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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 [1]. Next, I show that the topological formula well explains giant SHG responses in Weyl semimetal that were observed in TaAs [2]. 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 [3].

[1] T. Morimoto, and N. Nagaosa, Sci. Adv. 2, e1501524 (2016).
[2] Liang Wu, et. al., Nat. Phys. 13, 350 (2017).
[3] F. de Juan, A. G. Grushin, T. Morimoto, and J. E. Moore, Nat.
Commun. 8, 15995 (2017).

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