Confinement-deconfinement transition in three-dimensional QED

We argue that, at finite temperature, parity-invariant electrodynamics with massive electrons in 2+1 dimensions can exist in both confined and deconfined phases and has a confinement-deconfinement phase transition of Berezinskii-Kosterlitz-Thouless type. We show that an order parameter for the confinement-deconfinement phase transition is a version of the Polyakov loop operator whose average measures the free energy of an external charge that is not an integral multiple of the electron charge.