  Topological materials are of interest to both fundamental science and
advanced technologies, because topological states are robust with respect to
perturbations and dissipation. Experimental detection of topological invariants
is thus in great demand, but it remains extremely challenging. Ultrafast
laser-matter interactions, and in particular high-harmonic generation (HHG),
meanwhile, were proposed several years ago as tools to explore the structural
and dynamical properties of various matter targets. Here we show that the
high-harmonic emission signal produced by a circularly-polarized laser contains
signatures of the topological phase transition in the paradigmatic Haldane
model. In addition to clear shifts of the overall emissivity and harmonic
cutoff, the high-harmonic emission shows a unique circular dichroism, which
exhibits clear changes in behavior at the topological phase boundary. Our
findings pave the way to understand fundamental questions about the ultrafast
electron-hole pair dynamics in topological materials via non-linear
high-harmonic generation spectroscopy.
