Linear and nonlinear optical responses in Green's function formula

TL;DR

This paper derives formulas for linear and nonlinear optical responses using Green's function methods, connecting them to physical quantities like Berry curvature, and highlights their potential for studying many-body effects.

Contribution

It introduces a Green's function-based approach to calculate high-order nonlinear optical conductivities and links them to key physical quantities.

Findings

Derived optical conductivities of various orders using Green's function

Connected nonlinear responses to Berry curvature and related quantities

Highlighted advantages for many-body effect studies in nonlinear optics

Abstract

Linear and nonlinear optical effect has been widely discussed in large quantity of materials using theoretical or experimental methods. Except linear optical conductivity, higher-order nonlinear responses are not studied fully. Starting from density operator method, we derive optical conductivities of different orders in Green's function formula, and also connect them to novel physical quantities, such as Berry curvature, Berry curvature dipole, third-order nonlinear Hall conductivity and so on. Based on the advantages of Green's function formulas, we believe that these formulas have a lot of benefits for many-body effect study in high-order nonlinear optical responses.