Anti-Correlation between Energy-Gap and Phonon Energy for Cuprate Bi2212 Superconductor

Using the electron--phonon mechanism, we explain the spatial anti-correlation between the energy-gap and the energy of phonon mode for cuprate superconductor found in tunnelling spectrum by STM measurements of Bi2212, which is the direct effect of an important relationship (or constraint) I=const, where I is superconducting parameters. By relaxing above constraint, we study the correlation of energy gap and phonon energy
when I has a distribution. We calculate a map of transition temperature in space constructing by phonon energy and the parameter of electron--phonon interaction, which is helpful for understanding of the relation.