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

In three-dimensional quantum electrodynamics (QED(3)) 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 xi is smaller than a finite critical value xi(cv) but is suppressed when xi>xi(cv). We further show that the critical value xi(cv) 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 xi, 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 xi is generated via the instanton effect in a compact QED(3) of massless fermions, our result shows that CSB coexists with the instanton effect in a wide region of xi, which can be used to study the confinement-deconfinement phase transition.