Influence of Rashba spin-orbit coupling on the 0-$\pi$ transition and Kondo temperature in 1D superconductors

TL;DR

This study investigates how Rashba spin-orbit coupling influences the 0-$\

Contribution

It demonstrates that Rashba coupling alters the critical points of the 0-$\pi$ transition and reduces the Kondo temperature, using DMRG and benchmarking with NRG results.

Findings

Rashba coupling shifts the 0-$\pi$ transition to higher values.

Rashba coupling lowers the Kondo temperature.

DMRG results agree well with NRG benchmarks.

Abstract

Using the framework of the density-matrix renormalization group (DMRG), we study a quantum dot coupled to a superconducting nanowire with strong Rashba spin-orbit coupling. Regarding the singlet-to-doublet "0-$\pi$" transition that takes place when the Kondo effect is overcome by the superconducting gap, we show that the Rashba coupling modifies the critical values at which the transition occurs, favouring the doublet phase. In addition, using a generalized Haldane's formula for the Kondo temperature $T_K$, we show that it is lowered by the Rashba coupling. We benchmark our DMRG results comparing them with previous numerical renormalization group (NRG) results. The excellent agreement obtained opens the possibility of studying chains or clusters of impurities coupled to superconductors by the means of DMRG.