Electronic correlation effects are the heart of complex problems in condensed matter physics. It can induce a wealth of fascinating properties like high-temperature superconductivity and complex magnetic and charge ordering. In real materials, the structural complexity can makes it hard to disentangle these various ordering and trace back their origin to a well-defined theoretical model. We propose in this experimental internship to study a model system of Mott physics on a triangular lattice with an extremely simple chemical structure. We propose to pursue investigations already started in our group on the Pb/Ge(111) phase and reveal the nature of the groundstate. It is predicted not to undergo the Mott transition but to present a charge/lattice ordering. This work could pursued in the framework of a PhD thesis to induce an unconventionnal superconducting phase out of the Sn/Si(111) Mott insulating state by appropriate doping.