Zero modes on zero-angle grain boundaries in graphene

Electronic states confined to zero-angle grain boundaries in single-layer graphene are analyzed using topological band theoretic arguments. We identify a hidden chiral symmetry which supports symmetry-protected zero modes in projected bulk gaps. These branches occupy a finite fraction of the interface-projected Brillouin zone and terminate at bulk gap closures, manifesting topological transitions in the occupied manifolds of the bulk systems that are joined at an interface. These features are studied by numerical calculations on a tight-binding lattice and by analysis of the geometric phases of the bulk ground states.