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

Abstract

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. 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: Δ_p and Δ_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, Δ_p and Δ_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 Δ_p is larger than Δ_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 or from the formation of striped phases.