Tunable Van Hove singularities and the magnetization in a two-dimensional electron gas with the spin-orbit interaction in a parallel magnetic field

The problem of finding the single-particle density of states of a two-dimensional electron gas with the spin-orbit interaction in a parallel magnetic field has been solved. It has been shown that, with increasing field, the square-root singularity of the density of states $(N(E)\sim1/\sqrt{E+1})$ existing at the minimum energy in zero magnetic field becomes logarithmic (the Van Hove singularity) and is displaced inside the spectrum, and the minimum energy of the spectrum decreases. The presence of two types of spin-orbit interaction (Rashba and Dresselhaus) is responsible for two peaks of the density of states and for an additional step in the density of states at certain directions of the magnetic field. The energy position of these features can be determined from the magnetization of the electron gas. This makes it possible to find the Rashba and Dresselhaus coupling constants.