Electronic structure of stacking dependent tri-layer graphene on Cu substrate

Free-standing tri-layer graphene shows stacking dependent band gap when external bias is applied. In this work, we have made an attempt to observe the electronic structure of tri-layer graphene with different stacking on Cu (111) substrate without applying any external bias. We have performed density functional theory (DFT) calculation and observe that band gap occurs and doping takes place due to the interaction of graphene-metal surface. We have also calculated density of states for different stacking systems. We observe that the band gap and doping of graphene on substrate largely depend on the stacking system and such study would be beneficial for material science as well as electronic industry.