Nonlinear effects in topological materials

Materials, where charge carriers have a linear energy dispersion, usually exhibit a strong nonlinear optical response in the absence of disorder scattering. This nonlinear response is particularly interesting in the terahertz frequency region. We present a theoretical and numerical investigation of charge transport and nonlinear effects, such as the high harmonic generation in topological materials including Weyl semimetals (WSMs) and alpha-T-3 systems. The nonlinear optical conductivity is calculated both semi-classically using the velocity operator and quantum mechanically using the density matrix. We show that the nonlinear response is strongly dependent on temperature and topological parameters, such as the Weyl point (WP) separation tb and Berry phase phi(B). A finite spectral gap opening can further modify the nonlinear effects. Under certain parameters, universal behaviors of both the linear and nonlinear response can be observed. Coupled with experimentally accessible critical field values of 10(4)-10(5) V/m, our results provide useful information on developing nonlinear optoelectronic devices based on topological materials.