Vanishing of phase coherence in underdoped Bi₂Sr₂CaCu₂O(8+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. Here we report measurements of high-frequency conductivity that track the phase- correlation time τ in the normal state of the Bi₂Sr₂CaCu₂O(8+δ) family of underdoped copper oxide superconductors. Just above T(c), we find that τ reflects the motion of thermally generated topological defects in the phase, or vortices. However, vortex proliferation reduces τ to a value indistinguishable from the lifetime of normal-state electrons at 100 K, well below T(*).