Crystalline topological insulators in ultrashort optical pulse

We study theoretically interaction of ultrastrong and ultrashort optical pulse with crystalline topological insulators, which have quadratic band degeneracy at the surface. Coherent electron surface dynamics in such optical pulse is determined by interband dipole coupling, which is highly anisotropic in these materials. Within two-band k.p model of the surface states of topological insulator the electron dynamics is describe in terms of the mixing of two (valence and conduction) bands. Such mixing is characterized by residual, i.e., after the pulse, conduction band population. Residual electron momentum distribution in the conduction band is highly anisotropic and follows the profile of the interband dipole coupling.~ Depending on polarization of the optical pulse, the residual conduction band population has one or two strong peaks in the momentum space, where the shapes of the peaks change with the amplitude of the pulse. The conduction band population is almost one at these peaks.