  Motivated by the recent observation of correlated insulator states and
unconventional superconductivity in twisted bilayer graphene, we study the
dependence of electron correlations on the twist angle and reveal the existence
of strong correlations over a narrow range of twist-angles near the magic
angle. Specifically, we determine the on-site and extended Hubbard parameters
of the low-energy Wannier states using an atomistic quantum-mechanical
approach. The ratio of the on-site Hubbard parameter and the width of the flat
bands, which is an indicator of the strength of electron correlations, depends
sensitively on the screening by the semiconducting substrate and the metallic
gates. Including the effect of long-ranged Coulomb interactions significantly
reduces electron correlations and explains the experimentally observed
sensitivity of strong correlation phenomena on twist angle.
