Anomalous Higgs oscillations mediated by Berry curvature and quantum metric

Higgs spectroscopy, the study of bosons a superconductor, is an emerging field in studying superconductivity. Here we show that Berry curvature and quantum metric bands play central role mode generation. They allow detection even when conventional contribution from band vanishes. Furthermore, can couple to external electromagnetic linearly mediated by connection. As result, predict existence second-harmonic generation, addition well-known third-harmonic We elucidate our theory further considering flat superconductor realized Harper-Hubbard model geometric lower bounded Chern number. demonstrate twisted bilayer graphene geometrically induced modes superconductivity realised nearly at magic angle.