Precise determination of the superconducting gap along the diagonal direction of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+y}$: Evidence for extended $s$-wave gap symmetry

We have analyzed the data of electron self-energy along the diagonal ($\Gamma-Y$) direction for a nonsuperconducting La$_{1.97}$Sr$_{0.03}$CuO$_{4}$ (LSCO) crystal and a superconducting Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+ y}$ (BSCCO) crystal with $T_{c}$ = 91 K. The high-resolution spectra of the second derivative of electron self-energy show clear peak features associated with the phonon modes strongly coupled to electrons. By precisely matching the phonon structures of the superconducting BSCCO with those of nonsuperconducting LSCO, we accurately determine the diagonal superconducting gap to be 9$\pm$1 meV for the BSCCO. The substantial non-zero diagonal gap observed in the optimally doped cuprate definitively rules out seemingly well accepted $d$-wave gap symmetry and strongly supports an extended $s$-wave gap symmetry with eight line nodes.