Stable magic angle and van Hove singularity in twisted bilayer Graphene with proximitized spin orbit coupling

We propose that the electronic structure of magic-angle twisted bilayer graphene can be stabilized by the proximitized Kane-Mele spin-orbit coupling. These terms bring a quadratic dispersion relation between the bandwidth and twisted angle, which leads to stable van Hove singularities even with angle disorders. We then investigate the fractional Chern insulator(FCI) as an example, and find the FCI indicator gets significantly reduced with the Kane-Mele spin-orbit coupling. Furthermore, in hBN encapsulated twisted bilayer Pt$_2$HgSe$_3$ with intrinsic Kane-Mele spin-orbit coupling, we identify a topological flat band at a large twist angle($>4 ^circ$).