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Topological materials are of interest to both fundamental science andadvanced technologies, because topological states are robust with respect toperturbations and dissipation. Experimental detection of topological invariantsis thus in great demand, but it remains extremely challenging. Ultrafastlaser-matter interactions, and in particular high-harmonic generation (HHG),meanwhile, were proposed several years ago as tools to explore the structuraland dynamical properties of various matter targets. Here we show that thehigh-harmonic emission signal produced by a circularly-polarized laser containssignatures of the topological phase transition in the paradigmatic Haldanemodel. In addition to clear shifts of the overall emissivity and harmoniccutoff, the high-harmonic emission shows a unique circular dichroism, whichexhibits clear changes in behavior at the topological phase boundary. Ourfindings pave the way to understand fundamental questions about the ultrafastelectron-hole pair dynamics in topological materials via non-linearhigh-harmonic generation spectroscopy.

Circular dichroism in high-order harmonic generation: Heralding topological phases and transitions in Chern insulators