Evidence for forward scattering and coupling to acoustic phonon modes in   high-T$_c$ cuprate superconductors
  Recent laser angle-resolved photoemission spectroscopy studies have established the presence of a new kink in the low-energy nodal dispersion of Bi$_2$Sr$_2$CaCu$_2$O$+{8+\delta}$ (Bi-2212). The energy scale (~8-15 meV) of this kink appears below the maximum of the superconducting gap $\delta_0$. Therefore it is difficult to interpret this feature in terms of the usual coupling to a sharp dispersionless mode. In this paper we examine electron-phonon coupling to the in-plane acoustic phonon branch arising from the modulation of the screened Coulomb potential. We demonstrate that such a coupling has a strong forward scattering peak, and as a consequence, a kink occurs in the dispersion at an energy scale shifted by the local gap $\delta(k)$. In addition, considerations for the reduction of screening with underdoping naturally explains the observed doping dependence of the low-energy kink. These results point to a strong coupling to the acoustic branch which is peaked in the forward scattering direction and has important implications for transport and pairing in the high-T$_c$ cuprates. 
S. Johnston, I. M. Vishik, W. S. Lee, F. Schmitt, S. Uchida, K.   Fujita, S. Ishida, N. Nagaosa, Z. X. Shen, T. P. Devereaux
cond-mat.supr-con