Topological chiral superconductivity beyond BCS pairing mechanism

We investigate a mechanism to produce superconductivity by strong purely repulsive interactions for flat dispersion ε∼k^4, without using pairing instability in Fermi-liquid. The resulting superconductors break both time-reversal and reflection symmetries in the orbital motion of electrons, and exhibit non-trivial topological order. Our findings suggest that this topological chiral superconductivity is more likely to emerge near or between fully spin-valley polarized metallic phase and Wigner crystal phase in multi-layer graphene. These topological chiral superconductors can be fully or partially spin-valley polarized. For partial spin-valley polarization, the ratios of electron densities associated with different spin-valley quantum numbers are quantized as simple rational numbers. Furthermore, many of these topological chiral superconductors exhibit charge-4 or higher condensation, neutral quasiparticles with fractional statistics, and/or gapless chiral edge states. Two of the topological chiral superconductors are in the same phases as the ``spin''-triplet or spinless p+ip BCS superconductor, while others are in different phases than any BCS superconductors.