Interaction corrections to the minimal conductivity of graphene via dimensional regularization

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