Twisted Moire bilayer physics in square-lattice surfaces of time-reversal symmetric topological superconductors

Twisted bilayer graphene brings the flat energy bands from the Dirac cones serving as a new playground for strong correlations and topological phases. Beyond the hexagonal lattice, we study the physics of the twisted bilayer in the square lattice and focus on the scattering between the nodal points at M points in each layer. In particular, we consider the surface of time-reversal symmetric topological superconductors as a layer. Different from twisted bilayer graphene, time reversal symmetry and particle-hole symmetry protect the entire energy bands from separation in the Moire ´ Brillouin zone. We show that different ordered nodal points on the surface evolve to different types of flat bands with and without magic angles.