The possibility of superconductivity in twisted bilayer graphene

We discuss the possibility of superconductivity in Twisted Bilayer Graphene (TBG). In this study we use TBG model with commensurate rotation θ=1.16° in which the van-Hove singularities (VHS) arise at 6 meV from the Fermi level. We use BCS standard formula that include Density of States (DOS) to calculate the critical temperature (TC). Based on our calculation we predict that superconductivity will not arise in Pristine TBG because pairing potential has infinity value. In this situation, Dirac Fermions do not interact with each other since they do not form the bound states. Superconductvity may arise when the Fermi level is shifted towards the VHS. Based on this calculation, we predict that TC has value between 0.04 K and 0.12 K. The low value of TC is due to highly energetic of in plane phonon vibration which reduce the effective electron-phonon coupling. We conclude that doped TBG is candidate for Dirac Fermion superconductor.