Effect of electron-phonon coupling in the ARPES spectra of the tri-layer   cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$
  Angle-resolved photoemission spectroscopy using tunable low energy photons allows us to study the quasi-particle (QP) dispersions of the inner and outer CuO2 planes (IP and OP) separately in the tri-layer cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ (Bi2223). The kink energy of the OP band is $\sim$ 70 meV, as observed in various high-$T_c$ cuprates, while that of the IP band is as large as 100 meV in the superconducting (SC) state. This large kink energy is attributed to the $\sim$ 35 meV buckling mode plus the large ($\sim$ 60 meV) SC gap of IP. The IP band also shows a weak kink feature at 70 meV in the SC state. The latter feature can be explained either by the 70 meV half-breathing mode or by the $\sim$ 35 meV buckling-phonon mode plus the $\sim$ 40 meV SC gap of OP if interlayer scattering of QP is involved. 
S. Ideta, T. Yoshida, M. Hashimoto, A. Fujimori, H. Anzai, A. Ino, M.   Arita, H. Namatame, M. Taniguchi, K. Takashima, K. M...
cond-mat.supr-con