Low Energy Phonons in $Bi_2Sr_2CaCu_2O_{8+\delta}$ and their Possible Interaction with Electrons Measured by Inelastic Neutron Scattering

Angle-resolved photoemission (ARPES) experiments on copper oxide superconductors revealed enigmatic kinks in electronic dispersions near 10 meV presumably due to phonons or impuritites. We used inelastic neutron scattering to measure phonon branches below 15 meV in a large single crystal sample of optimally-doped $Bi_2Sr_2CaCu_2O_{8+\delta}$ (BSCCO). The high quality dataset covered several Brilloiun zones with different final energies. In addition to acoustic branches, optic branches disperse from 4 meV and 7 meV zone center energies. The 4 meV branch interacts with acoustic phonons at small wavevectors, which destroys the LA character of the acoustic branch beyond ~0.15 reciprocal lattice units. We propose a mechanism that explains the low energy electronic dispersion features based on this observation.