Third order susceptibility: general formalism for photoinduced current density in semiconductors

TL;DR

This paper derives a comprehensive formalism for third order photoinduced current density in semiconductors, utilizing advanced many-body theory and diagrammatic representations to clarify complex exciton interactions.

Contribution

It introduces a novel derivation of third order current density using composite-boson many-body theory, addressing longstanding computational challenges.

Findings

Compact expression for third order current density in terms of exciton scatterings

Representation of contributions using Shiva diagrams

Enhanced understanding of exciton-exciton interactions

Abstract

This paper contains a detailed derivation of the photoinduced current density at third order in the coupling between a semiconductor and a multifrequency photon field, starting from its standard textbook expression as a third order time integral of a triple commutator. Due to a major intrinsic problem linked to this triple commutator, such a derivation has been made possible quite recently only, thanks to the tools developed in the composite-boson many-body theory we have just constructed. The photoinduced current density is shown to ultimately read in a compact form, in terms of the Pauli and Coulomb scatterings for exciton-exciton interactions introduced in this theory. Representation in Shiva diagrams is also given to better grasp the physics of the various contributions.