Supplementary Materials for: Topological Dirac and chiral phonons in isotope-substituted single-layer and bilayer graphene

We derive the dynamic matrix elements for single-layer and bilayer graphene in detail in Sections S1 and S2, respectively. Calculation details are provided in Section S3 and phonon band dispersions with one type of interlayer interaction are presented in Section S4.

我们将分别在补充材料S1与S2章节中，详细推导单层石墨烯与双层石墨烯的动力学矩阵元（dynamic matrix elements）。具体计算细节已在补充材料S3章节给出，而包含单一种类层间相互作用（interlayer interaction）的声子能带色散（phonon band dispersions）则展示于补充材料S4章节。