Interface states at the boundary between ABC and ABA multilayer graphene structures

We study the interfaces between ABC and ABA regions in multilayer graphene, in particular we consider regions in which the transition between the ABA and ABC structure arises due to the local compression in one of the graphene layers for a zigzag interface, and to a local shear of the atoms for the armchair interface. When we consider an infinite ribbon configuration we find that interface bands form in these regions, more pronouncedly for the armchair-type interfaces. We note that these states are not topological. For fully-finite-size structures the continuous interface bands transform into sets of quantized levels.