Cooper pair condensation from entanglement-entropy collapse of many-body states in sheared bilayer graphene

It is known that the sheared graphene bilayers can be tuned to have flat low-energy bands for sufficiently large size of their moiré supercell. In this regime, we adopt an exact diagonalization approach, on top of a Hartree-Fock approximation, to show how the condensation of Cooper pairs takes place in the strong-coupling limit of a valley-polarized flat band. A key factor of our proposal is the existence of zero entanglement-entropy many-body states, just made of a single Slater determinant, which are immune to the hybridization with the rest of many-body states under the strong Coulomb interaction. Moreover, we show that single-particle states with reverse sign of valley symmetry breaking have complementary charge distributions in the supercell, leading to a ground state where the Coulomb repulsion is minimized by placing electrons with opposite spin in different valleys. We argue that the collapse of the entanglement entropy causes the formation of many-body ground states with Cooper pairs made of electrons and their respective partners under valley symmetry, unveiling a strong-coupling mechanism of condensation in a flat band with initially no Fermi line.