We predict that a single oscillation of a strong optical pulse can significantly populate the surface conduction band of a three-dimensional topological insulator, Bi2Se3. Both linearly-and circularlypolarized pulses generate chiral textures of interference fringes of population in the surface Brillouin zones. These fringes constitute a self-referenced electron hologram carrying information on the topology of the surface Bloch bands, in particular, on the effect of the warping term of the lowenergy Hamiltonian. These electron-interference phenomena are in a sharp contrast to graphene where there are no chiral textures for a linearly-polarized pulse and no interference fringes for circularly-polarized pulse. These predicted reciprocal space electron-population textures can be measured experimentally by time resolved angle resolved photoelectron spectroscopy (TR-ARPES) to gain direct access to non-Abelian Berry curvature at topological insulator surfaces.

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We study theoretically interaction of crystalline topological insulator (CTI), characterized by surface quadratic gapless bands, with an ultrashort (few-femtosecond) optical pulse. The electron dynamics in such an optical pulse is determined by a strong lattice-momentum dependence of the interband dipole coupling, which is anisotropic and singular at the degeneracy point. The interband mixing induced by the ultrashort pulse results in a finite conduction band population, the distribution of which in the reciprocal space is correlated with the profile of the interband dipole matrix elements and has high contrast. The number of such high contrast regions depends on the polarization direction of the optical pulse. The ultrashort pulse also causes an electrical current and a net charge transfer through the system in the direction of the maximum field. These findings open up roots to ultrafast optical-field control of the TCI's and petahertz-band opto-electronics

We theoretically study the interaction of ultrashort optical pulses with gapped graphene. Such a strong pulse results in a finite conduction band population and a corresponding electric current, both during and after the pulse. Since gapped graphene has broken inversion symmetry, it has an axial symmetry about the y -axis but not about the x-axis. We show that, in this case, if the linear pulse is polarized along the x-axis, the rectified electric current is generated in the y  direction. At the same time, the conduction band population distribution in the reciprocal space is symmetric about the x-axis. Thus, the rectified current in gapped graphene has an inter-band origin, while the intra-band contribution to the rectified current is zero.