  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. The theory has the form of 2+1 dimensional
quantum electrodynamics (QED3), and is proposed as an effective description of
the T=0 superconductor-insulator transition in underdoped cuprates. The
coupling constant ("charge") in this theory is proportional to the dual order
parameter of the XY model, which is assumed to be describing the quantum
fluctuations of the phase of the superconducting order parameter. The principal
result is that the destruction of phase coherence in d-wave superconductors
typically, and immediately, leads to antiferromagnetism. The transition can be
understood in terms of the spontaneous breaking of an approximate "chiral"
SU(2) symmetry, which may be discerned at low enough energies in the standard
d-wave superconductor. The mechanism of the symmetry breaking is analogous to
the dynamical mass generation in the QED3, with the "mass" here being
proportional to staggered magnetization. Other insulating phases that break
chiral symmetry include the translationally invariant "d+ip" and "d+is"
insulators, and various one dimensional charge-density and spin-density waves.
The theory offers an explanation for the rounded d-wave-like dispersion seen in
ARPES experiments on Ca2CuO2Cl2 (F. Ronning et. al., Science 282, 2067 (1998)).
