Nonlinear optical response of graphene family materials near topological phase transitions*

The graphene family materials behave as topological insulators due to non-negligible spin-orbit coupling. The gaps at each Dirac cone can be tailored when static electric fields and/or non-resonant circularly polarized lasers are applied to the system. Various electronic phases, characterized by Chern numbers, have been explored by changing the external fields. In this work we study the interaction of graphene family materials with ultrashort (~10’s of femtosecond) linearly polarized optical pulses both in time and frequency domain. In order to observe the nonlinear response of these materials, we develop a non-perturbative approach to solve the massive Dirac equation for each valley and spin. Then we compute the longitudinal and transverse currents to investigate signatures of the ultrafast dynamics of the material. We demonstrate that the asymmetry of different Dirac cones plays a crucial role in the nonlinear response of the graphene family materials near topological phase transition boundaries.