Shift-current response as a probe of quantum geometry and electron-electron interactions in twisted bilayer graphene

Abstract

Moir\'e materials, and in particular twisted bilayer graphene (TBG), exhibit a range of fascinating phenomena that emerge from the interplay of band topology and interactions. We show that the nonlinear second-order photoresponse is an appealing probe of this rich interplay. A dominant part of the photoresponse is the shift current, which is determined by the geometry of the electronic wave functions and carrier properties and thus becomes strongly modified by electron-electron interactions. We analyze its dependence on the twist angle and doping and investigate the role of interactions. In the absence of interactions, the response of the system is dictated by two energy scales: (i) the mean energy of direct transitions between the hole and electron flat bands and (ii) the gap between flat and dispersive bands. Including electron-electron interactions both enhances the response at the noninteracting characteristic frequencies and produces new resonances. We attribute these changes to the filling-dependent band renormalization in TBG. Our results highlight the connection between nontrivial geometric properties of TBG and its optical response, as well as demonstrate how optical probes can access the role of interactions in moir\'e materials.