Doping and gap size dependence of high-harmonic generation in graphene: Importance of consistent formulation of light-matter coupling

High-harmonic generation (HHG) in solids is a fundamental nonlinear phenomenon, which can be efficiently controlled by modifying system parameters such as doping-level and temperature. In order to correctly predict the dependence of HHG on these parameters, consistent theoretical formulation light-matter coupling crucial. Recently, contributions current that are often missing analysis based semiconductor Bloch equations have been pointed out [J. Wilhelm, et.al. PRB 103 125419 (2021)]. this paper, systematically analyzing doping gap-size gapped graphene, we discuss practical impact terms. particular, focus role $J_{\rm ra}^{(2)}$, originates from change intraband dipole via interband transition. When gap small close half filling, currents mostly cancel, thus suppressing signal - an important property broken when neglecting ra}^{(2)}$. Furthermore, without becomes qualitatively different full evaluation. Our results demonstrate importance expression study parameter for systems.