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

Abstract

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 ( sin γ 1 e r + cos γ 1 e z ) and E D = E D ( sin γ 2 e r + cos γ 2 e 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 γ 1 , γ 2 . 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 γ 1 or γ 2 . 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 B ⩽ 1 T the influence of the Zeeman term on the transmission, assessed by perturbation theory, is negligible.