Effect of interactions on Dirac points in organic solids

We examine the effect of inter-site interactions in the anisotropic triangular lattice with α- type symmetry, which has a linear energy dispersion called Dirac point. Charge disproportionation without inversion symmetry breaking is made a sharp distinction from charge order which is accompanied by the symmetry breaking, and only the latter is found to be responsible for the destruction of Dirac points. We also show that in the weak coupling case, the small density of states near the Fermi level protects the Dirac points from the instability towards charge order.