Anomalous Higgs oscillations mediated by Berry curvature and quantum metric

Higgs spectroscopy, the study of Higgs bosons of a superconductor, is an emerging field in studying superconductivity. It is used to probe various superconductor properties. In the conventional theory, the Higgs mode only couples non-linearly to the external optical field via the band curvature and hence vanishes in flat band superconductors such as the twisted bilayer graphene at magic angle. In this work we show that the Berry curvature and the quantum metric of bands play a central role in the Higgs mode generation. They allow detection of Higgs bosons even when the conventional contribution from the band curvature vanishes. Furthermore, we show that the Higgs mode can couple to the external electromagnetic field linearly when mediated by the Berry connection. As a result, we predict the existence of a second harmonic generation, in addition to the well-known third harmonic generation. We apply our theory to the important case of twisted bilayer graphene and demonstrate that it has Higgs modes when superconductivity is realized in the flat band at the magic angle.