Spin–Orbit Interaction in the Tight-Binding Model —Toward the Comprehension of the Rashba Effect at Surfaces—

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The linear combination of atomic orbitals (LCAO) tight-binding approach is adopted to obtain spin–orbit interaction at surfaces leading to the Rashba effect. Starting from the Dirac equation, the spin–orbit interaction is given by the nonrelativistic limit. All terms, i.e., intra-atomic L · S, and spin-flipping transfer matrix elements, are obtained. The tight-binding Hamiltonian is diagonalized resulting in the spin-splitting energy bands for a one-dimensional atomic chain and a two-dimensional triangular atomic sheet. The spin textures induced by the Rashba effect are also revealed.