Two-photon absorption in semiconductors: a multi-band length-gauge analysis

TL;DR

This paper presents a length-gauge analysis of multi-band models for two-photon absorption in semiconductors, demonstrating that complex multi-band systems can be described with simple analytical expressions, validated on graphene, bilayer graphene, and Zincblende semiconductors.

Contribution

It extends two-band models to generic multi-band systems, providing simplified analytical expressions for optical responses in the absence of scattering.

Findings

Validated theory on graphene and bilayer graphene

Applied model to bulk Zincblende semiconductors

Demonstrated simplicity of multi-band optical response expressions

Abstract

The simplest approach to deal with light excitations in direct-gap semiconductors is to model them as a two-band system: one conduction and one valence band. For such models, particularly simple analytical expressions are known to exist for the optical response such as multi-photon absorption coefficients. Here we show that generic multi-band models do not require much more complicated expressions. Our length-gauge analysis is based on the semiconductors Bloch equations in the absence of all scattering processes. In the evaluation, we focus on two-photon excitation by a pump-probe scheme with possibly non-degenerate and arbitrarily polarized configurations. The theory is validated by application to graphene and its bilayer, described by a tight-binding model, as well as bulk Zincblende semiconductors described by k.p theory.