  In this work, we demonstrate that the mixing of scalar and vector condensates
produces spatially oscillating, but exponentially damped correlation functions
in fermionic theories at finite density and temperature. We find a regime
exhibiting this oscillatory behavior in a Gross-Neveu-type model that also
features vector interactions within the mean-field approximation. The existence
of this regime aligns with expectations based on symmetry arguments, that are
also applicable to QCD at finite baryon density. We compute the phase diagram
including both homogeneous phases and regions with spatially oscillating,
exponentially damped correlation functions at finite temperature and chemical
potential for different strengths of the vector coupling. Furthermore, we find
that inhomogeneous condensates are disfavored compared to homogeneous ones akin
to previous findings without vector interactions. We show that our results are
valid for a broad class of $\left(2+1\right)$-dimensional models with local
four-fermion interactions.
