Geometric Higgs spectroscopy

Higgs spectroscopy is an emerging field in studying superconductivity. It is used to probe superconductor properties such as the pairing symmetry of the Cooper pairs. In the conventional theory, the Higgs mode is generated via a nonlinear coupling with the external electromagnetic field and mediated by the band curvature. This coupling vanishes for flat band superconductors and is expected to be weak for narrow-band superconductors such as in twisted bilayer graphene. We have recently shown that geometric quantities such as the quantum metric and Berry curvature also mediates the coupling of the external field to the Higgs mode. More importantly, this geometric Higgs mode dominates over the conventional one for flat and narrow band superconductors. In this work, we use this result to study the geometric Higgs mode for various pairing symmetries. We consider the Harper-Hubbard model with p wave pairing and the ten-band model of twisted bilayer graphene with s and d+id pairings. We show that Higgs spectroscopy can be a useful experimental tool in probing the pairing symmetries, and thus the microscopic nature of the narrow band superconductors.