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/t ₂, and the Dirac cones are elliptical when -2 < t ₁/t₂ < -1. This anisotropic Dirac Hamiltonian leads to electron current direction misalignment with the wave vector, and the transmission spectrum is asymmetric about the incident angle of current, j. This interesting feature is useful for direction-dependent wave filter devices.