Nonadiabatic Molecular Dynamics with Non-Condon Effect of Charge Carrier Dynamics

Abstract

Nonradiative multiphonon transitions play a crucial role in understanding charge carrier dynamics. To capture the non-Condon effect in nonadiabatic molecular dynamics (NA-MD), we develop a simple and accurate method to calculate noncrossing and crossing k-point NA coupling in momentum space on an equal footing and implement it with a trajectory surface hopping algorithm. Multiple k-point MD trajectories can provide sufficient nonzero momentum multiphonons coupled to electrons, and the momentum conservation is maintained during nonvertical electron transition. The simulations of indirect bandgap transition in silicon and intra-and intervalley transitions in graphene show that incorporation of the non-Condon effect is needed to correctly depict these types of charge dynamics. In particular, a hidden process is responsible for the delayed nonradiative electron−hole recombination in silicon: the thermal-assisted rapid trapping of an excited electron at the conduction band minimum by a long-lived higher energy state through a nonvertical transition extends charge carrier lifetime, approaching 1 ns, which is about 1.5 times slower than the direct bandgap recombination. For graphene, intervalley scattering takes place within about 225 fs, which can occur only when the intravalley relaxation proceeds to about 50 fs to gain enough phonon momentum. The intra-and intervalley scattering constitute energy relaxation, which completes within sub-500 fs. All the simulated time scales are in excellent agreement with experiments. The study establishes the underlying mechanisms for a long-lived charge carrier in silicon and valley scattering in graphene and underscores the robustness of the non-Condon approximation NA-MD method, which is suitable for rigid, soft, and large defective systems.

Two-Dimensional Molybdenum Boride (MBene) Mo4/3B2Tx with Broadband and Termination-Dependent Ultrafast Nonlinear Optical Response

“…The characteristic times of τ 2 and τ 3 are <10 ps and <100 ps, respectively, corresponding to the electron–phonon scattering and phonon–phonon scattering processes. , Notably, an τ 4 time scale of 2 ns appears when the probe wavelength is less than 1100 nm. Similar to previous reports, , this process can be attributed to the intervalley reorganization process of indirect semiconductor Mo 4/3 B 2 O 2 . Combined with previous calculations and discussions, the fast PIA signal mainly corresponds to the intraband relaxation process in Mo 4/3 B 2 F 2 with metallic characteristics.…”

Nonadiabatic Molecular Dynamics in Momentum Space Beyond Harmonic Approximation: Hot Electron Relaxation in Photoexcited Black Phosphorus

“…This analysis further suggests the momentum space NA-MD in SC is nearly equivalent to that observed with a single k -point in BC, yet offers additional advantages, such as considering the non-Condon effect and providing more accurate physics. This is crucial for accurately describing charge dynamics involved in intervalley scattering and indirect bandgap recombination. , …”