  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.
