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

We present the effective low-energy theory for interacting one-dimensional (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 Ruderman-Kittel-Kasuya-Yosida (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)/parallel to x parallel to 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 Ruderman-Kittel-Kasuya-Yosida interaction for large separation.