Dirac Fermion State with Real Space π-Flux on Anisotropic Square Lattice and Triangular Lattice

We demonstrate that the presence of real space π-flux enlarges the parameter space where a Dirac fermion spectrum is realized. This type of Dirac fermions is characterized not only by the Berry phase π but also by the real space π-flux. We show that this type of Dirac fermions is stabilized on a square lattice and on a triangular lattice in the presence of anisotropy in hopping parameters by the exchange interaction effect associated with the nearest-neighbor interaction, which plays a key role in organic compounds. In the case of a triangular lattice a stripe pattern appears.