Phase Fluctuations and Spectral Properties of Underdoped Cuprates
  We consider the effect of classical phase fluctuations on the quasiparticle spectra of underdoped high-$T_c$ cuprate superconductors in the pseudogap regime above $T_c$. We show that photoemission and tunneling spectroscopy data are well accounted for by a simple model in which mean field d-wave quasiparticles are semiclasically coupled to supercurrents induced by fluctuating unbound vortex-antivortex pairs. We argue that the data imply that transverse phase fluctuations are important at temperatures above $T_c$, while longitudinal fluctuations are unimportant at all temperatures. 
M. Franz and A. J. Millis