Intriguing features of Dirac cones in phagraphene with site specific doping

The non-honeycomb lattice phagraphene is energetically comparable with graphene and has recently been experimentally realized in 1D form. This carbon allotrope exhibits asymmetric Dirac cone feature with tunable Fermi velocity against external strain. This work critically presents an analytical scheme to address the emergence and robustness of Dirac fermions in phagraphene network. In particular, the lattice has judicially been renormalized from twenty atomic sites per unit cell to an equivalent two-level model. The electronic band structure of the renormalized system agrees well with the first principles results near the Fermi level. Besides, the Fermi velocity obtained from the analytical dispersion relation also supports the density functional theory results. Moreover, phagraphene is dynamically stable even after the introduction of boron and nitrogen as foreign atoms. It has been revealed that the degeneracy at the Fermi level is preserved for certain doping sites. Therefore, the criterion of band gap opening in this Dirac system has been explained in terms of appropriate hopping constraints. Furthermore, we have explored that some of the particular lattice sites significantly contribute to the formation of Dirac cones in the low-energy lattice. In addition, proper effective hopping anisotropy between these renormalized sites essentially removes the degeneracy of the Dirac point and opens a bandgap. Our approach is elegant and will serve as an essential reference for realizing the underlying mechanism behind the occurrence of Dirac fermions in the next-generation non-honeycomb lattices. [Display omitted] •Single boron or nitrogen atom doping makes the system metallic. However, semimetallic and semiconducting nature is persuaded for site specific codoping.•Horizontal shift in the position of the Dirac cone is marked depending upon the percentage of doping and interaction between the dopants.•Real space renormalization scheme reduces the lattice to a two level system and reconstructs the band degeneracy near the Fermi level.•Analytical calculation about the position of the Dirac point and Fermi velocity agrees very well with DFT results.•The emergence of Dirac cone is supported by analytical condition deduced from hopping parameters.