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We theoretically study exotic superconducting phases in graphenelikesingle-sheet material BC$_3$ doped to its type-II Van Hove singularity whosesaddle point momenta are {\it not} time-reversal-invariant. From combinedrenormalization group analysis and RPA calculations, we show that the dominantsuperconducting instability induced by weak repulsive interactions is in thetime-reversal-invariant $p+ip$ pairing channel because of the interplay amongdominant ferromagnetic fluctuations, subleading spin fluctuations at finitemomentum, and spin-orbit coupling. Such time-reversal-invariant $p+ip$superconductivity has nontrivial $\mathbb{Z}_2$ topological invariant. Ourresults show that doped BC$_3$ provides a promising route to realize a genuine2D helical $p+ip$ superconductor.

Topological p+ip superconductivity in doped graphene-like single-sheet materials BC$_3$