Nodal Gap Energy in High-Tc Cuprate Superconductors: A new Paradigm

In high-Tc cuprate superconductors, the d-wave-like superconducting gap appears to depart from the standard proportionality with critical temperature Tc, and shows different doping dependences between the nodal and antinodal regions of momentum space. The failure of the attempts so far to formulate these momentum-resolved gaps with Tc has posed questions to their roles in electron pairing and their mutual relationship. Here, we report a simple proportional relation between nodal gap and critical temperature in superconducting Bi2Sr2CaCu2O8+δ and Bi2Sr1.6La0.4CuO6+δ. Using low-energy synchrotron radiation on angle-resolved photoemission spectroscopy, we observed the strongly curved gap profile in the underdoped cuprates, and found that a nodal-gap component 2∆N at the nodal limit of the gap slope closely follows 8.5kBTc and concomitantly related to the antinodal-gap energy ∆ * through a reduction factor of square-root superfluid density ρs. These empirical formulae provide a new gap-based paradigm on the principle governing Tc in strong-coupling superconductors.