Phonon spectra, quantum geometry, and the Goldstone theorem
Abstract
Phonons are essential quasi-particles of all crystals and play a key role in fundamental properties such as thermal transport and superconductivity. In particular, acoustic phonons can be interpreted as Goldstone modes that emerge due to the spontaneous breaking of translational symmetry. In this article, we investigate the quantum geometric contribution to the phonon spectrum in the absence of Holstein phonons. Using graphene as a case study, we decompose the dynamical matrix into distinct terms that exhibit different dependencies on the electron energy and wavefunction. We then examine the role of quantum geometry in shaping the material's phonon spectrum, and we find that removing the nontrivial quantum geometric contribution from the dynamical matrix causes the acoustic phonon modes to behave in a non-analytic fashion.
Cite
@article{arxiv.2502.04221,
title = {Phonon spectra, quantum geometry, and the Goldstone theorem},
author = {Guglielmo Pellitteri and Zenan Dai and Haoyu Hu and Yi Jiang and Guido Menichetti and Andrea Tomadin and B. Andrei Bernevig and Marco Polini},
journal= {arXiv preprint arXiv:2502.04221},
year = {2025}
}
Comments
7 pages, 3 figures + extensive Supplemental Material (23 pages, 2 figures)