Exchange and Correlation in Graphene

Chirality and Correlations in Graphene

Y. Barlas, T. Pereg-Barnea, M. Polini, R. Asgari, and A.H. MacDonald

PRL 98, 236601 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e236601

This article was a pleasure to read. I've been reading about the use of techniques from field theory in condensed matter physics lately, and I got to see them in action here.

This group from Texas has evaluated the effects of exchange and correlation on the charge and spin susceptibility of graphene. They start from the massless Dirac equation that describes low energy excitations in graphene and calculate the interaction energy. The technique they used was new to me.

First, they write down an expression for the interaction energy that depends on the structure factor of the interacting system. The interaction energy appears to be calculated by adiabatically turning on the coupling between particles. The structure factor is calculated from the density-density response function, a relation based on the fluctuation dissipation theorem. The response function can be calculated in the random phase approximation using methods of quantum field theory. The authors combine a lot of neat tools to obtain the interaction energy. It's all condensed into one paragraph in this paper. I'll have to check out their reference, Giuliani and Vignale's "Quantum Theory of the Electron Liquid."

Though the techniques are well-established, they lead to surprising results in graphene. The authors find that the sign of the correections to the spin and charge susceptibilities is opposite that of the usual electron gas. The similarity of the response functions is also different from an electron gas. The exchange effect decreases the susceptibilities in graphene, while it enhances them in the normal 2DEG. The authors trace the difference in behavior to the renormalized fermi velocity, which increases with the interaction strength.

Once I am more comfortable with the techniques I'm learning from Abrikosov and Mattuck, I'm going to try and reproduce these results.