A monolayer of jacutingaite (${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$) has recently been identified as a novel quantum spin Hall insulator. By first-principles calculations, we study its Fermiology in the doped regime and unveil a type-I and type-II van Hove singularity for hole and electron doping, respectively. We find that the common link between the propensity for a topological band gap at pristine filling and unconventional superconductivity at finite doping is rooted in the longer-ranged hybridization integrals on the honeycomb lattice. In a combined effort of random phase approximation and functional renormalization group, we find chiral $d$-wave order for the type-I and odd-parity $f$-wave order for the type-II regime. When longer-ranged Coulomb interaction is included, a propensity of the type-II regime towards a topological $p_x+i{p}_y$-wave order emerges.

• Received 15 November 2018

DOI:https://doi.org/10.1103/PhysRevB.100.041117