Quantum electrodynamics in three dimensions: Dynamical chiral symmetry breaking, confinement, and disorder effects

Abstract

We study dynamical chiral symmetry breaking (DCSB), confinement, and disorder effects in $(2+1)$-dimensional quantum electrodynamics (QED) of massless fermion $\ensuremath{\psi}$ and scalar boson $\ensuremath{\phi}$. It is found that gauge symmetry breaking (GSB) induced by nonzero $⟨\ensuremath{\phi}⟩$ rapidly suppresses the occurrence of DCSB, and certain disorders tend to enhance it. While DCSB leads to confinement in the gauge symmetric state, the matter fields are always deconfined in the GSB state whether chiral symmetry is broken or not. According to the symmetries and the classical potential between particles, ${\text{QED}}_{3}$ has three possible phases, which exhibit distinct phenomena and can be identified by appropriate observable quantities.