  We consider three dimensional quantum electrodynamics (cQED3) with massless
relativistic fermions coupled to a compact gauge field using a combined
perturbative variational approach. Coupling to matter renders the bare
interaction between magnetic monopoles logarithmic at large distances,
suggesting the possibility of a confinement-deconfinement transition of the
Berezinskii-Kosterlitz-Thouless type in the theory. Our self-consistent
calculation suggests, however, that screening effects always destabilise the
confined phase, in agreement with the previous renormalisation group study of
the same model.
