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Kondo effect in a quantum wire with spin-orbit coupling

The influence of spin-orbit interactions on the Kondo effect has been under debate recently. Studies conducted recently on a system composed by an Anderson impurity on a 2DEG with Rashba spin-orbit have been shown that it can enhance or suppress the Kondo temperature ($T_{\rm K}$), depending on the relative energy level position of the impurity with respect to the particle-hole symmetric point. Here we investigate a system composed by a single Anderson impurity side-coupled to a quantum wire with spin-orbit coupling (SOC). We derive an effective Hamiltonian in which the Kondo coupling is modified by the SOC. In addition, the Hamiltonian contains two other scattering terms, the so called Dzaloshinskyi-Moriya interaction, know to appear in these systems, and a new one describing processes similar to the Elliott-Yafet scattering mechanisms. By performing a renormalization group analysis on the effective Hamiltonian, we find that the correction on the Kondo coupling due to the SOC favors and enhancement of the Kondo temperature even in the particle-hole symmetric point of the Anderson model, agreeing with the NRG results. Moreover, away from the particle-hole symmetric point, $T_{\rm K}$ always increases with the SOC, accordingly with the previous renormalization group analysis.