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 σ ↑ /σ ↓ 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.

Symmetry-protected spin gaps in quantum wires

“…This behaviour arises instead from the spin texture in the cross-section of the wire which gives rise to phenomena otherwise expected in 1D systems with an attractive interaction. We may contrast the present results with previous studies of interactions in spin-orbit coupled systems in which inversion symmetry is lifted and such features are absent [15][16][17]20 . This work shows that extremely similar physical setups in which the appropriate symmetries are restored will yield the realization of a peculiar strongly correlated phase with remarkable observable features.…”

Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction

“…To overcome this limitation we use the Luttinger liquid (LL) theory. 12 Much attention was given recently to the connection between LL and SOI physics, [13][14][15][16][17][18][19][20][21][22][23][24][25][26] yet the addressed regimes are far from the regime considered in this work, and the resulting physics is different. The LL theory is exact for a linear electron dispersion, and band curvature can lead to modified physics.…”

Low-energy theory and RKKY interaction for interacting quantum wires with Rashba spin-orbit coupling

“…We mention in passing that in the presence of a magnetic field (which we do not consider), a spin gap can be present because of spin-nonconserving e-e "Cooper" scattering processes; 39,40 the effects of e-e forward scattering in Rashba wires with magnetic field were studied as well. 41,42,43,44 Below, we also provide estimates for the renormalized couplings entering the modified LL theory, see Eq. ( 26) below.…”