Single-particle theory of persistent spin helices in two-dimensional electron gas: the general approach for quantum wells with different growth direction

Abstract: We present a detailed theoretical investigation of persistent spin helices in two-dimensional electron systems with spin-orbit coupling. For this purpose we consider a single-particle effective mass Hamiltonian with generalized linear-in-k spin-orbit coupling term corresponding to a quantum well grown in an arbitrary crystallographic direction, and derive the general condition for the formation of the persistent spin helix. This condition applied for the Hamiltonians describing quantum wells with different growth directions indicates the possibility of existence of the persistent spin helix in a wide class of 2D systems apart from [001] model with equal Rashba and Dresselhaus spin-orbit coupling strengths and the [110] Dresselhaus model. In addition, we employ the translation operator formalism for analytical calculation of space-resolved spin density and visualization of the persistent spin helix patterns.