  A Chern--Simons system in $2+1$ dimensions invariant under local Lorentz
rotations, $SU(2)$ gauge transformations, and local $\mathcal{N}=2$
supersymmetry transformations is proposed. The field content is that of
$(2+1)$-gravity plus an $SU(2)$ gauge field, a spin-1/2 fermion charged with
respect to $SU(2)$ and a trivial free abelian gauge field. A peculiarity of the
model is the absence of gravitini, although it includes gravity and
supersymmetry. Likewise, no gauginos are present. All the parameters involved
in the system are either protected by gauge invariance or emerge as integration
constants. An effective mass and effective cosmological constant emerge by
spontaneus breaking of local scaling invariance. The vacuum sector is defined
by configurations with locally flat Lorentz and $SU(2)$ connections sporting
nontrivial global charges. Three-dimensional Lorentz-flat geometries are
spacetimes of locally constant negative --or zero--, Riemann curvature, which
include Minkowski space, AdS$_3$, BTZ black holes, and point particles. These
solutions admit different numbers of globally defined, covariantly constant
spinors and are therefore good candidates for stable ground states. The
fermionic sector in this system could describe the dynamics of electrons in
graphene in the long wavelength limit near the Dirac points, with the spin
degree of freedom of the electrons represented by the $SU(2)$ label. If this is
the case, the $SU(2)$ gauge field would produce a spin-spin interaction giving
rise to strong correlation of electron pairs.
