Relation between the nodal and antinodal gap and critical temperature in superconducting Bi2212

Abstract

An energy gap is, in principle, a dominant parameter in superconductivity. However, this view has been challenged for the case of high- T _c cuprates, because anisotropic evolution of a d-wave-like superconducting gap with underdoping has been difficult to formulate along with a critical temperature T _c. Here we show that a nodal-gap energy 2Δ _N closely follows 8.5 k _B T _c with underdoping and is also proportional to the product of an antinodal gap energy Δ ^* and a square-root superfluid density √ P _s for Bi ₂Sr ₂CaCu ₂O _{8+ δ} , using low-energy synchrotron-radiation angle-resolved photoemission. The quantitative relations imply that the distinction between the nodal and antinodal gaps stems from the separation of the condensation and formation of electron pairs, and that the nodal-gap suppression represents the substantial phase incoherence inherent in a strong-coupling superconducting state. These simple gap-based formulae reasonably describe a crucial part of the unconventional mechanism governing T _c.

Abstract

In conventional superconductors, the critical temperature is proportional to the superconducting energy gap, but this is not so in unconventional superconductors. Anzai et al. identify an alternative relationship involving nodal and antinodal gaps in an underdoped cuprate superconductor.