Phonon spectra, quantum geometry, and the Goldstone theorem
arXiv:2502.04221 · doi:10.1103/jg8x-l6h6
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.
7 pages, 3 figures + extensive Supplemental Material (23 pages, 2 figures)
References in corpus (40)
- Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
- The Raman Fingerprint of Graphene
- Van der Waals heterostructures
- Phonons and related properties of extended systems from density-functional perturbation theory
- Advanced capabilities for materials modelling with Quantum ESPRESSO
- Raman spectroscopy as a versatile tool for studying the properties of graphene
- Berry Phase Effects on Electronic Properties
- Electron-phonon interactions from first principles
- Substrate-induced bandgap in graphene on hexagonal boron nitride
- High-accuracy first-principles determination of the structural, vibrational and thermodynamical properties of diamond, graphite, and derivatives
- Highly confined low-loss plasmons in graphene-boron nitride heterostructures
- Gauge fields in graphene
- Precision and efficiency in solid-state pseudopotential calculations
- Superfluidity in topologically nontrivial flat bands
- Tuning quantum non-local effects in graphene plasmonics
- Phonon Transport in Graphene
- Superfluidity and Quantum Geometry in Twisted Multilayer Systems
- Density functional perturbation theory for gated two-dimensional heterostructures: Theoretical developments and application to flexural phonons in graphene
- The Insulating State of Matter: A Geometrical Theory
- Symmetry-based approach to electron-phonon interactions in graphene
- Solid Inflation
- Direct measurement of the quantum geometric tensor in a two-dimensional continuous medium
- Essay: Where Can Quantum Geometry Lead Us?
- Cavity QED of Strongly Correlated Electron Systems: A No-go Theorem for Photon Condensation
- Experimental measurement of the quantum geometric tensor using coupled qubits in diamond
- Plasmon losses due to electron-phonon scattering: the case of graphene encapsulated in hexagonal Boron Nitride
- Superconductivity, pseudogap, and phase separation in topological flat bands: a quantum Monte Carlo study
- Semi-classical wave packet dynamics in non-uniform electric fields
- Fundamental bound on topological gap
- Superconductivity, charge density wave, and supersolidity in flat bands with tunable quantum metric
- Fluctuations, uncertainty relations, and the geometry of quantum state manifolds
- Phonon dispersion in graphene
- The quantum geometric origin of capacitance in insulators
- Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling
- Electron-Phonon Interactions Using the PAW Method and Wannier Functions
- Extracting the Quantum Geometric Tensor of an Optical Raman Lattice by Bloch State Tomography
- Optical manifestations and bounds of topological Euler class
- Terahertz photocurrent probe of quantum geometry and interactions in magic-angle twisted bilayer graphene
- Instantaneous response and quantum geometry of insulators
- Effective Field Theory for Acoustic and Pseudo-Acoustic Phonons in Solids