Resonant reflection of interacting electrons from an impurity in a quantum wire: interplay of Zeeman and spin-orbit effects

A single-channel quantum wire with two well-separated Zeeman subbands and in the presence of a weak spin-orbit coupling is considered. An impurity level which is split off the upper subband is degenerate with the continuum of the lower subband. We show that, when the Fermi level lies in the vicinity of the impurity level, the transport is completely blocked. This is the manifestation of the effect of resonant reflection and can be viewed as resonant tunneling between left-moving and right-moving electrons via the impurity level. We incorporate electron-electron interactions and study their effect on the shape of the resonant-reflection profile. This profile becomes a two-peak structure, where one peak is caused by resonant reflection itself, while the origin of the other peak is reflection from the Friedel oscillations of the electron density surrounding the impurity.