Interaction corrections to the minimal conductivity of graphene via dimensional regularization

Abstract

We compute the two-loop interaction correction to the minimal conductivity of\ndisorder-free intrinsic graphene with the help of dimensional regularization.\nThe calculation is done in two different ways: via density-density and via\ncurrent-current correlation functions. Upon properly renormalizing the\nperturbation theory, in both cases, we find that: $\\sigma = \\sigma_0\\,( 1 +\n\\al\\,(19-6\\pi)/12) \\approx \\sigma_0 \\,(1 + 0.01\\, \\al)$, where $\\al = e^2 / (4\n\\pi \\hbar v)$ is the renormalized fine structure constant and $\\sigma_0 = e^2 /\n(4 \\hbar)$. Our results are consistent with experimental uncertainties and\nresolve a theoretical dispute.\n