Flat bands and superconductivity in twisted bilayer graphene: insights from full scale Bogoliubov-de Gennes solutions.

The recently experimentally observed, possibly unconventional, superconducting state in twisted bilayer graphene (TBLG) opens up a highly tunable playground for correlated systems and exotic orders, where optimal conditions for exotic superconductivity are believed to result from a twist induced flattening of the electronic bands. Here we test the distinctive role of the flat bands in the formation and enhancement of superconductivity in TBLG and we detail the resulting implications for unconventional chiral d+id superconductivity. We show these results from the self-consistent solutions of the complete Bogoliubov-de Gennes (BdG) equations of the full tight-binding Hamiltonian of TBLG, which in the case of magic twist angle TBLG with its long wavelength moiré interference pattern poses a formidable computational challenge that we rigorously address with a novel numerical approach.