Volkov-Pankratov states in a 2d material: excited states of a structural soliton

We show that partial dislocations, defects that naturally arise in bilayer graphene, host an analogue of the mass inversion Volkov-Pankratov (VP) states, the spectrum of excited states at a topologically non-trivial interface. In contrast to the dislocation states arising from the change in valley Chern index, such states (i) exist both with and without an interlayer bias, i.e. for metallic as well as insulating bulk and (ii) have distinct electron and hole bound states, whose number is proportional to the dislocation width. Recently discovered at heterojunctions of 3d topological insulators, their existence at the partial dislocations of a 2d material opens a rich structural playground for their investigation, and we demonstrate that the dislocation type, i.e. screw or edge, as well as the dislocation width, both play a decisive role in the creation of a topological spectrum of exited states.