Optical Manifestations of Quantum Geometry in Electron-Phonon Coupling

TL;DR

This paper uncovers the quantum geometric structure of electron-phonon coupling, revealing how it influences optical responses and can be experimentally detected, extending traditional electronic quantum geometry to include phononic effects.

Contribution

It introduces the concept of quantum geometry in electron-phonon coupling, incorporating phonon effects into the geometric framework of condensed matter systems.

Findings

EPC quantum metric and Berry curvature quantify EPC-induced velocities and polarization.

The EPC shift vector relates to anomalous charge-center shifts.

Connection established between EPC quantum geometry and phonon-mediated optical responses.

Abstract

Quantum geometry is crucial for understanding intricate condensed matter systems, governing transport phenomena and optical responses. However, traditional studies predominantly consider a static crystal lattice, focusing exclusively on the pure-electronic quantum geometry of the Hilbert space parameterized by electronic wave vectors, thereby overlooking the dynamic effects arising from phonons and their coupling with electrons. In this work, we reveal the intrinsic quantum geometry of the electron-phonon coupling (EPC), which resides in the hybrid Hilbert space parameterized by both the electronic wave vectors and phonon displacements. The EPC quantum metric, EPC Berry curvature and EPC shift vector, as central elements, quantify the EPC-induced velocity, polarization, and anomalous charge-center shift, respectively. We further connect this geometry to phonon-mediated optical responses, particularly in-gap resonances, enabling experimental detection and characterization of EPC quantum geometry.