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

10 pages, 8 figures

References in corpus (5)

• Transport properties of single channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise
• Competing effects of interactions and spin-orbit coupling in a quantum wire
• Coulomb corrections to the extrinsic spin-Hall effect of a two-dimensional electron gas
• Influence of the contacts on the conductance of interacting quantum wires
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Cited by in corpus (9)

• Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction
• Low-energy theory and RKKY interaction for interacting quantum wires with Rashba spin-orbit coupling
• Modulated Rashba interaction in a quantum wire: Spin and charge dynamics
• Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids
• High-temperature Aharonov-Bohm-Casher interferometer
• Transport through a band insulator with Rashba spin-orbit coupling: metal-insulator transition and spin-filtering effects
• Half-metal phases in a quantum wire with modulated spin-orbit interaction
• Electron-electron interactions in partially mixed helical states
• Symmetry-protected spin gaps in quantum wires