Defects of the nearest-neighbor tight-binding model in the study of solid harmonics

At present, the nearest-neighbor tight-binding model is often used to study the high-order harmonic generation (HHG) in solids, but its defects are little known. We theoretically investigate the defects of the nearest-neighbor tight-binding model in the study of solid HHG by developing the semiconductor Bloch equations with the accelerated Bloch-like basis consisting of the maximally localized Wannier functions. To achieve this goal, we calculate the harmonic spectra, orientation and ellipticity dependence of harmonic yield in monolayer black phosphorus using the nearest-neighbor tight-binding model, and the ab initio model, respectively. It is found that there are obvious differences between the calculation results of the two models. This indicates the limitations of the nearest-neighbor tight-binding approximation in the study of solid HHG. Furthermore, we study the role of the matrix elements of the position operator under the Wannier basis in solid HHG, which are often discarded in many previous works. It is found that these matrix elements have an important influence on the orientation and ellipticity dependence of higher-order harmonic yield. This work remedies some defects of previous theories and will greatly promote the accurate calculation of strong-field nonlinear responses in solids.