Coherence and single-particle excitations in the high-temperature superconductors

The 'pseudogap' observed in the electron excitation spectrum of underdoped copper oxide superconductors has become the focus of considerable attention in the field of high-temperature superconductivity. In conventional superconductors, described by 'BCS' theory, an energy gap appears at the superconducting transition temperature (T-c); the pseudogap, in contrast, is observed well above T-c (ref. 1) and can be large compared to the conventional BCS gap(2-4). Here I compare gap energies, measured by different experimental techniques, for the copper oxide superconductors and show that these reveal the existence of two distinct energy scales: Delta(p) and Delta(c). The first, determined either by angle-resolved photoemission spectroscopy or by tunnelling, is the single-particle excitation energy-the energy (per particle) required to split the paired charge-carriers that are required for superconductivity. The second energy scale is determined by Andreev reflection experiments, and I associate it with the coherence energy range of the superconducting state-the macroscopic quantum condensate of the paired charges. I find that, in the overdoped regime, Delta(p) and Delta(c) converge to approximately the same value, as would be the case for a BCS superconductor where pairs form and condense simultaneously. But in the underdoped regime, where the pseudogap is observed, the two values diverge and Delta(p) is larger than Delta(c). Models that may provide a framework for understanding these results involve the existence of pairing above the condensation temperature, as might occur in a crossover from BCS to Bose-Einstein condensation behaviour(5) or from the formation of striped phases(6).