Evidence for forward scattering and coupling to acoustic phonon modes in high-T$_c$ cuprate superconductors

摘要

Recent laser angle-resolved photoemission spectroscopy studies haveestablished the presence of a new kink in the low-energy nodal dispersion ofBi$_2$Sr$_2$CaCu$_2$O$+{8+\delta}$ (Bi-2212). The energy scale (~8-15 meV) ofthis kink appears below the maximum of the superconducting gap $\delta_0$.Therefore it is difficult to interpret this feature in terms of the usualcoupling to a sharp dispersionless mode. In this paper we examineelectron-phonon coupling to the in-plane acoustic phonon branch arising fromthe modulation of the screened Coulomb potential. We demonstrate that such acoupling has a strong forward scattering peak, and as a consequence, a kinkoccurs in the dispersion at an energy scale shifted by the local gap$\delta(k)$. In addition, considerations for the reduction of screening withunderdoping naturally explains the observed doping dependence of the low-energykink. These results point to a strong coupling to the acoustic branch which ispeaked in the forward scattering direction and has important implications fortransport and pairing in the high-T$_c$ cuprates.