Vanishing of phase coherence in underdopedBi_2Sr_2CaCu_2O_8+d

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 Tc, 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 Tc. In underdoped high-Tc copper oxides, spectroscopic evidence for some form of pairing is found up to a temperature T*, which is roughly 100 K above Tc (refs 1,2,3). How this pairing and Cooper-pair formation are related is a central problem in high-Tc superconductivity. The nature of this relationship hinges on the extent to which phase correlations accompany pairing in the normal state4. Here we report measurements of high-frequency conductivity that track the phase-correlation time tau in the normal state of the Bi2Sr2CaCu2O8+delta family of underdoped copper oxide superconductors. Just above Tc, we find that tau reflects the motion of thermally generated topological defects in the phase, or vortices5,6. However, vortex proliferation reduces tau to a value indistinguishable from the lifetime of normal-state electrons at 100 K, well below T*.