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

TL;DR

This study uses realistic simulations to determine which regions of the Brillouin zone most significantly contribute to high-harmonic generation in materials, challenging common assumptions and providing guidance for simplified modeling.

Contribution

It reveals that a large portion of the Brillouin zone must be included for accurate HHG modeling, and identifies minimal electronic bands needed for realistic simulations.

Findings

Only 0.4% of the Brillouin zone can sometimes produce semi-quantitative HHG spectra.

Most situations require including 30-50% of the Brillouin zone for accurate results.

Full Brillouin zone integration is necessary for below-gap harmonic responses.

Abstract

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.