Exploration of the high-order harmonic generation from periodic potentials by Bohmian trajectories

The recombination processes of the electrons in solid are illustrated by solving the time-dependent Schrodinger equation. The results show that the Bohmian trajectories and the time evolution of the electronic probability density agrees very well, which demonstrates that we can use the Bohmian trajectories to investigate the recombination processes of the electrons in solid. We select the region where the probability density of the electron reached the strongest and the weakest as the initial position of the calculated Bohmian trajectories, one can see that the Bohmian trajectories have similar structures. In addition, our results show that the emission time of the solid high-order harmonic generation (HHG) spectra from the time-frequency distribution agrees well with the time that the Bohmian trajectories change direction. By regulating the phase of the electric field, the electrons can move farther, which will result in the broad cutoff of the HHG. We have also demonstrated that the similar structure of the Bohmian trajectories of the solid with a defect for different initial positions disappears due to the broken periodic structure, which further illustrates that the motion processes of the electrons in solid depend on the structure of the solid.