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 semiclassically 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.