Nonlinear optical responses from topology and quantum geometry

Recently, nonlinear optical phenomena have also been shown to have a deep connection with the quantum geometric and topological properties of band structures in crystalline solids. A remarkable example occurs when chiral semimetals with topologically protected band degeneracies are illuminated with circularly polarized light. Under the right conditions, the part of the generated photocurrent that switches sign upon reversal of the light's polarization, known as the circular photo-galvanic effect, is predicted to depend only on fundamental constants. First, I will present our most recent results on the circular photo-galvanic effect in chiral topological materials. Secondly, the link between nonlinear optics and quantum geometry of the band structure provides a more general guiding principle for the discovery and design of strongly nonlinear optical materials. I will present photo-galvanic effects on correlated systems.