Spin-dependent magnetotransport through one or more rings in the presence of the Rashba and Dresselhaus terms of the spin–orbit interaction

Magnetotransport through one or several quasi-one-dimensional rings, in the presence of the Rashba (RSOI) and Dresselhaus (DSOI) terms of the spin–orbit interaction (SOI) and of a magnetic field B, is investigated. The RSOI field and an effective DSOI field are taken as E_R=E_R(sinγ₁e_r+cosγ₁e_z) and E_D=E_D(sinγ₂e_r+cosγ₂e_z), their strengths are denoted by α and β, respectively. The exact one-electron eigenvalues and eigenfunctions are obtained and used to evaluate the transmission as a function of α, β, and of the angles γ₁,γ₂. Because the RSOI term couples the electronic orbit (along the θ direction) with the Pauli matrices σ_z and σ_r while the DSOI term couples it with σ_θ, they affect the electronic spin transport through a ring in distinctly different ways. The resulting transmission shows a considerable structure as a function of the angles γ₁ or γ₂. The same holds for the transmission, versus α or β, with the SOI present only in one arm of the ring and for that through two rings with the same or different radii. Various results of the literature, valid for β=0, are readily recovered. For weak magnetic fields the influence of the Zeeman term on the transmission, assessed by perturbation theory, is negligible.