Intralayer Phonons in Multilayer Graphene Moire Superlattices

Moir?? pattern in twisted multilayers (tMLs) induces many emergent phenomena by subtle variation of atomic registry to modulate quasiparticles and their interactions, such as superconductivity, moir?? excitons, and moir?? phonons. The periodic superlattice potential introduced by moir?? pattern also underlies patterned interlayer coupling at the interface of tMLs. Although this arising patterned interfacial coupling is much weaker than in-plane atomic interactions, it is crucial in moir?? systems, as captured by the renormalized interlayer phonons in twisted bilayer transitional metal dichalcogenides. Here, we determine the quantitative relationship between the lattice dynamics of intralayer out-of-plane optical (ZO) phonons and patterned interfacial coupling in multilayer graphene moir?? superlattices (MLG-MS) by the proposed perturbation model, which is previously challenging for MLGs due to their out-of-phase displacements of adjacent atoms in one atomic plane. We unveil that patterned interfacial coupling introduces profound modulations on Davydov components of nonfolded ZO phonon that are localized within the AB-stacked constituents, while the coupling results in layer-extended vibrations with symmetry of moir?? pattern for moir?? ZO phonons. Our work brings further degrees of freedom to engineer moir?? physics according to the modulations imprinted on the phonon frequency and wavefunction.