The anisotropy of Dirac cones in rectangular lattices

Thanks to the perfect hexagonal lattice, graphene holds the isotropic Dirac cone. This means the group velocities of charge carriers in the vicinity of Dirac point are isotropic in the momentum space. When the lattice structure varies, 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 two-dimensional carbon allotropes with the rectangular lattice are studied using the first-principles method. Although the existence of Dirac cone critically depends on the hopping parameters within the unit cell, the anisotropy of Dirac cone is another story. This is because the anisotropy of Dirac cone describes the relation between carrier's velocities, and thus is momentum-dependent. It is demonstrated that the anisotropy of Dirac cone can be regarded as an information carrier. This will be the focus of future research.