Phonon spectra, quantum geometry, and the Goldstone theorem

Phonons are essential quasiparticles of all crystals and play a key role in fundamental properties such as thermal transport and superconductivity. 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 wave function. We then examine the role of quantum geometry in shaping the phonon spectrum of the material, and we find that removing the nontrivial quantum geometric contribution from the dynamical matrix causes the acoustic phonon modes to behave in a nonanalytic fashion.

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Publication Details

Journal
Physical review. B./Physical review. B
Published
2025-11-21
DOI
https://doi.org/10.1103/jg8x-l6h6
Primary Topic
Thermal properties of materials
Type
article
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article

Phonon spectra, quantum geometry, and the Goldstone theorem

Marco Polini, Haoyu Hu, Bogdan Andrei Bernevig, Andrea Tomadin et al.
Physical review. B./Physical review. B
Thermal properties of materials
article

Phonon spectra, quantum geometry, and the Goldstone theorem

Marco Polini, Haoyu Hu, Bogdan Andrei Bernevig, Andrea Tomadin, Guido Menichetti, Y. Jiang, Z. Dai, Guglielmo Pellitteri
article en

Abstract

Phonons are essential quasiparticles of all crystals and play a key role in fundamental properties such as thermal transport and superconductivity. 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 wave function. We then examine the role of quantum geometry in shaping the phonon spectrum of the material, and we find that removing the nontrivial quantum geometric contribution from the dynamical matrix causes the acoustic phonon modes to behave in a nonanalytic fashion.

Physical review. B./Physical review. BVol. 112(24)
University of Pisa (IT), Ikerbasque (ES), Scuola Normale Superiore (IT), Institute of Photonic Sciences (ES), Shanghai Jiao Tong University (CN), Princeton University (US), Italian Institute of Technology (IT), Shanghai Institute for Science of Science (CN), Barcelona Institute of Science and Technology (ES), Institute of Science and Technology, Donostia International Physics Center (ES)
Openalex Percentile: Top 67%
Thermal properties of materials
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Phonon spectra, quantum geometry, and the Goldstone theorem — Marco Polini, Haoyu Hu, et al. · Physical review. B./Physical review. B (2025) | TGRS Research Map | TGRS