  As a promising avenue to obtain new extreme ultraviolet light source and
detect electronic properties, high-harmonic generation (HHG) has been actively
developed in both theory and experiment. In solids lacking inversion symmetry,
when electrons undergo a nonadiabatic transition, a directional charge shift
occurs and is characterized by shift vector, which measures the real-space
shift of the photoexcited electron and hole. For the first time, we have
revealed that shift vector plays prominent roles in the real-space tunneling
mechanism of three-step model for electrons under strong laser fields. Since
shift vector is determined by the topological properties of related wave
functions, we expect HHG with its contribution can provide direct knowledge on
the band topology in noncentrosymmetric topological insulators (TIs). In both
Kane-Mele model and realistic material BiTeI, we have found that the shift
vector reverses when band inversion happens during the topological phase
transition between normal and topological insulators. Under oscillating strong
laser fields, the reversal of shift vector leads to completely opposite
radiation time of high-order harmonics. This makes HHG a feasible all-optical
strong-field method to directly identify the band inversion in
non-centrosymmetric TIs.
