Quantum Geometric Injection and Shift Optical Forces Drive Coherent Phonons

Abstract

We develop a gauge-invariant quantum-geometric theory of light-induced Raman forces driving coherent lattice dynamics in solids. We show that the resonant interband response separates into injection and shift forces, providing the lattice analogue of injection and shift photocurrents. Crucially, the electronic quantum metric and Berry curvature directly govern these forces, weighted by distinct electron--phonon quantities. The injection force is controlled by the quantum geometric tensor and differences between band-diagonal electron--phonon couplings, producing the resonant displacive response. The shift force is a resonant impulsive response governed by quantum geometry and a phononic shift vector arising from interband electron--phonon coherence. We derive polarization selection rules, symmetry constraints, and temporal signatures. Applied to interlayer shear phonons in a bilayer Haldane model, the theory predicts tunability with optical frequency, topology, electronic temperature, and current-induced symmetry breaking. These results establish a quantum-geometric framework for coherent lattice dynamics and identify coherent phonons as experimentally accessible signatures of electronic quantum geometry in quantum materials.

arXiv commentExpanded the analysis and scope of our previous results (12+21 pages, 5+3 figures)