Topologicalp+ipsuperconductivity in doped graphene-like single-sheet materialsBC3

We theoretically study exotic superconducting phases in graphenelike\nsingle-sheet material BC$_3$ doped to its type-II Van Hove singularity whose\nsaddle point momenta are {\\it not} time-reversal-invariant. From combined\nrenormalization group analysis and RPA calculations, we show that the dominant\nsuperconducting instability induced by weak repulsive interactions is in the\ntime-reversal-invariant $p+ip$ pairing channel because of the interplay among\ndominant ferromagnetic fluctuations, subleading spin fluctuations at finite\nmomentum, and spin-orbit coupling. Such time-reversal-invariant $p+ip$\nsuperconductivity has nontrivial $\\mathbb{Z}_2$ topological invariant. Our\nresults show that doped BC$_3$ provides a promising route to realize a genuine\n2D helical $p+ip$ superconductor.\n