  Correlated ad-atom systems on the Si(111) surface have recently attracted an
increased attention as strongly correlated systems with a rich phase diagram.
We study these materials by a single band model on the triangular lattice
including 1/r long-range interaction. Employing the recently proposed TRILEX
method we find an unconventional superconducting phase of chiral d-wave
symmetry in hole-doped systems. The superconductivity is driven simultaneously
by both charge and spin fluctuations and is strongly enhanced by the long-range
tail of the interaction. We provide an analysis of the relevant collective
bosonic modes and explain how in triangular symmetry both charge and spin
channels contribute to the Cooper-pairing.
