Topological p+ip superconductivity in doped graphene-like single-sheet materials BC₃

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We theoretically study exotic superconducting phases in graphenelike single-sheet material BC₃ doped to its type-II Van Hove singularity whose saddle point momenta are not time-reversal-invariant. From combined renormalization group analysis and RPA calculations, we show that the dominant superconducting instability induced by weak repulsive interactions is in the time-reversal-invariant p+ip pairing channel because of the interplay among dominant ferromagnetic fluctuations, subleading spin fluctuations at finite momentum, and spin-orbit coupling. Such time-reversal-invariant p+ip superconductivity has nontrivial Z₂ topological invariant. Our results show that doped BC₃ provides a promising route to realize a genuine 2D helical p+ip superconductor.