Phonon spectra, quantum geometry, and the Goldstone theorem

TL;DR

This paper explores how quantum geometry influences phonon spectra in crystals, specifically in graphene, revealing that removing quantum geometric effects leads to non-analytic behavior of acoustic phonons.

Contribution

It introduces a decomposition of the dynamical matrix to isolate quantum geometric effects on phonons in graphene, highlighting their crucial role in phonon behavior.

Findings

Quantum geometry significantly affects phonon spectra.

Removing quantum geometric contributions causes non-analytic phonon modes.

Study emphasizes the importance of quantum geometry in understanding phonon properties.

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.