Analytical expressions for the polarizability of the honeycomb lattice

作者：Stauber T^*

来源：Physical Review B, 2010, 82(20): 201404.

DOI：10.1103/PhysRevB.82.201404

We present analytical expressions for the polarizability P-mu(q(x), omega)of graphene modeled by the hexagonal tight-binding model for small wave number q(x) (Gamma- M direction) but arbitrary chemical potential mu. Generally, we find P-mu(q(x), omega) = P-mu(<)(omega/omega(q))+q(x)(2)P(mu)(>)(omega) with omega(q) = upsilon(F)q(x) the Dirac energy, where the first term is due to intraband and the second due to interband transitions. Explicitly, we derive the analytical expression for the imaginary part of the polarizability including intraband contributions and recover the result obtained from the Dirac cone approximation for mu -> 0. For mu < root 3t, there is a square-root singularity at omega(q) = upsilon(F)q(x) independent of mu. For doping levels close to the van Hove singularity, mu = t +/- delta mu, Im P-mu(q(x), omega) is constant for delta mu/t < omega/omega(q) << 1.

• 出版日期2010-11-8