Extended Coupled Cluster approach to Twisted Graphene Layers

A study of correlation effects in twisted bilayer graphene, using the extended coupled cluster method, is presented. This approach considers 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. The superconducting gap is found to be maximal at a twist angle of $\theta_c = 1.00 \deg$ with a roughly equal combination of s-wave and f-wave components. Using BCS theory, the size of the gap corresponds to a critical temperature value of $T_\text{c}^\text{BCS} = 0.5$K. This matches qualitatively with experimental data. Within the limitation of the numerical truncations used, a novel candidate for the mechanism behind superconductive phases in twisted bilayer graphene is proposed.