High-temperature superconductivity in flat-band sheared bilayer graphene

Abstract

We propose a new route to induce flat bands with a strong superconducting instability in graphene bilayers with heteroshear, where the 1D character of the moir\'e leads to stronger correlations than in twisted bilayer graphene. We adopt an exact diagonalization approach, on top of a real-space self-consistent Hartree-Fock approximation, to show how the valley polarization of the flat band of a sheared bilayer drives the condensation of Cooper pairs. A unique feature of the 1D moir\'e is that single-particle states with reverse sign of the valley polarization have complementary charge distributions in the moir\'e supercell. This leads to many-body states where the Coulomb repulsion in a Cooper pair is greatly reduced by placing electrons with opposite spin in different valleys. At small hole-doping of the flat band, the many-body ground states are formed by recursive addition of single-hole states, which allows us to reconstruct a quasi-1D Fermi line in the originally flat band. We show that even (odd) numbers of holes lead consistently to ground states with lower (higher) values of the compressibility. This provides the signature of the condensation of Cooper pairs with emergent quasiparticles above a large energy gap, unveiling a strong-coupling route to high-temperature superconductivity in topological flat-band systems.