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

TL;DR

This paper analyzes how the tilt in Dirac cones affects the polarization function of electrons, revealing unique cusps and nonmonotonic behaviors that influence optical and screening properties.

Contribution

It provides an analytical study of the dynamical polarization function in tilted Dirac cones, highlighting features absent in isotropic graphene.

Findings

Polarization function exhibits cusps and nonmonotonic structures.

Dependence on both magnitude and direction of momentum.

Tilted cone significantly influences optical and screening properties.

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.