Analytical expressions for the polarizability of the honeycomb lattice

Details Analytical expressions for the polarizability of the honeycomb lattice Analytical expressions for the polarizability of the honeycomb lattice

2010-10-23

arxiv.org/abs/1010.4860v2

Phys. Rev. B 82, 201404(R) (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, 3 figures, 1 table

Scientific paper

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 $q_x$, but arbitrary chemical potential $\mu$. Generally, we find $P_\mu(q_x,\omega)=P_\mu^<(\omega/\omega_q)+q_x^2P_\mu^>(\omega)$ with $\omega_q=v_Fq_x$ the Dirac energy, where the first term is due to intra-band and the second due to inter-band transitions. Explicitly, we derive the analytical expression for the imaginary part of the polarizability including intra-band contributions and recover the result obtained from the Dirac cone approximation for $\mu\rightarrow0$. For $\mu<\sqrt{3}t$, there is a square-root singularity at $\omega_q=v_Fq_x$ independent of $\mu$. For doping levels close to the van Hove singularity, $\mu=t\pm\delta\mu$, $ImP_\mu(q_x,\omega)$ is constant for $\delta\mu/t<\omega/\omega_q\ll1$.

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