Fermi velocity and magic angle renormalization in twisted bilayer graphene

We discuss the Fermi-velocity renormalization in twisted bilayer graphene due to Coulomb exchange interaction within an atomistic tight-binding model. Adopting the Slater-Koster parametrization for the hopping parameters obtained from first principles, our results only depend on the effective dielectric constant $ε$ and the Hubbard-interaction U. The Fermi velocity of graphene increases twist-angle independent by $~25%$ for $ε=10$ and $U=4eV$, leading to an increase by more than $100%$ of the flat bandwidth at twist-angle θ=1.4^∘. Including also the renormalization of the out-of-plane hopping terms, we further observe a shift of the magic angle from 1.02^∘ to 0.96^∘. Our results offer a microscopic explanation of the critical temperature, Tc, as function of the twist angle where the largest Tc is found at θₘₐₓ=1.1^∘. For θ>θₘₐₓ, Tc is obtained from the Bethe-Salpeter equation of the Cooper channel. For θ<θₘₐₓ, the discussion is based on the critical line of the Berezinskii-Kosterlitz-Thouless phase transition.