General description of the spin-orbit coupling in quasi-two-dimensional structures

A general description of electron states in quasi-two-dimensional structures, such as semiconducting films or heterostructures, with account of the spin-orbit coupling is developed in the nonrelativistic approximation. The method is based on the generalized spin invariant for two-dimensional systems. It is shown that the corresponding Hamiltonian in the nonrelativistic approximation can be represented as the sum of the Hamiltonians of the quantum well and of the periodic two-dimensional crystal potential. The states of an isolated level in the discrete spectrum, corresponding to two-dimensional electrons bound by the layer of the quantum well, are calculated in the general form in the assumption that the given level is energetically distant from other levels. The dispersion law in the Brillouin zone in the tight binding approximation is calculated in the explicit form for a square two-dimensional lattice with one ion in an elementary cell using strongly localized Wannier functions.