Gap opening at the Dirac point of graphene on Cu(111): Hybridization versus sublattice symmetry breaking

Abstract

Gap opening at the Dirac point of graphene on metals has been ascribed to hybridization, sublattice symmetry breaking, or combination of both. However, how and what to extent gap opens under the influence of these effects has been a question in controversy. In this paper, we explore gap opening in graphene on metals using a simple tight-binding (TB) model for a hypothetical heterobilayer, which mimics a system of graphene/metal. A theoretical framework for the gap opening is obtained using exact solutions to the TB-model Hamiltonian through small-parameter expansions. This result is formally similar to that obtained for an ad hoc model graphene with pseudospin asymmetry originating from the spin-orbit proximity effect, which is not considered in the present analysis but is taken over by more substantial effect of orbital-hybridization indispensable for the gap opening in graphene on metals. The present result reveals, for the first time, that sublattice symmetry breaking and hybridization asymmetry compensate each other and disruptively contribute to the gap opening at the Dirac point of graphene on metals. The picture is in marked contrast to the previous ones such as hybridization-induced sublattice symmetry breaking or an additive model, in which sublattice symmetry breaking and hybridization additively contribute to the gap opening. The results obtained by the present TB-model analysis are successfully used to interpret the results of ab initio density functional theory (DFT) calculations for graphene/Cu(111) and thereby, for the first time, to discriminate sublattice symmetry breaking and hybridization asymmetry explicitly. We also find, through these analyses of the DFT calculations, that hybridization asymmetry dominates gap opening at the Dirac point for large graphene-substrate separations (d), while sublattice symmetry breaking is dominant for small d, and both are balanced with each other in between to yield a small gap, which is practically closed in the system of graphene/Cu(111). Another point revealed by those analyses is that sublattice symmetry breaking and hybridization are necessarily in combination with each other and are together large or small depending on interface structures. All these results are expected to provide a useful insight into gap opening at the Dirac point of graphene in other systems including graphene/metal superstructures resulting from lattice mismatch, misorientation, intercalation, or other structural modifications.