Extended coupled-cluster approach to twisted graphene layers

A study of correlation effects in graphene and twisted bilayer graphene is presented, using the extended-coupled-cluster method. The extended coupled-cluster approach contains both self-consistent mean-field and beyond mean-field contributions, and can describe phase transitions in such strongly correlated systems, without further inputs or assumptions. Detailed expressions and a suitable implementation for the method are developed. Combining modern tensor contraction techniques with singular value decomposition, the correlation effects are successfully described in a qualitative manner, including contributions from the short-range and long-range parts of the Coulomb interaction. We demonstrate validity of the method for use in graphene. Within the approximations used, the superconducting gap shows a possible maximum near a twist angle of 𝜃𝑐 ≈ 1.00°. A rough Bardeen-Cooper-Schrieffer (BCS) scale estimate gives 𝑇BCSc ≈ 0.5K, broadly consistent in order of magnitude with experimental reports. These results constitute a qualitative, proof-of-principle indication of a correlation-driven pairing tendency in twisted bilayer graphene; a more quantitative identification of the superconducting mechanism would require substantial further computational resources.