Spin densities in parabolic quantum wires with Rashba spin-orbit interaction

TL;DR

This paper develops an approximate method to diagonalize the Hamiltonian of a parabolic quantum wire with Rashba spin-orbit interaction, enabling accurate calculation of energy dispersions, wavefunctions, and non-equilibrium spin densities related to the spin Hall effect.

Contribution

It introduces a canonical transformation approach to accurately approximate eigenstates in systems with strong Rashba coupling in quantum wires.

Findings

Accurate energy dispersion relations obtained.

Calculated non-equilibrium spin densities show the spin Hall effect.

Method effective even for strong Rashba interactions.

Abstract

Using canonical transformations we diagonalize approximately the Hamiltonian of a gaussian wire with Rashba spin-orbit interaction. This proceedure allows us to obtain the energy dispersion relations and the wavefunctions with good accuracy, even in systems with relatively strong Rashba coupling. With these eigenstates one can calculate the non-equilibrium spin densities induced by applying bias voltages across the sample. We focus on the $z$-component of the spin density, which is related to the spin Hall effect.