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

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.