Magnon band in twisted bilayer CRI3

We use Holstein–PrimakoffTransformation and symmetry analysis to get the Hamiltonian for magnon dispersion in twisted bilayer CrI3. We reveal how to use DFT calculation to get all indepedent parameters in the Hamiltonian. We find flat Γ magnon bands and DIrac cons in the band dispersion. With the intralayer Dzyaloshinskii- Moriya interactions, the Dirac cons can be opened.