There has been considerable recent interest in the phenomenology of high harmonic generation (HHG) in topological insulators. We study HHG in the Qi-Wu-Zhang (QWZ) model for a Chern insulator, which satisfies spatial inversion symmetry but breaks time-reversal symmetry. The QWZ model is particularly interesting because it combines rich physics with unique simplicity. Our theoretical approach is based on the semiconductor Bloch equations, and we present two distinct numerical methods for simulating HHG which are immune to topological obstruction of the Bloch phase. We obtain highly converged HHG spectra in both trivial and topological phases of the QWZ model, and we use these results to investigate spectral characteristics which have been proposed as signatures of band topology. We derive a simple relationship between harmonic ellipticity and material Berry curvature for two-band systems, and we show that this can be used for accurate prediction of the helicity of emitted harmonics. While this clarifies the relationship between ellipticity and Berry curvature, it also uncovers limitations that restrict the scope of ellipticity as an indicator of topological phase. More generally, our findings contribute to the important discussion surrounding topological signatures in HHG spectra. Beyond that, we also observe a dual plateau structure of the HH spectrum in the topological phase which is absent in the trivial phase, but the origin of this phenomenon is not topological. Rather, the multiple plateaus are clearly attributed to the interference of HHG originating from different regions of the full two-dimensional Brillouin zone (BZ). As a consequence, our study reinforces the importance of including the entire BZ for accurate modeling of HHG in solids.

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• High-order harmonic generation
• Semiconductor Bloch equations
• Ultrafast phenomena
• Topological materials