Torsion Induced Asymmetric Luttinger Liquids

TL;DR

This paper models a Luttinger liquid with broken symmetries, showing how torsion and magnetic fields induce asymmetric velocities and a spinless effective model, with potential experimental signatures.

Contribution

It generalizes previous minimal models by including spin and all possible interactions, revealing symmetry-breaking effects on Luttinger liquids.

Findings

Broken symmetries lead to asymmetric velocities in the band structure.

Spin degrees of freedom become gapped, resulting in an effective spinless Luttinger liquid.

Spectral function asymmetry can serve as an experimental signature.

Abstract

We consider a general model of a Luttinger liquid with broken parity and time reversal symmetry, but with their composite symmetry intact. Such a scenario can be due to a combination of torsion and a Zeeman field in nanowires, or a result of bringing different helical Luttinger liquids into proximity. The broken symmetries result in a band structure with no axis of symmetry, and therefore with asymmetric velocities between left and right moving contributions. By taking a general spin-full model with all possible scattering and interaction terms in the bosonic model we show that generically the spin degree of freedom becomes gapped out, resulting in an effective spinless Luttinger liquid with asymmetric velocities. Our work generalizes and extends previous studies which focused on a minimal model of a spinless Luttinger liquid. We further demonstrate that a possible experimental signature of the asymmetry of such asymmetric models can be seen in the spectral function.