Nonlinear optical response of the alpha-T-3 model due to the nontrivial topology of the band dispersion

We study the electronic contribution to the nonlinear optical response of the α-T3 model. This model is an interpolation between a graphene (α = 0) and dice (α = 1) lattice. Using a second-quantized formalism, we calculate the first- and third-order responses for a range of α and chemical potential values as well as considering a band gap in the first-order case. Conductivity quantization is observed for the first-order, while higher-order harmonic generation is observed in the third-order response with the chemical potential determining which applied field frequencies both quantization and harmonic generation occur at. We observe a range of experimentally accessible critical fields between 102-106 V/m with dynamics depending on α, μ, and the applied field frequency. Our results suggest an α-T3-like lattice could be an ideal candidate for use in terahertz devices.