Second order divergence in the third order DC response of a cold semiconductor

TL;DR

This paper derives an analytical expression for the second order divergence in the third order DC response of cold semiconductors, validated by numerical calculations on gapped graphene, advancing understanding of nonlinear optical responses.

Contribution

It provides the first analytical formula for the second order divergence in the third order DC response, validated against numerical results for gapped graphene.

Findings

Analytical expression matches numerical results

Validates the use of the derived formula for different electric field setups

Enhances understanding of nonlinear responses in cold semiconductors

Abstract

In this work, we present the analytical expression for the second order divergence in the third order DC response of a cold semiconductor, which can be probed by different electric field setups. Results from this expression were then compared, for the response of the gapped graphene monolayer, with numerical results from a velocity gauge calculation of the third order conductivity. The good agreement between the two validates our analytical expression.