Breaking of Lorentz invariance caused by the interplay between spin-orbit interaction and transverse phonon modes in quantum wires

TL;DR

This paper demonstrates how the interplay between spin-orbit interaction and transverse phonons in quantum wires leads to Lorentz invariance breaking, especially at a phase transition, with potential applications in nano-mechanical sensing.

Contribution

It introduces a theoretical framework showing Lorentz invariance breaking due to spin-orbit and phonon interactions, highlighting a quantum phase transition with unique phonon modes.

Findings

Identification of a gapped phonon mode at the transition

Discovery of a quadratic dispersion gapless mode

Proposal of nano-mechanical back-action as a detection tool

Abstract

We investigate Lorentz invariance breaking in quantum wires due to Rashba spin-orbit interaction and transverse phonons. Using bosonization, we derive an effective action coupling electronic and mechanical degrees of freedom. Stikingly, at a quantum phase transition between straight and bent wire states, we find a gapped phonon mode and a gapless mode with quadratic dispersion, signaling the breaking of Lorentz invariance. We explore stability conditions for general potentials and propose nano-mechanical back-action as a sensitive tool for detecting this transition, with implications for Sliding Luttinger Liquids and dimensional crossover studies.