Effects of a single impurity in a Luttinger liquid with spin-orbit coupling

TL;DR

This paper investigates how a single impurity affects a Luttinger liquid with spin-orbit coupling, revealing modifications to the phase behavior due to the interplay of impurity scattering and spin-charge coupling.

Contribution

It extends the phase diagram analysis of Luttinger liquids by including spin-orbit coupling effects on impurity renormalization.

Findings

Spin-orbit coupling destroys spin-charge separation in the TLL.

Impurity renormalization is significantly affected by spin-orbit interactions.

The phase diagram in $K_s$ - $K_c$ space is extended to include these effects.

Abstract

In quasi-1D conducting nanowires spin-orbit coupling destructs spin-charge separation, intrinsic to Tomonaga-Luttinger liquid (TLL). We study renormalization of a single scattering impurity in a such liquid. Performing bosonization of low-energy excitations and exploiting perturbative renormalization analysis we extend the phase portrait in $K_s$ - $K_c$ space, obtained previously for TLL with decoupled spin-charge channels.