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

TL;DR

This study uses density functional theory to explore the electronic properties, topological surface states, and nonlinear dielectric response of rhombohedral (ABC) graphene stacks, revealing their potential for tunable electronic applications.

Contribution

It demonstrates that (ABC) graphene stacks are topologically non-trivial with surface states and exhibit a strongly nonlinear dielectric response, unlike (AB) stacks, highlighting their unique electronic tunability.

Findings

(ABC) stacks have topologically protected surface states crossing the Fermi level.

Bulk-like states in (ABC) stacks develop a gap at finite thickness.

Dielectric response of (ABC) stacks is strongly nonlinear and layer-dependent.

Abstract

A DFT-based investigation of rhombohedral (ABC)-type graphene stacks in finite static electric fields is presented. Electronic band structures and field-induced charge densities are compared with related literature data as well as with 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-$\Gamma$. In contrast to (AB) stacks, the breaking of translational symmetry by the surface of finite (ABC) stacks produces a gap in the bulk-like states for slabs up to a yet unknown critical thickness $N^{\rm semimet} \gg 10$, while ideal (ABC) bulk ($\beta$-graphite) is a semi-metal. Unlike in (AB) stacks, the ground state of (ABC) stacks is shown to be topologically non-trivial in the absence of 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 bulk-like states have two major implications. First, electronic transport parallel to the slab is confined to a surface region up to the critical layer number $N^{\rm semimet}$. 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.