Nature of the surface states at the single-layer graphene/Cu(111) and graphene/polycrystalline-Cu interfaces

Single-layer graphene supported on a metal surface has shown remarkable properties relevant for novel electronic and optoelectronic devices. However, the nature of the electronic states derived from unoccupied surface states and quantum well states, lying in the real-space gap between the graphene and the solid surface, has not been explored and exploited yet. Herein, we use ultraviolet nonlinear angle-resolved photoemission spectroscopy to unveil the coexistence at the graphene/Cu(111) interface of a highest occupied Shockley surface state (HOSS) and the two lowest unoccupied surface states (LUSS). The experimental results and electronic structure calculations, based on one-dimensional model potential, indicate that the two unoccupied states originate from the hybridization of an n=1 image potential state with a quantum well state. The hybridized nature of these unoccupied states is benchmarked by a similar experiment done on single-layer graphene grown on copper polycrystalline foil where only the image state survives being the quantum well state at this interface inhibited.