Extending universal nodal excitations optimizes superconductivity in Bi₂Sr₂CaCu₂O_8+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 condensedmatter physics. Our high-resolution scanning tunneling microscopy measurements of the high-transition temperature (T_c) superconductor Bi₂Sr₂CaCu ₂O_8+δ 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.