Interdimensional effects in a three-dimensional electron gas with a Rashba spin-orbit coupling interface

We examine the bound-state and free-state contributions to the density of states in a three-dimensional electron gas with a two-dimensional interface or quantum well with Rashba spin-orbit coupling. The motivation for our research comes from the interest in materials that exhibit Rashba spin splitting of energy bands and the Edelstein and inverse Edelstein effects in quantum wells or interfaces. By modifying the Hamiltonian of three-dimensional electron gas models to include a two-dimensional component with Rashba spin-orbit coupling, we are able to calculate the bound-state and free-state wave functions and corresponding densities of states analytically. In the case of weak asymmetry across the interface, we find that one of the spin-split energy bands has an upper bound where it merges into a three-dimensional energy band. On the other hand, with strong asymmetry across the interface, only one spin-momentum-locked band exists as an interface energy band, which emerges from a three-dimensional energy band.