Robustness of type-II Dirac cones in biphenylene: From nanoribbons to symmetric bilayer stacking

The electronic properties of one- and two-dimensional biphenylene-based systems, such as nanoribbons and bilayers, are studied within a unified approach. Besides the bilayer with direct (AA) stacking, we found two additional symmetric stackings for bilayer biphenylene that we denote by AB, in analogy with bilayer graphene, and AX, which can be derived by a small translation (slip) from the AA bilayer, with distinct electronic band structures. We combine first-principles calculations with a long-range tight-binding model to provide a realistic effective description of these biphenylene materials. Our approach provides a global framework to analyze realistically the robustness of the characteristic type-II Dirac cones present in all the bilayers studied and of the nanoribbons. In particular, we capture the opening in the Dirac cone for certain nanoribbons, which we relate to the symmetries of the system, as well as the variations caused by different stackings. We expect that these structures will constitute an avenue to explore novel physics, as they occur with bilayer graphene and the one-dimensional derivatives of graphene, such as nanoribbons and nanotubes.