Moiré phonons and electron-phonon couplings in magic-angle twisted bilayer graphene

In this work, we study the moiré phonon properties and electron-phonon couplings in magic-angle twisted bilayer graphene based on both ab initio deep potential molecular dynamics (DPMD) and an effective continuum model approach. We calculate the phonon dispersions and analyze the moiré phonon vibrational modes at high-symmetry points in the moiré Brillouin zone. Both of our methods predict the presence of low-frequency optical soft modes at Γ point exhibiting dipolar, quadrupolar, and octupolar-type out-of-plane vibrations. Additionally, the in-plane “phason” (or “sliding”) modes that were gapless calculated from the continuum-model approach turn out to be gapped from the DPMD calculations, which are due to the lattice commensuration effects. We also study effects of electron-phonon couplings, and find that some of the frozen soft moiré phonon may lead to peculiar charge order and gapped Dirac states.