  Magic-angle twisted bilayer graphene (TBG) has attracted significant interest
recently due to the discoveries of diverse correlated and topological states in
this system. Despite the extensive research on the electron-electron
interaction effects and topological properties of the electrons, the phonons of
magic-angle TBG are relatively less explored. In this work, we study the phonon
properties in magic-angle TBG based on \textit{ab} \textit{initio} deep
potential molecular dynamics. We have calculated phonon band structures and
density of states at the magic angle, and have systematically analyzed the
phonon eigenmodes at high-symmetry points in the moir\'e Brillouin zone. In
particular, at the moir\'e $\Gamma$ point, we have discovered a number of soft
modes which can exhibit dipolar-like, stripe-like, and octupolar-like
vibrational patterns within the moir\'e supercell, as well as some "vortical"
modes with nonzero curl in real space. At the moir\'e $K$/$K'$ points, there
are time-reversal breaking chiral phonon modes with nonzero local phonon
polarizations. We have further studied the phonon effects on the electronic
structures by freezing certain soft phonon modes. We find that if a soft
"stripe" phonon mode at moir\'e $\Gamma$ point is assumed to be frozen, the
system would exhibit a charge order which naturally explains the recent
observations from scanning tunnelling microscopy. Moreover, there are also
low-frequency $C_{2z}$-breaking modes at moir\'e $\Gamma$ point, which would
gap out the Dirac points at the charge neutrality point once these modes get
frozen. This provides a new perspective to the origin of correlated insulator
state at the charge neutrality point.
