Probing time-reversal breaking and quantum geometry in topological twisted superconductors with nonlinear optical response

Nonlinear optical response is a sensitive probe of the geometry of electronic Bloch bands in solids. Here, we present a theory of photocurrents in topological superconductors that shows that the (normal) resonant dc photocurrent, driven by quasiparticles in the superconductor, sensitively depends on the quantum geometry of the charge-neutral excitation spectrum contained within the Bogoliubov de Gennes (BdG) Hamiltonian. For linearly polarized light, the current is generated by the dipole of the quantum metric of the BdG bands, while for circularly polarized light, the current depends on the Berry curvature of BdG bands. Importantly, broken time-reversal symmetry (TRS) is a necessary condition for inducing the photocurrent with linearly polarized light. We successfully apply this formalism to probe the ground state nature of twisted nodal superconductors, finding that the photocurrent strongly depends on the twist angle, and it is maximal at exactly the “magic angle” for these systems.