Topological nature of nonlinear optical effects in solids

TL;DR

This paper reveals that diverse nonlinear optical effects in solids can be understood through topological properties involving Berry connections and curvature, offering a unified theoretical framework.

Contribution

It introduces a topological approach using Floquet formalism to describe nonlinear optical effects in terms of Berry phase quantities.

Findings

Nonlinear effects like shift current and photovoltaic Hall response are governed by topological quantities.

Vector fields from Berry connections dictate the nonlinear responses.

The topological perspective enables new design strategies for nonlinear optical materials.

Abstract

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by the strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by the nonlinear susceptibilities $\chi$'s, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under a electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. Here, we theoretically show by using the Floquet formalism that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. It is found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a new route to design the nonlinear optical materials.