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); the pseudogap, in contrast, is observed well above T (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 and Δ. 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 and Δ 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 is larger than Δ. 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.

Gap and pseudogap evolution within the charge-ordering scenario for superconducting cuprates

“…independent of T c , whereas the slope at the nodes is v ∆ = ∆ 0 (φ = π/4) ∝ ∆ ∝ T c , in agreement with the experimental finding [4,6,7]. Note instead that LE M ≈ ∆ for formula:…”

“…However, by using the term LE we want to put more emphasis on the distribution of spectral weight than on its coherent character, which is an artifact of our description of the cuprates in terms of a semiconducting band structure. [2,3,4,6,7]. The amplitude at the M points (LE M ) is given essentially by the value of the LE in the normal state, i.e.…”

On the nature of the superconducting gap in the cuprates

“…The theoretical prediction for the superconducting gap in the single-particle spectrum ∆ 0 compared to the experimental data for the "coherence energy" ∆ c (filled symbols) and the "pseudogap" energy ∆ p (open symbols) from ref. [1]. All quantities are normalised to the critical temperature at optimal doping, T c,max .…”

“…The basic idea is to exploit the fact that certain properties of cuprate superconductors seem to be approximately materialindependent. In particular, the critical temperature T c [4] as well as the two energy scales ∆ c and ∆ p [1], when normalised to the critical temperature at optimal doping, T c,max , appear to be fairly universal functions of the number of holes per CuO 2 unit, n h . Thus one could expect that a very simple model which captures the essential physics in these systems can describe this behaviour.…”

“…Recently, Deutscher has identified two distinct energy scales at low temperatures (in the superconducting state), which he calls the coherence energy ∆ c and the single-particle excitation energy ∆ p [1]. The former corresponds to the superconducting gap seen in phase-sensitive experiments (Andreev reflection, penetration depth and Raman scattering), while the later is the "pseudogap" seen in experiments that probe the one-particle spectrum (photoemission and tunnelling).…”