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In this work, we present the analytical expression for the second orderdivergence in the third order DC response of a cold semiconductor, which can beprobed by different electric field setups. Results from this expression werethen compared, for the response of the gapped graphene monolayer, withnumerical results from a velocity gauge calculation of the third orderconductivity. The good agreement between the two validates our analyticalexpression.

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