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.
Highlights
The recent discovery of graphene1) has attracted much attention in the field of condensed matter because graphene exhibits 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 -(BEDT-TTF)2 I3 [BEDT-TTF = bis(ethylene-dithio)tetrathiafulvalene]
Using the Weyl equation,2,3) which describes the motion of massless Dirac fermions, several anomalous electronic properties have been investigated for a long time.4,5) Another massless Dirac fermion is found in the quasi-two-dimensional organic conductor -(BEDT-TTF)2 I3 [BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene] under pressure.6,7) The existence was demonstrated theoretically8,9) using the band calculation, which is based on the transfer integrals estimated from the X-ray structure analysis.10) Such an energy band has been confirmed by first-principles calculations.11,12) This novel state elucidates a long standing problem of anomalous phenomena observed in the conductor under pressure.13,14)
Summary
The recent discovery of graphene1) has attracted much attention in the field of condensed matter because graphene exhibits massless Dirac fermions. We analytically examine the dynamical polarization function with the arbitrary wavevector and frequency, and compare it with that in the isotropic case of graphene.26–30) We examine the metallic state where the contact point of the Dirac cone is located below the Fermi energy as expected for the organic conductor -(BEDT-TTF) I3 .7,9,10) In §2, formulation for the polarization function is given. We consider the zero-gap state in -(BEDT-TTF) I3 , which has two tilted Dirac cones.9) Among two contact points, k0 , corresponding to two valleys of cones, we focus on one of them, which is given by the state located close to k0 (1⁄4 k0x ; k0y ) with k0x < 0 and k0y > 0 For such a state, the effective Hamiltonian is expressed as). We note that, by taking account of the freedom of both spin and valley, the polarization function of the total system is given by total ðq; !Þ 1⁄4 ðq; !Þ þ ðq; !Þ: Polarization Function
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
