Magnetic bloch states and carrier transport in two-dimensional semiconductor lattice structures with spin-orbit interaction

Quantization rules have been obtained for the Hall conductance of fully occupied Landau subbands of the two-dimensional electron gas with the Dresselhaus spin-orbit interaction in a periodic electrostatic field of a superlattice and a transverse magnetic field. The spin-orbit interaction mixes states of different magnetic subbands and changes the quantization rule for the Hall conductance compared to spinless particles. The calculations have been performed for the two-dimensional electrons in the structures with both a weak (AlGaAs/GaAs) and sufficiently strong (GaAs/In_0.23Ga_0.77As) spin-orbit interaction and Zeeman splitting. It has been found that the distribution of the Hall conductance among the magnetic subbands depends on the geometric parameters of the superlattices and promptly changes upon the touching of the adjacent subbands in the spectrum. The quantization rule for the Hall conductance in real semiconductor structures with relatively strong spin-orbit interaction has been shown to differ from that calculated by Thouless et al. [Phys. Rev. Lett. 49, 405 (1982)] for the systems without the spin-orbit interaction and Zeeman effect.