As a promising avenue to obtain new extreme ultraviolet light source and detect electronic properties, high harmonic generation (HHG) has been actively developed both theoretically and experimentally. 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. We have revealed that shift vector plays prominent roles in the three-step model of real-space tunneling mechanism for electrons under strong laser fields. Since shift vector is determined by the topological properties of related wavefunctions, we expect HHG with its contribution can provid 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 strong laser fields, the reverse of shift vector leads to the sign change of HHG tropisms to the polarization direction of the laser field. This makes HHG a feasible all-optical strong-field method to directly identify the band inversion in non-centrosymmetric TIs.
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