Crystal momentum-dependent anisotropy of the Dirac cone in the rectangular carbon allotropes

Abstract

Thanks to the perfect hexagonal lattice, graphene holds an isotropic Dirac cone. This means that the group velocities of charge carriers in the vicinity of Dirac points are isotropic in momentum space. When the lattice structure varies, the Dirac cone will undergo a dramatic change accordingly. This is the case of 6,6,12-graphyne. Due to the rectangular lattice, Dirac cones of 6,6,12-graphyne are anisotropic. To understand its underlying nature, three additional derivates of 6,6,12-graphyne with the rectangular lattice are studied by using an ab initio method. Although the existence of a Dirac cone critically depends on the hopping energies within the unit cell, the anisotropy of the Dirac cone is another story. This is because the anisotropy of the Dirac cone describes the relation between carriers' group velocities, and is thus direction-dependent in momentum space. Our study demonstrates that the anisotropy of the Dirac cone is tunable through changing the lattice constants or the lattice ratios in the rectangular carbon allotropes. This will be the focus of future research as the anisotropy of the Dirac cone can be regarded as an information carrier.