Strong-field physics in three-dimensional topological insulators

We investigate theoretically the strong-field regime of light-matter interactions in the topological-insulator class of quantum materials. In particular, we focus on the process of non-perturbative high-order harmonic generation from the paradigmatic three-dimensional topological insulator bismuth selenide (Bi$_2$Se$_3$) subjected to intense mid-infrared laser fields. We analyze the contributions from the spin-orbit-coupled bulk states and the topological surface bands separately and reveal a major difference in how their harmonic yields depend on the ellipticity of the laser field. Bulk harmonics show a monotonous decrease in their yield as the ellipticity increases, in a manner reminiscent of high harmonic generation in gaseous media. However, the surface contribution exhibits a highly non-trivial dependence, culminating with a maximum for circularly polarized fields. We attribute the observed anomalous behaviour to: (i) the enhanced amplitude and the circular pattern of the interband dipole and the Berry connections in the vicinity of the Dirac point; and (ii) the influence of the higher-order, "hexagonal warping" terms in the Hamiltonian, which are responsible for the hexagonal deformation of the energy surface at higher momenta. The latter are associated directly with spin-orbit-coupling parameters. Our results thus establish the sensitivity of strong-field driven high harmonic emission to the topology of the band structure as well as to the manifestations of spin-orbit interaction.