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

Abstract

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 ͑antiresonances͒, 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.

Thermoelectric effects in graphene with local spin-orbit interaction

“…This type of interaction leads to band splittings and enriched spintronic effects [18,19]. In semiconductor quantum wires with parabolic confinement, the presence of localized Rashba interaction has been predicted to yield Fano antiresonances [20][21][22][23][24][25], to help the detection of entangled electrons [26][27][28], and to assist electron-spin resonance manipulation [29][30][31]. The effect of nonhomogeneous Rashba couplings has also been considered in the transport characteristics of two-dimensional systems [32][33][34][35][36].…”

Spin nutation and polarization in ballistic semiconductor nanostructures

“…To study various ballistic spin transport phenomena, wave function approaches [34][35][36][37]46 within the scattering matrix formalism, and Green's function techniques 30,32,33 with discrete lattices have been used in quasi-one-dimensional systems. As another way, in Ref.…”

Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids

“…They consist of one-dimensional (1D) conductors exhibiting spin-filtered transport, for instance, of right moving modes carrying spin up, (R ↑), and left moving modes carrying spin down, (L ↓). Such conductors appear on the edges of two-dimensional (2D) topological insulators (where spin should more correctly be addressed as Kramers partner), 1,2 in nanowires made of tree-dimensional (3D) topological insulators, [3][4][5] in 1D semiconductor wires with strong spin-orbit interaction in an external magnetic field (with approximate spinfiltering), [6][7][8][9][10][11][12][13] or in carbon nanotubes, where the combination of spin-orbit interaction and strong external electric fields can cause helical conduction.…”