  We analyze the possible dynamical chiral symmetry breaking patterns taking
place within Weyl type of materials. Here, these systems are modeled by the
(2+1)-dimensional Gross-Neveu model with a tilt in the Dirac cone. The
optimized perturbation theory (OPT) is employed in order to evaluate the
effective potential at finite temperatures and chemical potentials beyond the
traditional large-$N$ limit. The nonperturbative finite-$N$ corrections
generated by the OPT method and its associated variational procedure show that
a first-order phase transition boundary, missed at large $N$, exists in the
regime of low temperatures and large chemical potentials. This result, which
represents our main finding, implies that one should hit a region of mixed
phases when exploring the low-temperature range. The associated first order
transition line, which starts at $T=0$, terminates at a tricritical point such
that the transitions taking place at high $T$ are of the second kind. In
particular, we discuss how the tilt in the Dirac cone affects the position of
the tricritical point as well as the values of critical temperature and
coexistence chemical potential among other quantities. Some experimental
implications and predictions are also briefly discussed.
