Nonlinear optical response of a two-dimensional semi-Dirac system in the terahertz regime

We demonstrate a strong nonlinear optical response in a two-dimensional semi-Dirac system in the terahertz regime. By applying the Boltzmann transport theory for the intra-band process and a quantum mechanics method for the inter band process, we obtained the three-photon current response. It is found that both the intra- and inter-band excitations make significant contributions to the nonlinear response. The third order conductivities (TOCs) [Formula: see text] are about two magnitudes higher than that of [Formula: see text]. Interestingly, for the inter-band TOCs, there is a sign change when the chemical potential varies across the saddle point in the conduction band in [Formula: see text] direction (that is parabolic), due to the competition between the two opposite nonlinear current contributed by the electrons at states [Formula: see text] and [Formula: see text], respectively. Finally, we show that the nonlinear response in the terahertz regime is significant at experimentally accessible field strengths. Our results suggest that this system could be of potential applications in photonic device for frequency up-conversion.