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Data-driven recovery of topology is challenging for networks beyond pairwise interactions. The authors propose a framework to reconstruct complex networks with higher-order interactions from time series, focusing on networks with 2-simplexes where social contagion and Ising dynamics generate binary data.

As a quantum material, Weyl semimetal has a series of electronic-band-structure features, including Weyl points with left and right chirality and corresponding Berry curvature, which have been observed in experiments. These band-structure features also lead to some unique nonlinear properties, especially high-order harmonic generation (HHG) due to the dynamic process of electrons under strong laser excitation, which has remained unexplored previously. Herein, we obtain effective HHG in type-II Weyl semimetal β-WP2 crystals, where both odd and even orders are observed, with spectra extending into the vacuum ultraviolet region (190 nm, 10th order), even under fairly low femtosecond laser intensity. In-depth studies have interpreted that odd-order harmonics come from the Bloch electron oscillation, while even orders are attributed to Bloch oscillations under the "spike-like" Berry curvature at Weyl points. With crystallographic orientation-dependent HHG spectra, we further quantitatively retrieved the electronic band structure and Berry curvature of β-WP2. These findings may open the door for exploiting metallic/semimetallic states as solid platforms for deep ultraviolet radiation and offer an all-optical and pragmatic solution to characterize the complicated multiband electronic structure and Berry curvature of quantum topological materials. Weyl semimetals have interesting band-structure features that lead to unique properties. Here, the authors observe and study high-harmonic generation in type-II Weyl semimetal β-WP2 crystals. [ABSTRACT FROM AUTHOR]