Revealing Material-Dependent Bicircular High-Order Harmonic Generation in 2D Semiconductors via Real-Space Trajectories

Abstract: Solid-state high-order harmonic generation (HHG) presents unique features different from gases.Whereas the gaseous harmonics driven by counter-rotating bicircular (CRB) pulse universally peak at a "magic" field ratio approximately E_2{\omega}:E_{\omega}=1.5:1, crystals exhibit significant material-dependent responses. In monolayer MoS2, the harmonic yield experiences two maxima at the gas-like 1.5:1 ratio, and again in the single-color limit, whereas monolayer hBN shows a monotonic increase as the 2{\omega} component dominates. Combining time-dependent density-functional theory (TDDFT) and a minimal real-space trajectory analysis, we show that these differences arise from the interplay of Bloch velocity and anomalous Hall velocity. The trajectory model quantitatively reproduces the ab-initio results, and offers an intuitive prediction of the harmonics yield without further heavy computation. These insights provide practical guidance for tailoring solid-state HHG and for selecting 2D compounds with desirable responses.