The Unconventional Transport Properties of Dirac Fermions in Graphyne

A two-band Hamiltonian for β-graphyne is derived by the k?p method. The energy dispersions around the Dirac points are analytically obtained depending on the relative amplitude of the hopping terms t₁/t₂, and the Dirac cones are elliptical when ?2t₁/t₂j. This interesting feature is useful for direction-dependent wave filter devices.