Fig. 3

Simulations of high harmonic generation. a and b show calculated intraband contributions, whereas c and d depict interband results. For direct comparison, the experimental data for different orientations is shown as solid lines in (b) and (d). Comparison of a, c shows that interband dominates over intraband contributions for all intensities along the ΓK direction. b The dots show harmonic intensity due to intraband transitions for three distinct crystal orientations (ΓA, ΓM, ΓK), calculated following ref. ³. While the other two directions have similar cut-offs, intraband transitions produce much higher harmonics along the ΓA direction, in contradiction to experimental results. This provides an independent confirmation that intraband contributions are unlikely to explain experimental measurements. d The dashed lines show interband contributions. Maximum harmonic orders are comparable for all three orientations, showing up to the 13th harmonic, in agreement with experiment. Calculations in b and d were done close to the experimentally calibrated field strength of F_0,exp = 0.014 atomic units (F₀ = 0.0112 and 0.013 atomic units for intra and interband, respectively). The high harmonic yields in between b and d are not directly comparable because of different numerical approaches. For details on computational methods, see Supplementary Note 2