Modulation of high-harmonic generation by coherent two-phonon dynamical coupling.

We study delay-dependent high-harmonic generation in a two-dimensional (2D) material modulated by two coherent phonons. In our first-principles calculations, two phonon modes are simultaneously initiated by displacive launch and a time-delayed probe is used to drive the HHG. We observe two robust enhancement windows (13 and50 fs) in the HHG plateau yield. Notably, these enhancements do not coincide with displacive extrema of either single composed phonon mode. Based on a minimal harmonic model, we describe this behavior involving the delay ordering and phonon-phase sensitivity. Through analysis of the phonon-enhanced excited-electron number and the k-selective photocarrier injection concentration, we reveal a complex phonon coupling effect: the out-of-plane ZO mode predominantly modulates the band gap, establishing the phonon-driven carrier-excitation baseline and the characteristic momentum-space distribution, whereas longitudinal optical-induced valley reshaping further enhances carrier accumulation nearand strengthens plateau emission at the optimal delays. These findings establish two-phonon mixing as an effective control knob for optimizing HHG in 2D materials.