On the effective models of spin-orbit coupling in a two-dimensional electron gas

We use the method of invariants to derive one-and two-band effective Hamiltonians of a noncentrosymmetric two-dimensional electron gas, in the presence of magnetic field. A complete classification of the antisymmetric spin-orbit and magnetic coupling terms near the Gamma point is developed for all two-dimensional crystal symmetries. The effective Hamiltonian depends on the symmetry of the Bloch bands at the Gamma point, which is described by one of the double-valued corepresentations of the two-dimensional magnetic point group. In some bands, the spin- orbit coupling is cubic in the electron momentum and the effective Zeeman interaction is strongly anisotropic. As an example of a two-band effective Hamiltonian, we introduce a simple model of a topological insulator with the intraband and inter band spin-orbit coupling and investigate its bulk and boundary properties. (C) 2021 Elsevier Inc. All rights reserved.