Rashba spin splitting in quantum nanowires in the presence of hydrogenic donor impurity

The electronic subband states in the presence of hydrogenic donor impurity in quantum nanowires at the interface of semiconductor heterostructures devoid of structural inversion symmetry, are modeled and described in terms of a quasi-one-dimensional hydrogen atom with Rashba spin-orbit coupling. The energy levels and the spin-dependent subband states of the corresponding one-electron Schrodinger equation, are obtained using a two-step analytic solution as a function of the width L of the nanowire and the strength of the Rashba spin-orbit coupling α. The results thus obtained are checked against purely perturbative calculations in the limit of small spin-orbit coupling. In particular, it is found that the level splitting in a suitable range of the control parameters, L and α, results in spin-dependent electronic states of negative energy (bound states) as well as positive energy (scattering states). This novel result is of considerable interest for the generation of spin currents in the presence of hydrogenic donor impurity, as electrons in the scattering states can contribute to a spin current while those in the bound states tend to remain bound to the hydrogenic impurity.