High Harmonic Spectroscopy from Lower-Order to Higher-Order Topological Insulators

Over the past decades, high-harmonic spectroscopy (HHS) has emerged as a powerful tool for all-optical probing of topological properties of solids. There are outstanding questions regarding universal nature of the spectral features of harmonics in their relationship to the non-trivial topological properties. Here, we present a systematic theoretical study of HHS in topological materials, including lower-order and higher-order topological insulators (LOTIs and HOTIs), focusing on observables such as helicity, circular dichroism, ellipticity dependence, and channel-resolved intensity yields. Using the Haldane, Kane-Mele, and breathing Kagome lattice models, we theoretically extend all-optical approaches from the LOTI to the HOTI regime by explicitly incorporating contributions from bulk, edge, and it corner states. Depending on the crystalline system, our calculations suggest that these observables can encode topological information through distinct modifications of the HHG spectra in topological phases. In particular, we identify significant enhancements of the harmonic intensity yields, reaching up to two orders of magnitude relative to trivial phases, together with distinct spectral signatures associated with edge and corner contributions revealed through channel-resolved intensity yields. These results show that channel-resolved HHS provides a promising route for probing topological states in both LOTIs and HOTIs.