Topological aspects of nonlinear optical effects

The responses of materials to high intensity light, i.e., nonlinear optical responses, constitute a vast field of physics and engineering. While topology has been playing a central role in recent studies of condensed matters, topological aspects of nonlinear optical effects have not been fully explored so far. In this talk, I will show a few examples of nonlinear optical effects that have topological origins. First, I discuss that the second-order nonlinear optical effects including the shift-current and second harmonic generation (SHG) are described by topological quantities, the Berry connection of Bloch wave functions. Next, I show that the topological formula well explains giant SHG responses in Weyl semimetal that were observed in TaAs. Finally, I discuss that another second-order nonlinear effect, circular photogalvanic effect (CPGE), is governed by Berry curvature and measuring CPGE in Weyl semimetals allows an access to monopole physics of Weyl fermions.