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

TL;DR

This paper develops a low-energy theory for interacting quantum wires with Rashba spin-orbit coupling, showing electron-electron interactions modify the RKKY interaction decay and induce anisotropic oscillations.

Contribution

It provides a one-loop renormalization group analysis demonstrating the irrelevance of backscattering and characterizes the modified RKKY interaction in interacting Rashba wires.

Findings

Electron-electron interactions slow the decay of the RKKY interaction.

Rashba spin-orbit coupling causes anisotropic oscillations in the RKKY range function.

Backscattering remains irrelevant, preserving a modified Luttinger liquid description.

Abstract

We present the effective low-energy theory for interacting 1D quantum wires subject to Rashba spin-orbit coupling. Under a one-loop renormalization group scheme including all allowed interaction processes for not too weak Rashba coupling, we show that electron-electron backscattering is an irrelevant perturbation. Therefore no gap arises and electronic transport is described by a modified Luttinger liquid theory. As an application of the theory, we discuss the RKKY interaction between two magnetic impurities. Interactions are shown to induce a slower power-law decay of the RKKY range function than the usual 1D noninteracting $\cos(2k_F x)/|x|$ law. Moreover, in the noninteracting Rashba wire, the spin-orbit coupling causes a twisted (anisotropic) range function with several different spatial oscillation periods. In the interacting case, we show that one special oscillation period leads to the slowest decay, and therefore dominates the RKKY interaction for large separation.