Transport properties for a Luttinger liquid wire with Rashba spin-orbit coupling and Zeeman splitting

TL;DR

This paper analytically investigates how Rashba spin-orbit coupling and Zeeman splitting influence the charge and spin transport in a Luttinger-liquid quantum wire, revealing the dominant effects of electron-electron interactions on conductivity modifications.

Contribution

It provides an analytical solution for the transport properties of a Luttinger-liquid wire with SOC and magnetic field, highlighting the interplay between interactions and spin-related effects.

Findings

AC conductivity oscillates with interaction strength, SOC, magnetic field, frequency, and position.

Electron-electron interactions have a more significant impact on conductivity than SOC.

The ratio of spin-polarized conductivities depends on interactions without SOC, but not without Zeeman splitting.

Abstract

We study the transport properties for a Luttinger-liquid (LL) quantum wire in the presence of both Rashba spin-orbit coupling (SOC) and a weak external in-plane magnetic field. The bosonized Hamiltonian of the system with an externally applied longitudinal electric field is established. And then the equations of motion for the bosonic phase fields are solved in the Fourier space, with which the both charge and spin conductivities for the system are calculated analytically based on the linear response theory. Generally, the ac conductivity is an oscillation function of the strengths of electron-electron interaction, Rashba SOC and magnetic field, as well as the driving frequency and the measurement position in the wire. Through analysis with some examples it is demonstrated that the modification on the conductivity due to electron-electron interactions is more remarkable than that due to SOC, while the effects of SOC and Zeeman splitting on the conductivity are very similar. The spin-polarized conductivities for the system in the absence of Zeeman effect or SOC are also discussed, respectively. The ratio of the spin-polarized conductivities $\sigma_\uparrow/\sigma_\downarrow$ is dependent of the electron-electron interactions for the system without SOC, while it is independent of the electron-electron interactions for the system without Zeeman splitting.