Spin and charge transport in U-shaped one-dimensional channels with spin-orbit couplings

TL;DR

This paper derives a Hamiltonian for electrons in curved 1D channels with spin-orbit coupling, applies it to a U-shaped channel, and explores charge and spin transport properties using the Landauer-Keldysh formalism, revealing new modulation effects.

Contribution

It introduces a general Hamiltonian for curved 1D channels with SOC, applies a tight-binding model, and analyzes transport regimes and properties with a focus on geometric potential effects.

Findings

Charge density modulation from Rashba and Dresselhaus SOCs

Validation of eigenstates for Rashba and Dresselhaus rings

Transport behavior varies between adiabatic and nonadiabatic regimes

Abstract

A general form of the Hamiltonian for electrons confined to a curved one-dimensional (1D) channel with spin-orbit coupling (SOC) linear in momentum is rederived and is applied to a U-shaped channel. Discretizing the derived continuous 1D Hamiltonian to a tight-binding version, the Landauer-Keldysh formalism (LKF) for nonequilibrium transport can be applied. Spin transport through the U-channel based on the LKF is compared with previous quantum mechanical approaches. The role of a curvature-induced geometric potential which was previously neglected in the literature of the ring issue is also revisited. Transport regimes between nonadiabatic, corresponding to weak SOC or sharp turn, and adiabatic, corresponding to strong SOC or smooth turn, is discussed. Based on the LKF, interesting charge and spin transport properties are further revealed. For the charge transport, the interplay between the Rashba and the linear Dresselhaus (001) SOCs leads to an additional modulation to the local charge density in the half-ring part of the U-channel, which is shown to originate from the angle-dependent spin-orbit potential. For the spin transport, theoretically predicted eigenstates of the Rashba rings, Dresselhaus rings, and the persistent spin-helix state are numerically tested by the present quantum transport calculation.