  The description of the electromagnetic interaction in two-dimensional Dirac
materials, such as graphene and transition-metal dichalcogenides, in which
electrons move in the plane and interact via virtual photons in 3d, leads
naturally to the emergence of a projected non-local theory, called
pseudo-quantum electrodynamics (PQED), as an effective model suitable for
describing electromagnetic interaction in these systems. In this work, we
investigate the role of a complete set of four-fermion interactions in the
renormalization group functions when we coupled it with the anisotropic version
of massive PQED, where we take into account the fact that the Fermi velocity is
not equal to the light velocity. We calculate the electron self-energy in the
dominant order in the $1/N$ expansion in the regime where $m ^ 2 \ll p ^ 2$. We
show that the Fermi velocity renormalization is insensitive to the presence of
quartic fermionic interactions, whereas the renormalized mass may have two
different asymptotic behaviors at the high-density limit, which means a
high-energy scale.
