Magnetization and dynamically induced finite densities in three-dimensional Chern-Simons QED

We show that the spontaneous magnetization occurs as realization of finite density vacua, those are the lowest Landau levels fully or half occupied by fermions, in (2+1)-dimensional QED with a Chern-Simons term. The charge condensation is shown to appear so as to complement the fermion anti-fermion condensate which breaks the flavor U(2N) symmetry and causes the fermion mass generation. The solutions to the Schwinger-Dyson gap equation show that the fermion self-energy contributes separately to the induction of the finite fermion density and/or the fermion mass. The magnetization can be supported by the charge condensation for the theories with the Chern-Simons coefficient κ = Ne2/2π, and κ = Ne2/4π, under the Gauss law constraint. Especially, for κ = Ne2/4π, both the magnetic field and the fermion mass are simultaneously generated on the half-filled ground state which breaks the U(2N) symmetry as well as the Lorentz symmetry. 11.10.Kk, 11.30.Cp, 11.30.Qc, 12.20.Ds Typeset using REVTEX