Theoretical study of the cubic Rashba effect at theSrTiO3(001) surfaces

Abstract

The origin of Rashba spin splitting in the two-dimensional electron gas at the (001) surface of ${\mathrm{SrTiO}}_{3}$ is studied using first-principles calculations and tight-binding model. Calculations of oxygen vacancies under virtual crystal approximation reveal a two-dimensional electron-gas subband structure similar to polar materials, consistent with observations on ${\mathrm{SrTiO}}_{3}$. Our studies also confirm that $k$ dependence of the spin splitting is predominantly cubic in the surface $\mathrm{Ti}\ensuremath{-}{t}_{2g}$ states, even though structural relaxations diminish the effect in ${d}_{xy}$ bands. A tight-binding model, explicitly including $\mathrm{Ti}\ensuremath{-}d$ and $\mathrm{O}\ensuremath{-}p$ states as well as next-nearest-neighbor interactions, is derived to understand the first-principles results. Effective Rashba Hamiltonians for the surface bands are derived using quasidegenerate perturbation theory and scenarios in which linear $k$ contribution may be suppressed are discussed. However, the cubic terms in the Hamiltonian are found to be different from the model derived using $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ theory, leading to different pseudospin symmetry in the Brillouin zone.