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We investigate the superconductivity (SC) driven by correlation effects inelectron-doped bilayer BiH near a type-II van Hove singularity (vHS). Byfunctional renormalization group, we find triplet $p$-wave pairing prevails inthe interaction parameter space, except for spin density wave (SDW) closer tothe vHS or when the interaction is too strong. Because of the large atomicspin-orbital coupling (SOC), the $p$-wave pairing occurs between equal-spinelectrons, and is chiral and two-fold degenerate. The chiral state supportsin-gap edge states, even though the low energy bands in the SC state aretopologically trivial. The absence of mirror symmetry allows Rashba SOC thatcouples unequal spins, but we find its effect is of very high order, and canonly drive the chiral $p$-wave into helical $p$-wave deep in the SC state.Interestingly, there is a six-fold degeneracy in the helical states, reflectedby the relative phase angle $\theta=n\pi/3$ (for integer $n$) between the spincomponents of the helical pairing function. The phase angle is shown to bestable in the vortex state.

Chiral and helical $p$-wave superconductivity in doped bilayer BiH