High-harmonic generation in topological materials: a comprehensive review

In solids, high-harmonic generation (HHG) has emerged as a crucial technique for studying ultrafast electron dynamics and band structure properties. Topological quantum materials, including topological insulators, semimetals and topological superconductors are an emerging class of materials distinguished by their unique edge or surface states along with nontrivial Berry curvature and topological invariants. These fundamental properties impart distinctive signatures onto their high-harmonic spectra, offering a novel nonlinear-optical window into topological order. Several theoretical and experimental investigations have shown that HHG in topological materials exhibits distinct signatures, including significant circular dichroism, enhanced harmonic yields, and distinctive ellipticity dependence, highlighting its sensitivity to underlying topological properties. This article aims to describe the basic dynamics that drive HHG in these materials, point out important theoretical and experimental results, and evaluate which spectral features may be genuinely topology-specific, which are topology-sensitive but not unique, and which remain debated. We organized the review into three main sections covering topological insulators, semimetals, and superconductors. For each class, after providing a basic overview, we explore the distinctive HHG mechanisms and spectral characteristics.