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We study the transport properties for a Luttinger-liquid (LL) quantum wire inthe presence of both Rashba spin-orbit coupling (SOC) and a weak externalin-plane magnetic field. The bosonized Hamiltonian of the system with anexternally applied longitudinal electric field is established. And then theequations of motion for the bosonic phase fields are solved in the Fourierspace, with which the both charge and spin conductivities for the system arecalculated analytically based on the linear response theory. Generally, the acconductivity is an oscillation function of the strengths of electron-electroninteraction, Rashba SOC and magnetic field, as well as the driving frequencyand the measurement position in the wire. Through analysis with some examplesit is demonstrated that the modification on the conductivity due toelectron-electron interactions is more remarkable than that due to SOC, whilethe effects of SOC and Zeeman splitting on the conductivity are very similar.The spin-polarized conductivities for the system in the absence of Zeemaneffect or SOC are also discussed, respectively. The ratio of the spin-polarizedconductivities $\sigma_\uparrow/\sigma_\downarrow$ is dependent of theelectron-electron interactions for the system without SOC, while it isindependent of the electron-electron interactions for the system without Zeemansplitting.Comment: 10 pages, 8 figure

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