Interface-induced topological phase and doping-modulated bandgap of two-dimensioanl graphene-like networks

Biphenylene is a new topological material that has attracted much attention recently. By amplifying its size of unit cell, we construct a series of planar structures as homogeneous carbon allotropes in the form of polyphenylene networks. We first use the low-energy effective model to prove the topological three periodicity for these allotropes. Then, through first-principles calculations, we show that the topological phase has the Dirac point. As the size of per unit cell increases, the influence of the quaternary rings decreases, leading to a reduction in the anisotropy of the system, and the Dirac cone undergoes a transition from type II to type I. We confirm that there are two kinds of non-trivial topological phases with gapless and gapped bulk dispersion. Furthermore, we add a built-in electric field to the gapless system by doping with B and N atoms, which opens a gap for the bulk dispersion. Finally, by manipulating the built-in electric field, the dispersion relations of the edge modes will be transformed into a linear type. These findings provide a hopeful approach for designing the topological carbon-based materials with controllable properties of edge states.