Quartic semi-Dirac fermions

We propose the first lattice model for the realization of exotic quartic semi-Dirac fermions, i.e. quasiparticles exhibiting a dispersion with quartic momentum dependence in a given direction, and a linear dependence in the perpendicular direction. A tight binding model is employed, allowing for hopping between up to fourth nearest neighbors and anisotropic hopping parameters. In addition, we introduce short range electron–electron interactions which are necessary to stabilize the quartic semi-Dirac phase. Without interactions, or in the presence of long range correlations, the lattice is unstable towards formation of either anisotropic Dirac cones, or simple (quadratic) semi-Dirac phase.