Ultrafast dynamics in Kane-Mele two-dimensional topological insulators*

Two-dimensional (2D) materials described by the Kane-Mele (KM) model provide a unique platform for achieving various topological phases and transitions. The strong intrinsic spin-orbit coupling and potential staggered lattice structure of KM materials allow the control and manipulation of the Dirac gaps externally. Understanding the nonlinear ultrafast dynamics of these topological Dirac fermions in 2D systems driven by strong fields and their relation to topological properties is key to developing nonlinear optoelectronic devices. Nevertheless, the study of the ultrafast dynamics in these Dirac-like materials is still challenging. Recently high-harmonic generation (HHG) has shown the ability to capture anomalous effects of topological materials from both experimental and theoretical views. This paper  focuses on the topological signatures encoded in the HHG spectra. We also investigate the ultrafast (i) time delay, (ii) frequency shift, and asymmetry quantities such as (iii) the helicity and (iv) the normalized asymmetry of the harmonic emission between the parallel and perpendicular directions concerning the linear polarized laser. We show that all of these quantities contain signatures of topology and topological phase transitions, mapping the KM model phase diagram. This result paves the way to extract new insights about topological 2D Dirac and quantum materialS.