Chiral symmetry breaking and phase fluctuations:  A ${\mathrm{QED}}_3$ theory of the pseudogap state in cuprate superconductors

A d-wave superconductor, its phase coherence progressively destroyed by unbinding of vortex-antivortex pairs, suffers an instability related to chiral-symmetry breaking in ${\mathrm{QED}}_3.$ The chiral manifold exhibits large degeneracy spanned by physical states acting as inherent “competitors” of d-wave superconductivity. Two of these states are associated with antiferromagnetic insulator and “stripe” phases, known to be stable in the pseudogap regime of cuprates near half-filling. The theory also predicts an additional, yet unobserved state: a $d+ip$ phase-incoherent superconductor.