Which part of the Brillouin zone contributes most to the high-harmonic radiation?

Utilizing realistic simulations of high-harmonic generation (HHG) in several materials, we study how different regions of the Brillouin zone contribute to the nonlinear response. It is often assumed that only the vicinity of the Gamma point is predominantly responsible for the HHG spectrum, but it is shown here that such an approximation is inaccurate in general. While examples can be identified where merely 0.4% of the Brillouin zone produces semi-quantitatively accurate HHG-spectra, in most situations one must include at least thirty to fifty percent of the Brillouin-zone volume to obtain accurate above-the-gap harmonics. For the harmonic peaks below the bandgap energy, the current-density responses from the entire Brillouin zone must always be integrated. We also identify the minimal set of electronic bands necessary for the construction of reduced but still realistic HHG-models. The results should be useful for a number of HHG applications, including all-optical reconstructions of the band-structure and light-matter couplings, or considerations involving semi-classical approaches to solid-state high-harmonic radiation.