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 wavevector 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 (D_{2d},C_{4v},C_{2v},C_{3v} 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 (T_d) in the anion/cation and effective bond orbital model (EBOM) basis sets with full spin-orbit effects.
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