Unconventional superconductivity in a doped quantum spin Hall insulator

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.