Higher-order contributions to Rashba and Dresselhaus effects

We have developed a method to systematically compute the form of Rashba- and Dresselhaus-like contributions to the spin Hamiltonian of heterostructures to an arbitrary order in the in-plane wave vector k_. This is achieved by using the double-group representations to construct general symmetry-allowed Hamiltonians with full spin-orbit effects within the tight-binding formalism. We have computed full-zone spin Hamiltonians for $[001]$-, $[110]$-, and $[111]$-grown zinc-blende heterostructures (D2d,C₄ᵥ,C₂ᵥ,C₃ᵥ point-group symmetries), which are commonly used in spintronics. After an expansion of the Hamiltonian up to third order in k_, we are able to obtain additional terms not found previously. The present method also provides the matrix elements for bulk zinc blendes (Td) in the anion--cation and effective bond orbital model (EBOM) basis sets with full spin-orbit effects.