High-harmonic spectroscopy in solids gives insight into the inner workings of solids, such as reconstructing band structures or probing the topological phase of materials. High-harmonic generation (HHG) is a highly nonlinear phenomena and simulations guide interpretations of experimental results. These simulations often rely on the electric dipole approximation, even though the driving fields enter regimes that challenge its accuracy. Here, we investigate the effects of including nondipole terms in the light-matter coupling in simulations of HHG in materials with both topologically trivial and nontrivial phases. We show how the inclusion of nondipole terms breaks dipole selection rules, allowing for different polarizations of the generated light. Specifically, for the time-reversal-symmetric systems and linearly polarized driving geometry considered here, we find that helicity is absent in the electric-dipole approximation but is induced by the nondipole extension. This helicity cannot be uniquely identified as a topological signature.

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• High-order harmonic generation
• Kane-Mele model
• Topological insulators
• Topological order
• Topological phase transition
• Honeycomb lattice
• Semiconductors
• Topological materials
• Band structure methods
• Inversion symmetry
• T-symmetry
• Tight-binding model
• Wannier function methods