Abstract
High harmonic generation (HHG) has developed in recent years as a promising tool for ultrafast materials spectroscopy. At the forefront of these advancements, several works proposed using HHG as an all-optical probe for topology of quantum matter by identifying its signatures in the emission spectra. However, it remains unclear if such spectral signatures are indeed a robust and general approach for probing topology. To address this point, we perform a fully ab initio study of HHG from prototypical two-dimensional topological insulators in the Kane-Mele quantum spin-Hall and anomalous-Hall phases. We analyze the spectra and previously proposed topological signatures by comparing HHG from the topological and trivial phases and across the phase transition. We demonstrate and provide detailed microscopic explanations of why, in these systems, none of the observables proposed thus far uniquely and universally probes material topology. Specifically, we find that the (i) HHG helicity, (ii) anomalous HHG ellipticity, (iii) HHG elliptical dichroism, and (iv) temporal delays in HHG emission are all unreliable signatures of topological phases. Our results suggest that extreme care must be taken when interpreting HHG spectra for topological signatures and that contributions from the crystal symmetries and chemical nature might be dominant over those from topology. They hint that a truly universal topological signature in nonlinear optics is unlikely and raise important questions regarding possible utilization and detection of topology in out-of-equilibrium systems.
- Received 11 November 2022
- Revised 2 June 2023
- Accepted 20 June 2023
DOI:https://doi.org/10.1103/PhysRevX.13.031011
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. Open access publication funded by the Max Planck Society.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Topology—a mathematical field studying the invariant properties of systems under deformation—plays an enormous role in modern condensed-matter physics and beyond. It has changed the way we think of electronic structure and yielded numerous technological applications. It is, however, tricky to measure. One technique suggested in recent years is high-harmonic spectroscopy: A sample is irradiated by intense lasers, and one looks for theoretically predicted topological signatures in the ensuing nonlinear optical emission spectra. Here, we perform vast and comprehensive numerical ab initio calculations in realistic topological insulators, however, our results suggest that such signatures do not exist.
High harmonic generation is an appealing technique for revealing topological behavior of matter because it is all optical and offers ultrafast time resolution. Fundamentally, it relies on two main assumptions—topological information is imprinted onto the spectra, and information is extractable—and many previous studies supported this paradigm. Our study is the first ab initio investigation of high-harmonic generation from prototypical 2D topological insulators across the phase transition. We find that none of the previously proposed observables are reliable signatures of topology, and our massive attempts to uncover novel topological signatures have all failed.
Our results stress that topological fingerprints in optical spectroscopy are not straightforward and must be analyzed with extreme caution. We generally find that nontopological aspects of the system dominate its nonlinear response, suggesting that topology might play a more minor role than previously thought, and raising doubts about its use for applications in highly nonlinear optics.
