Anti-correlation between energy-gap and phonon energy for cuprate Bi2212 superconductor

Abstract

Using electron-phonon mechanism, we explains very well the spatial anti-orrelation between the energy-gap and the energy of phonon mode for cuprate superconductor found in d^2I/dV^2 spectrum by STM measurements [Jinho Lee, et.al Nature {\bf 442},546 (2006)], which is the direct effect of a relation $M<\omega^{2}>\lambda=const$. We calculate T$_{C}$ maps on $\lambda-\Omega_{P}$ plane which help us understanding the relation M<\omega^{2}>\lambda=const$ and the superconductivity of superconductors.