It is found that the two flat bands in TBG possess a fragile topology protected by the C2zT symmetry. When particle-hole symmetry (P) can be considered as a good approximation, the fragile topology of the two flat bands is enhanced to a P-protected stable topology. This implies (4l+2) (l ∈ N) Dirac points between the middle two bands. The (4l + 2) Dirac points cannot be supported by lattice models that preserve both C2zT and P symmetries. This symmetry anomaly is robust against gap closing and reopening.
Zhida Song et al, "TBG II: Stable Symmetry Anomaly in Twisted Bilayer Graphene", arXiv:2009.11872.
Zhida Song et al, "All Magic Angles in Twisted Bilayer Graphene are Topological" , Phys. Rev. Lett. 123, 036401 (2019).