Coexistence of Dirac cones and Kagome flat bands in a porous graphene

Abstract

We investigate the geometric and electronic structures of porous graphene networks consisting of phenalenyl and phenyl groups, which are connected alternately with C3 symmetry via single bonds to form a honeycomb network with an internal degree of freedom. The networks possess both Dirac cones and Kagome flat bands near the Fermi level (EF) because the phenalenyl and phenyl form hexagonal and Kagome lattices, respectively. Because of the large spacing between phenalenyl units, the networks possess very slow massless electrons/holes at EF, the Fermi velocity of which is a hundred times lower than that of graphene, leading to spin polarization on the networks with antiferromagnetic (AF) and ferromagnetic (F) ordering as their stable states. Our calculations show the AF state is the ground state whose energy is lower by 14 meV than that of the F state. We also demonstrate that the electronic structure of the 2D networks is sensitive to the rotation of the phenyl unit connecting phenalenyl units by changing the π electron network.