Density functional investigation of rhombohedral stacks of graphene: Topological surface states, nonlinear dielectric response, and bulk limit

Abstract

A comprehensive density-functional theory (DFT)-based investigation of rhombohedral (ABC)-type graphene stacks with finite and infinite layer numbers and zero or finite static electric fields applied perpendicular to the surface is presented. Electronic band structures and field-induced charge densities are critically compared with related literature data including tight-binding and DFT approaches as well as with our own results on (AB) stacks. It is found that the undoped AB bilayer has a tiny Fermi line consisting of one electron pocket around the K point and one hole pocket on the line K-$\ensuremath{\Gamma}$. In contrast to (AB) stacks, the breaking of translational symmetry by the surface of finite (ABC) stacks produces a gap in the bulklike states for slabs up to a yet unknown critical thickness ${N}^{\mathrm{semimet}}\ensuremath{\gg}10$, while ideal (ABC) bulk ($\ensuremath{\beta}$ graphite) is a semimetal. Unlike in (AB) stacks, the ground state of (ABC) stacks is shown to be topologically nontrivial in the absence of an external electric field. Consequently, surface states crossing the Fermi level must unavoidably exist in the case of (ABC)-type stacking, which is not the case in (AB)-type stacks. These surface states in conjunction with the mentioned gap in the bulklike states have two major implications. First, electronic transport parallel to the slab is confined to a surface region up to the critical layer number ${N}^{\mathrm{semimet}}$. Related implications are expected for stacking domain walls and grain boundaries. Second, the electronic properties of (ABC) stacks are highly tunable by an external electric field. In particular, the dielectric response is found to be strongly nonlinear and can, e.g., be used to discriminate slabs with different layer numbers. Thus, (ABC) stacks rather than (AB) stacks with more than two layers should be of potential interest for applications relying on the tunability by an electric field.