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

We examine the dynamical property of the polarization function for electrons with the tilted Dirac cone, considering the case where the chemical potential measured from the contact point is finite, as found in the organic conductor alpha-(BEDT-TTF)(2)I-3 [BEDT-TTF = bis(ethylene-dithio)tetrathiafulvalene] at ambient pressure. Using the tilted Weyl equation with the analytical treatment of the particle-hole excitation, we show that the polarization function as a function of both the frequency and the momentum exhibits cusps and nonmonotonic structures. The polarization function depends not only on the magnitude but also on the direction of the external momentum. These properties are characteristic of the tilted Dirac cone, and are in contrast to those in the isotropic case of graphene. Furthermore, the results are applied to calculate the optical conductivity, plasma frequency, and the screening of Coulomb interaction, which are also strongly influenced by the tilted cone.