Wannier pairs in superconducting twisted bilayer graphene and related systems

Unconventional superconductivity often arises from Cooper pairing between neighboring atomic sites, stipulating a characteristic pairing symmetry in the reciprocal space. The twisted bilayer graphene (TBG) presents a new setting where superconductivity emerges on the flatbands whose Wannier wave functions spread over many graphene unit cells, forming the so-called moiré pattern. To unravel how Wannier states form Cooper pairs, we study the interplay between electronic, structural, and pairing instabilities in TBG. For comparisons, we also study graphene on boron-nitride (GBN) possessing a different moiré pattern, and single-layer graphene (SLG) without a moiré pattern. For all cases, we compute the pairing eigenvalues and eigenfunctions by solving a linearized superconducting gap equation, where the spin-fluctuation mediated pairing potential is evaluated from materials-specific tight-binding band structures. We find an extended s wave as the leading pairing symmetry in TBG, in which the nearest-neighbor Wannier sites form Cooper pairs with same phase. In contrast, GBN assumes a p+ip-wave pairing between nearest-neighbor Wannier states with odd-parity phase, while SLG has the d+id-wave symmetry for intersublattice pairing with even-parity phase. Moreover, p+ip and d+id pairings are chiral, and nodeless, but the extended s-wave channel possesses accidental nodes. The nodal pairing symmetry makes it easily distinguishable via power-law dependencies in thermodynamical entities, in addition to their direct visualization via spectroscopies.