Effective Hamiltonian for silicene under arbitrary strain from multi-orbital basis

A tight-binding (TB) Hamiltonian is derived for strained silicene from a multi-orbital basis. The derivation is based on the Slater-Koster coupling parameters between different orbitals across the silicene lattice and takes into account arbitrary distortion of the lattice under strain, as well as the first and second-order spin-orbit interactions (SOI). The breaking of the lattice symmetry reveals additional SOI terms which were previously neglected. As an exemplary application, we apply the linearized low-energy TB Hamiltonian to model the current-induced spin accumulation in strained silicene coupled to an in-plane magnetization. The interplay between symmetry-breaking and the additional SOI terms induces an out-of-plane spin accumulation. This spin accumulation remains unbalanced after summing over the Fermi surfaces of the occupied bands and the two valleys, and can thus be utilized for spin torque switching.