Extending Universal Nodal Excitations Optimizes Superconductivity in Bi2Sr2CaCu2O8+δ

Understanding the mechanism by which d wave superconductivity in the cuprates emerges and is optimized by doping the Mott insulator is one of the major outstanding problems in condensed-matter physics. Our high-resolution scanning tunneling microscopy measurements of the high-transition temperature (T-c) superconductor Bi2Sr2CaCu2O8+delta show that samples with different T-c values in the low doping regime follow a remarkably universal d wave low-energy excitation spectrum, indicating a doping-independent nodal gap. We demonstrate that T-c instead correlates with the fraction of the Fermi surface over which the samples exhibit the universal spectrum. Optimal T-c is achieved when all parts of the Fermi surface follow this universal behavior. Increasing the temperature above T-c turns the universal spectrum into an arc of gapless excitations, whereas overdoping breaks down the universal nodal behavior.