Role of Shift Vector in High-Harmonic Generation from Noncentrosymmetric Topological Insulators under Strong Laser Fields

As a promising avenue to obtain a 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 a shift vector, which measures the real-space shift of the photoexcited electron and hole. For the first time, we reveal that the shift vector plays a prominent role in the real-space tunneling mechanism of the three-step model for electrons under strong laser fields. Since the shift vector is determined by the topological properties of related wave functions, we expect that the contribution of HHG can provide direct knowledge of the band topology in noncentrosymmetric topological insulators (TIs). In both the Kane-Mele model and the realistic material BiTeI, we find that the shift vector reverses when band inversion happens during the topological phase transition between the normal insulator and the TI. Under oscillating strong laser fields, the reversal of the 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 noncentrosymmetric TIs.