Multiple k-Point Nonadiabatic Molecular Dynamics for Ultrafast Excitations in Periodic Systems: The Example of Photoexcited Silicon

With the rapid development of ultrafast experimental techniques for the research of carrier dynamics in solid-state systems, a microscopic understanding of the related phenomena, particularly a first-principle calculation, is highly desirable. Nonadiabatic molecular dynamics (NAMD) offers a real-time direct simulation of the carrier transfer or carrier thermalization. However, when applied to a periodic supercell, there is no cross-k-point transitions during the NAMD simulation. This often leads to a significant underestimation of the transition rate with the single-k-point band structure in a supercell. In this work, based on the surface hopping scheme used for NAMD, we propose a practical method to enable the cross-k transitions for a periodic system. We demonstrate our formalism by showing that the hot electron thermalization process by the multi-k-point NAMD in a small silicon supercell is equivalent to such simulation in a large supercell with a single Γ point. The simulated hot carrier thermalization process of the bulk silicon is compared with the recent ultrafast experiments, which shows excellent agreements. We have also demonstrated our method for the hot carrier coolings in the amorphous silicons and the GaAlAs_{2} solid solutions with the various cation distributions.