Non-perturbative renormalization group calculation of the quasi-particle velocity and the dielectric function of graphene

Abstract

Using a non-perturbative functional renormalization group approach we calculate the renormalized quasi-particle velocity $v(k)$ and the static dielectric function $\hat{I}\mu (k)$ of suspended graphene as functions of an external momentum $k$. Our numerical result for $v(k)$ can be fitted by $v(k)/v_F=A+B\ln (\hat{I}{›}_0/k)$, where $v_F$ is the bare Fermi velocity, $\hat{I}{›}_0$ is an ultraviolet cutoff, and $A=1.37$, $B=0.51$ for the physically relevant value ($e^2/v_F=2.2$) of the coupling constant. In contrast to calculations based on the static random-phase approximation, we find that $\hat{I}\mu (k)$ approaches unity for $k\to 0$. Our result for $v(k)$ agrees very well with a recent measurement by Elias et al. [Nat. Phys. 7, 701 (2011)].

5 pages, 4 figures