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As a promising avenue to obtain new extreme ultraviolet light source anddetect electronic properties, high-harmonic generation (HHG) has been activelydeveloped in both theory and experiment. In solids lacking inversion symmetry,when electrons undergo a nonadiabatic transition, a directional charge shiftoccurs and is characterized by shift vector, which measures the real-spaceshift of the photoexcited electron and hole. For the first time, we haverevealed that shift vector plays prominent roles in the real-space tunnelingmechanism of three-step model for electrons under strong laser fields. Sinceshift vector is determined by the topological properties of related wavefunctions, we expect HHG with its contribution can provide direct knowledge onthe band topology in noncentrosymmetric topological insulators (TIs). In bothKane-Mele model and realistic material BiTeI, we have found that the shiftvector reverses when band inversion happens during the topological phasetransition between normal and topological insulators. Under oscillating stronglaser fields, the reversal of shift vector leads to completely oppositeradiation time of high-order harmonics. This makes HHG a feasible all-opticalstrong-field method to directly identify the band inversion innon-centrosymmetric TIs.

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