Effect of gauge boson mass on chiral symmetry breaking in three-dimensional QED

In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the Dyson-Schwinger equation for the fermion self-energy in the Landau gauge and find that chiral symmetry breaking (CSB) occurs when the gauge boson mass ξ is smaller than a finite critical value ξcv but is suppressed when ξ>ξcv. We further show that the critical value ξcv does not qualitatively change after considering higher order corrections from the wave function renormalization and vertex function. Based on the relation between CSB and the gauge boson mass ξ, we give a field theoretical description of the competing antiferromagnetic and superconducting orders and, in particular, the coexistence of these two orders in high temperature superconductors. When the gauge boson mass ξ is generated via the instanton effect in a compact QED3 of massless fermions, our result shows that CSB coexists with the instanton effect in a wide region of ξ, which can be used to study the confinement-deconfinement phase transition