sp-band tight-binding model for the Bychkov-Rashba effect in a two-dimensional electron system including nearest-neighbor contributions from an electric field

We present a tight-binding calculation for a two-dimensional electron gas (2DEG) including the spin-orbit interaction as well as an electric field perpendicular to the system in order to model the Bychkov-Rashba spin splitting. The associated potential gradient introduces two contributions to the tight-binding matrix: an on-site contribution coupling orbitals of the same atom and a nearest-neighbor contribution. At the $\overline{\ensuremath{\Gamma}}$ point the first-order Rashba constant ${\ensuremath{\alpha}}_{R}$ only depends on this nearest-neighbor contribution regardless of the lattices considered (square, hexagonal, honeycomb). Applying the model to graphene reveals that this nearest-neighbor contribution induces a significant increase in the zeroth-order Rashba constant ${\ensuremath{\lambda}}_{R}$ and introduces a spin-splitting component, which varies linearly in momentum.