling (SOC) based on the initial parabolic dispersion law and first order chirality terms. As a result of these combinations, eight 2D magnetoexciton states were formed. Their energy spectrum and the selection rules for the quantum transitions from the ground state of the crystal to exciton states were determined. On this base, optical orientation effects, such as spin polarization and magnetoexciton alignment, are discussed.