Integer Spin Hall Effect in Ballistic Quantum Wires

TL;DR

This paper explores the ballistic transport of electrons in a quantum wire with spin-orbit coupling, revealing a spin-dependent Hall effect and conditions for quantized spin Hall conductance.

Contribution

It demonstrates how electric confinement induces non-commutative effects leading to spin-dependent edge currents and quantized spin Hall conductance in ballistic quantum wires.

Findings

Edge localization of spin currents due to non-commutative effects

Quantized spin Hall conductance achievable in ballistic regime

Coupling between spin magnetic moment and orbital current

Abstract

We investigate the ballistic electron transport in a two dimensional Quantum Wire under the action of an electric field ($E_y$). We demonstrate how the presence of a Spin Orbit coupling, due to the uniform electric confinement field gives a non-commutative effect as in the presence of a transverse magnetic field. We discuss how the non commutation implies an edge localization of the currents depending on the electron spins also giving a semi-classical spin dependent Hall current. We also discuss how it is possible obtain a quantized Spin Hall conductance in the ballistic transport regime by developing the Landauer formalism and show the coupling between the spin magnetic momentum and the orbital one due to the presence of a circulating current.