Vanishing of phase coherence in underdoped Bi2Sr2CaCu2O8+δ

Although the binding of electrons into Cooper pairs is essential in forming the superconducting state, its remarkable properties-zero resistance and perfect diamagnetism-require phase coherence among the pairs as well. When coherence is lost at the transition temperature T-c, pairing remains, together with phase correlations which are finite in space and time. In conventional metals, Cooper pairs with short-range phase coherence survive no more than 1 K above T-c. In underdoped high-T-c copper oxides, spectroscopic evidence for some form of pairing is found up to a temperature T*, which is roughly 100 K above T-c (refs 1-3). How this pairing and Cooper-pair formation are related is a central problem in high-T-c superconductivity. The nature of this relationship hinges on the extent to which phase correlations accompany pairing in the normal state(4). Here we report measurements of high-frequency conductivity that track the phase-correlation time tau in the normal state of the Bi2Sr2CaCu2O8+delta,s family of underdoped copper oxide superconductors. Just above T-c,we find that tau reflects the motion of thermally generated topological defects in the phase, or vortices(5,6). However, vortex proliferation reduces tau to a value indistinguishable from the lifetime of normal-state electrons at 100 K, well below T*.