  The low-energy physics of rhombohedral $N$-layer graphene mainly arises on
the external layers, where most of the {\pi} electrons are located. Their Bloch
band structure defines a two-band semimetal; the dispersion relation scales as
$\pm q^{N}$ with the momentum norm $q$ in the vicinity of two nonequivalent
valleys. In this paper, we address the problem of elastic scattering through a
localized impurity located either on the surface of the material or within the
bulk, and focus on the quantum interferences it induces on the two external
layers. It is apprehended in the framework of a $T$-matrix approach, both
numerically and analytically, regardless of the impurity magnitude, which
enables the description of realistic scatters. In rhombohedral multilayer
graphene, the impurity induces Friedel oscillations that always decay as $1/r$.
As a result, monolayer graphene is the only material of the rhombohedral class
that exhibits $1/r^{2}$-decaying Friedel oscillations. The interference
patterns are subsequently analyzed in momentum space. This analysis enables a
clear distinction between monolayer graphene and multilayer graphene. It also
shows that the interference pattern reveals the whole Bloch band structure, and
highlights the number of layers stacked in the material, as well as the
${\pi}$-quantized Berry phases that characterize the existence of nodal points
in the semimetallic spectrum. Experimentally, these features may be probed from
scanning tunneling microscopy, when imaging the local density of states at the
surfaces of suspended rhombohedral $N$-layer graphene.
