Chiral symmetry breaking in rhombohedral multilayer graphene

We model the single-particle electronic properties of rhombohedral multilayer graphene focusing on the topological surface states that yield two flat degenerate bands in the vicinity of the Fermi level. We show that chiral-symmetry breaking tight-binding parameters produce a finite dispersion of the two low-energy bands, but do not lift their degeneracy owing to the conservation of PT symmetry. We model PT symmetry breaking due to external fields, including interlayer asymmetry due to an external gate or substrate (broken space inversion) or an external magnetic field (broken time reversal symmetry).