Nonlinear optical response of the α−T3 model due to the nontrivial topology of the band dispersion

Abstract

We study the electronic contribution to the nonlinear optical response of the $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$ model. This model is an interpolation between a graphene $(\ensuremath{\alpha}=0)$ and dice $(\ensuremath{\alpha}=1)$ lattice. Using a second-quantized formalism, we calculate the first- and third-order responses for a range of $\ensuremath{\alpha}$ 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 ${10}^{2}--{10}^{6}$ V/m with dynamics depending on $\ensuremath{\alpha},\ensuremath{\mu}$, and the applied field frequency. Our results suggest an $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$-like lattice could be an ideal candidate for use in terahertz devices.