Tilted-Cone Induced Cusps and Nonmonotonic Structures in Dynamical Polarization Function of Massless Dirac Fermions

Abstract

The polarization function of electrons with the tilted Dirac cone found in organic conductors is studied using the tilted Weyl equation. The dynamical property is explored based on the analytical treatment of the particle-hole excitation. It is shown that the polarization function as the function of both the frequency and the momentum exhibits cusps and nonmonotonic structures. The polarization function depends not only on the magnitude but also the direction of the external momentum. These properties are characteristic of the tilted Dirac cone, and are contrast to the isotropic case of grapheme. Further, the results are applied to calculate the optical conductivity, the plasma frequency and the screening of Coulomb interaction, which are also strongly influenced by the tilted cone.