Topological aspects of nonlinear excitonic processes in noncentrosymmetric crystals

TL;DR

This paper explores the topological properties of nonlinear excitonic processes in noncentrosymmetric crystals, deriving formulas for shift current and second harmonic generation that reveal their dependence on Berry connections and exciton resonance effects.

Contribution

It introduces a theoretical framework combining Floquet and Keldysh formalisms to analyze topological aspects of excitonic nonlinear optical responses.

Findings

Steady dc shift current can be generated by exciton creation without dissociation.

Second harmonic generation is significantly enhanced at exciton resonance.

The formulas connect excitonic processes to Berry connections, highlighting topological effects.

Abstract

We study excitonic processes second order in the electric fields in noncentrosymmetric crystals. We derive formulas for shift current and second harmonic generation produced by exciton creation, by using the Floquet formalism combined with the Keldysh Green's function method. It is shown that (i) the steady dc shift current flows by exciton creation without dissociation into free carriers and (ii) second harmonic generation is enhanced at the exciton resonance. The obtained formulas clarify topological aspects of these second order excitonic processes which are described by Berry connections of the relevant valence and conduction bands.