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Topological Superconductivity in Sn/Si(111) driven by non-local Coulomb interactions

Superconductivity was recently observed in boron-doped ($\sqrt{3}\times\sqrt{3}$)Sn/Si(111). The material can be described by an extended Hubbard model on a triangular lattice. Here, we use the random-phase approximation to investigate the charge and spin fluctuations as well as the superconducting properties of the system with respect to filling and the relative strength of the extended versus the on-site Hubbard interactions. Our calculations reveal that near half-filling and weak extended Hubbard interactions, the superconducting ground state exhibits chiral $d$-wave pairing. Far from half-filling and for stronger nearest-neighbor Coulomb interactions, the system shows chiral $p$-wave (hole-doping) and $f$-wave (electron-doping) pairings. The dependence of the pairing symmetry on the extended Hubbard interactions suggests that charge fluctuations play an important role in the formation of Cooper pairs. Finally, the temperature dependence of the Knight shift is calculated for all observed superconducting textures and put forward as an experimental method to examine the symmetry of the superconducting gap function.