Strongly modulated transmission of a spin-split quantum wire with local Rashba interaction

We investigate the transport properties of ballistic quantum wires in the presence of Zeeman spin splittings and a spatially inhomogeneous Rashba interaction. The Zeeman interaction is extended along the wire and produces gaps in the energy spectrum, which allow electron propagation only for spinors lying along a certain direction. For spins in the opposite direction, the waves are evanescent far away from the Rashba region, which plays the role of the scattering center. The most interesting case occurs when the magnetic field is perpendicular to the Rashba field. Then, the spins of the asymptotic wave functions are not eigenfunctions of the Rashba Hamiltonian, and the resulting coupling between spins in the Rashba region gives rise to sudden changes of the transmission probability when the Fermi energy is swept along the gap. After briefly examining the energy spectrum and eigenfunctions of a wire with extended Rashba coupling, we analyze the transmission through a region of localized Rashba interaction, in which a double interface separates a region of constant Rashba interaction from wire leads free from spin-orbit coupling. For energies slightly above the propagation threshold, we find the ubiquitous occurrence of transmission zeros antiresonances , which are analyzed by matching methods in the one-dimensional limit. We find that a minimal tight-binding model yields analytical transmission line shapes of Fano antiresonance type. The general angular dependence of the external magnetic field is treated within projected Schrödinger equations with the nondiagonal Hamiltonian matrix elements mixing different wave function components. Finally, we consider a realistic quantum wire where the energy subbands are coupled via the Rashba intersubband coupling term and discuss its effect on the transmission zeros. We find that the antiresonances are robust against intersubband mixing, magnetic field changes, and smooth variations of the wire interfaces, which paves the way for possible applications of spin-split Rashba wires as spintronic current modulators.