QED3theory of underdoped high-temperature superconductors

Abstract

The low-energy theory of d-wave quasiparticles coupled to fluctuating vortex loops that describes the loss of phase coherence in a two-dimensional d-wave superconductor at $T=0$ is derived from first principles. The theory has the form of (2+1) dimensional quantum electrodynamics $({\mathrm{QED}}_{3}),$ and is proposed as an effective description of the $T=0$ superconductor-insulator transition and of the pseudogap phase in underdoped cuprates. The coupling constant (``charge'') in this theory is proportional to the dual order parameter of the $\mathrm{XY}$ model, which is assumed to describe fluctuations of the phase of the superconducting order parameter. Finiteness of the charge is then tantamount to the appearance of infinitely large vortex loops, i.e., to the loss of phase coherence in the system. The principal result is that the destruction of the superconducting phase coherence in the d-wave superconductors typically, and immediately, leads to the appearance of antiferromagnetism. This transition can be understood in terms of the spontaneous breaking of an approximate ``chiral'' ${\mathrm{SU}}_{c}(2)$ symmetry, which may be discerned at low enough energies in the standard d-wave superconductor. The mechanism of this spontaneous symmetry breaking is formally analogous to the dynamical mass generation in ${\mathrm{QED}}_{3},$ with the ``mass'' here being proportional to staggered magnetization. Other phases with broken chiral symmetry include the translationally invariant $``d+ip''$ and $``d+is$'' insulators, and the one-dimensional charge-density and spin-density waves, which are all insulating descendants of the d-wave superconductor. All the insulating states have neutral spin-$1/2$ excitations that one can identify in the superconductor confined by the logarithmic potential. Electron repulsion is in this formalism represented by a particular quartic perturbation to the ${\mathrm{QED}}_{3}$ action, which breaks the chiral symmetry and selects the antiferromagnet as the preferred broken symmetry state. I formulate the mean-field theory of the antiferromagnetic instability in presence of a short-range repulsive interaction, and find the staggered magnetization to be significantly enhanced deeper inside the insulating state. The theory offers an explanation for the rounded d-wave-like dispersion seen in angle-resolved photoemission spectroscopy experiments on the insulating ${\mathrm{Ca}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}$ [F. Ronning et al., Science 282, 2067 (1998)]. Relations to other theoretical approaches to the high-${T}_{c}$ problem are discussed.