Tilted Dirac Cones in Two Dimensions

Abstract

Low symmetries of a crystal structure could allow the energy dispersion to exhibit Weyl fermions with several different velocities. The quasi-two-dimensional organic semiconductor \(\alpha \)-(BEDT-TTF)\(_2\)I\(_3\) has an anisotropic linear dispersion with a zero energy gap near its Fermi level. Since the density of states vanishes at the Fermi level, the Coulomb interaction is unscreened and long-ranged. We study the effect of the long-range Coulomb interaction and the low-energy behavior of the two-dimensional Weyl/Dirac fermions with tilted energy dispersion. The renormalization group analysis within nonrelativistic scheme reveals that the nearly logarithmic enhancement of the velocity parameters reshapes the tilted Dirac cones and changes the low-energy behavior. The suppression of the spin susceptibility at low temperatures is calculated theoretically, which well explains an NMR experiment. By taking into account of the relativistic effect, we observe the recovery of the isotropic Dirac cone and the Lorentz invariance in the low-energy limit, accompanying the Cherenkov radiation. This result applies even when the Dirac cone is strongly tilted and the velocity is negative in one direction.