Anisotropic flat bands on the surface of multilayer graphenelike lattice

The fermionic energy spectrum on the surface of the multilayer honeycomb lattice with rhombohedral stacking has topologically protected flat bands. It is shown that topological phase transition occurs in the anisotropic multilayer graphene-like structure with strongly anisotropic intra-layer coupling, at which two flat bands with opposite chirality merge into one and split, opening up a gap in the energy spectrum, depending on the anisotropy of the intralayer hopping. The dispersion of the flat bands of the multilayer is anisotropic and the density of states is more singular in the vicinity of the transition.