Will electrons in graphene behave as in pure 2D space, that is they interact with eachother by a Coulomb potential ~ $\ln r$ instead of $1/r$? I think many force lines will "leak" out of graphene membrane $M(x,y)$ so 2D Poisson's equation for charge distribution in graphene $\Delta V(x,y) = - \varepsilon _0^{ - 1}\rho (x,y)$ never hold. It should be $\Delta V(x,y,z) = - \varepsilon _0^{ - 1}\rho (x,y)\delta (z)$. Is there a 'modified 2D Poisson's equation' for graphene?
Sorry for my English!