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We present a detailed theoretical investigation of persistent spin helices intwo-dimensional electron systems with spin-orbit coupling. For this purpose weconsider a single-particle effective mass Hamiltonian with generalizedlinear-in-k spin-orbit coupling term corresponding to a quantum well grown inan arbitrary crystallographic direction, and derive the general condition forthe formation of the persistent spin helix. This condition applied for theHamiltonians describing quantum wells with different growth directionsindicates the possibility of existence of the persistent spin helix in a wideclass of 2D systems apart from [001] model with equal Rashba and Dresselhausspin-orbit coupling strengths and the [110] Dresselhaus model. In addition, weemploy the translation operator formalism for analytical calculation ofspace-resolved spin density and visualization of the persistent spin helixpatterns.

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