  Excitons, which are composite boson quasi-particles composed of bound
electrons and holes, have many fascinating properties and great potential in
practical applications. Though experimental studies on exciton dynamics are
well-developed, the ab initio simulation ones still remain vacant until two
years ago. Here, we apply the density functional theory (DFT) and many-body
perturbation theory (MBPT) on 2D MoSi$_2$N$_4$ to study its exciton-related
physics and non-adiabatic ultrafast exciton dynamics theoretically and
numerically for the first time. We calculate the photoluminescence (PL) spectra
with final states as bright excitons, yet lots of them are contributed by the
dark ones, and the results match the experimental ones perfectly. We also study
the dark-exciton-involved processes, which were barely studied in the past but
dominate in many physical processes, and obtain several main results like: (i)
High scattering rates over the whole Brillouin zone (BZ) within the order of
magnitude from 10$^{-2}$ fs$^{-1}$ to 10$^{-1}$ fs$^{-1}$; (ii) Thorough
analysis for the dynamics of the dark excitons at $\Lambda$ valley, which have
negative effective mass and the highest scattering rate among several exciton
states; (iii) Simulate the time-resolved evolution of the excitons after
photo-excitation with the real-time Boltzmann transport equation (rt-BTE)
techniques, in which process excitons at K/K' valley play an important role;
(iv) Exciton dynamics with spin-valley locking at K/K' valley are also
discussed here; (v) A new approach is proposed for modulating the non-adiabatic
effects for excitons, accompanied by a chiral phonon absorption/emission, by
tuning the chirality of the external circularly polarized light. All the
results show that the 2D material MoSi$_2$N$_4$ is an ideal platform to study
the exciton-involved physics and has great application value.

Materials Science