Spin edge states in two-dimensional electron systems in the presence of Zeeman effect

We study the spin edge states, induced by the combined effect of Bychkov-Rashba spinorbit and Zeeman interactions or of Dresselhaus spin-orbit and Zeeman interactions in a twodimensional electron system, exposed to a perpendicular quantizing magnetic field and restricted by a hard-wall confining potential. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum versus the momentum and the magnetic field. We calculate the average spin components and the average transverse position of electron. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. Depending on the type of spin-orbit coupling and the principal quantum number, the Zeeman term in the combination with spin-orbit interaction increases or decreases essentially the splitting of bulk Landau levels while it has a weak influence on the spin edge states.