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  • Letter
  • Open Access

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

D. V. Efremov1, Weyner Ccuiro2,3, Luis E. F. Foa Torres4, and M. N. Kiselev3

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Phys. Rev. Research 7, L022016 – Published 14 April, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022016

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. Strikingly, 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 nanomechanical back action as a sensitive tool for detecting this transition, with implications for sliding Luttinger liquids and dimensional crossover studies.

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Phys. Rev. Research 7, L022016– Published 14 April, 2025
  • Received 23 July 2024
  • Accepted 25 March 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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