Topological materials in ultrafast and strong laser fields

Strong ultrafast optical pulses with an amplitude of up to 1 V/A and a duration of a few femtoseconds provide an extra tool to probe topological properties of solids. In relation to ultrafast electron dynamics under the field of the pulse, the topology manifests itself in unique properties of interband dipole couplings, which are related to the non-Abelian Berry connections, and in large accumulation of topological phase during a long electron excursion induced by a laser pulse in the reciprocal space. We have studied theoretically ultrafast electron dynamics in different types of topological materials, such as graphene, transition metal dichalcogenides (TMDCs), 3D topological insulators, Weyl semimetals, and others. Our extensive numerical analysis has shown that the topologically-related features in interband and intraband electron dynamics result in experimentally observable effects, such as interference patterns in the conduction band population distributions in the reciprocal space of graphene, large ultrafast valley polarization in TMDCs, an ultrafast anomalous Hall effect in gapped graphene-like materials, Berry phase-induced singularities in the conduction band population distribution in specially designed graphene nanosystems, a highly nonlinear optical absorbance in graphene-like materials. Some of these processes are related to the effect of ultrafast topological resonance, which is due to a mutual compensation of the dynamic phase and the topological phase during the pulse.