We theoretically study exotic superconducting phases in graphene-like single-sheet material ${\mathrm{BC}}_3$ doped to its type-II van Hove singularity whose saddle-point momenta are not time-reversal invariant. From combined renormalization group analysis and random-phase approximation 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 ${\mathbb{Z}}_2$ topological invariant. Our results show that doped ${\mathrm{BC}}_3$ provides a promising route to realizing a genuine two-dimensional helical $p+ip$ superconductor.

• Received 4 May 2014

DOI:https://doi.org/10.1103/PhysRevB.92.174503