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-. 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 semimet 10, while ideal (ABC) bulk (β 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 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.

Rhombohedral Multilayer Graphene: A Magneto-Raman Scattering Study

“…When increasing the number of ABCstacked layers, the extend of the flat dispersion of the low energy bands increases, while the size of the bulk band gap decreases. 15,16 Notably, the surface states of ABC-stacked graphene multilayers have been reported as topologically protected, due to the symmetry of this material, 16 and may thus resemble those well-known surface states of 3D topological insulators. 17−20 Interestingly, due to weak spin−orbit interaction in carbon-based systems, an even closer analogy is found with the surface states of topological crystalline insulators.…”

Selective fabrication of free-standing ABA and ABC trilayer graphene with/without Dirac-cone energy bands

“…Band-structure calculations have predicted that the electronic states of TL graphene strongly depend on the stacking sequence. 13,14 As shown in Figures 1c and d, TL graphene with ABA stacking (called ABA graphene) features three bands near E F , two of which cross the Fermi level (E F ) at the K point. Importantly, the inner band shows massless Dirac-fermion-like behavior with a linear energy dispersion around E F .…”

Introduction

“…Few-layer graphene with specific stacking configurations, e.g. AA [78][79][80], AB [81][82][83][84][85][86][87][88][89][90][91][92][93], ABC [93][94][95][96][97][98][99] and AAB [64], are predicted to display unique electronic energy dispersions. This new material holds great promise for the development of next-generation electronic and optoelectronic nanodevices [41-47, [50][51][52][53][54][55][56] because the electronic and optical properties can be flexibly tuned by the application of external fields [64][65][66][67][68][69][70][71][72][73][74] as well as changes to the geometric structures and dopants [115][116][117][118][119]…”

“…Few-layer ABC-stacked graphene is a semimetal [93][94][95][96][97][98][99]. The electronic structure is characterized by one pair of partially flat subbands near = E 0 F , and pairs of sombrero-shaped subbands near the energy of the vertical atomic interactions between the nearest-neighboring layers [93][94][95][96][97][98][99].…”

“…The electronic structure is characterized by one pair of partially flat subbands near = E 0 F , and pairs of sombrero-shaped subbands near the energy of the vertical atomic interactions between the nearest-neighboring layers [93][94][95][96][97][98][99]. Contributed by the surface-localized states [97][98][99], the partially flat subbands give rise to a prominent peak in the density of states (DOS) and play an important role in the low-frequency optical spectrum [110,112].…”