Abstract
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.
- Received 29 July 2021
- Revised 17 February 2022
- Accepted 7 March 2022
DOI:https://doi.org/10.1103/PhysRevX.12.021030
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
High-harmonic generation (HHG) by intense laser fields can produce extreme ultraviolet attosecond light pulses for exploring electronic dynamics with ultrafast time resolution. In particular, HHG from solid materials offers opportunities to detect electronic properties in condensed matter. Here, we reveal the key role of a “shift vector” in solid HHG from noncentrosymmetric systems, which has been overlooked before. Moreover, this work proposes HHG as an all-optical method to directly probe the band inversion in noncentrosymmetric topological insulators.
In solids that lack inversion symmetry, when electrons undergo a nonadiabatic transition, a directional “charge shift” occurs. This shift—a displacement between the photoexcited electron and corresponding hole—is characterized by a shift vector, which plays a prominent role in the tunneling mechanism for electrons in strong laser fields.
In two models—one a paragon of the quantum spin Hall effect, the other a description of the layered polar material BiTeI—we find the shift vector reverses when a band inversion happens during the phase transition between a normal insulator and a topological one. Under oscillating strong laser fields, the reversal of the shift vector leads to harmonic radiation occurring at different subcycles of the laser field in the normal and topological phases.
Our findings will help characterize phase transitions of various topological materials, thus establishing a close link between the strong-field nonlinear optics and topological condensed matter physics.
