Abstract: Motivated by the recent successful synthesis of the layered platinum mineral jacutingaite (Pt2HgSe3), we have studied the optoelectronic, mechanical, and thermoelectric properties of graphene hetero-multilayer on Pt(2)HgSe(3)monolayer (PHS) heterostructures (LG/PHS) by using first-principles calculations. PHS is a topological insulator with a band gap of about 160 meV with fully relativistic calculations; when graphene layers are stacked on PHS, a narrow band gap of similar to 10-15 meV opens. In the presence of gate-voltage and out-of plane strain,i.e.pressure, the electronic properties are modified; the Dirac-cone of graphene can be shifted upwards (downward) to a lower (higher) binding energy. The absorption spectrum shows two peaks, which are located around 216 nm (5.74 eV) and protracted to 490 nm (2.53 eV), indicating that PHS could absorb more visible light. Increasing the number of graphene layers on PHS has a positive impact on the UV-vis light absorption and gives a clear red-shift with enhanced absorption intensity. To investigate the electronic performance of the heterostructure, the electrical conductance and thermopower of a device composed of graphene layers and PHS is examined by a combination of DFT and Green function formalism. The number of graphene layers can significantly tune the thermopower and electrical conductance. This analysis reveals that the heterostructures not only significantly affect the electronic properties, but they can also be used as an efficient way to modulate the optic and thermoelectric properties.