Theory of invariants-based formulation of k•p Hamiltonians with application to strained zinc-blende crystals

Group theoretical methods and kp theory are combined to determine spin-dependent contributions to the effective conduction band Hamiltonian. To obtain the constants in the effective Hamiltonian, in general all invariants of the Hamiltonian have to be determined. Hence, we present a systematic approach to keep track of all possible invariants and apply it to the kp Hamiltonian of crystals with zinc-blende symmetry, in order to find all possible contributions to effective quantities such as effective mass, g-factor and Dresselhaus constant. Additional spin-dependent contributions to the effective Hamiltonian arise in the presence of strain. In particular, with regard to the constants C-3 and D which describe spin-splitting linear in the components of k and epsilon, considering all possible terms allowed by symmetry is crucial.