Charge condensation in QED3 with a Chern-Simons term

Introducing an external source term — μψ†ψ in the functional method, we construct the effective action of QED3 with a Chern-Simons term. We examine the possibility that the charge condensation 〈ψ†ψ〉μ remains nonzero at the limit μ → 0. If it happens, spontaneous magnetization occurs due to the Gauss law constraint which connects the charge condensation to the background magnetic field. It is found that a stable vacuum with nonzero charge condensation is realized only when the fermion mass is sent to zero, keeping it lower than the external source μ. This result suggests that the spontaneous magnetization is closely related to the fermion mass.