Local Signatures and Spectral Inversion of Bosonic Mode Coupling in a High-Temperature Superconductor

High-resolution spectroscopy and mapping of the high-temperature superconductor Bi$_{2}$Sr$_{2}$Ca$_{0.93}$Y$_{0.07}$Cu$_{2}$O$_{8+d}$ was performed with a custom-built low-temperature scanning tunneling microscope. At optimal doping ($T_{c} \quad \approx $ 96 K), these materials exhibit~unusually strong spectral sidebands characteristic of electron-boson coupling. The magnitude of these Holstein-like $d$-wave density of states replicas facilitates a spectral inversion procedure, from which the critical parameters of the bosonic coupling can be directly extracted. This results in electron-boson coupling $\lambda \quad \approx $ 0.2-0.4 and boson energy $\Omega \quad \approx $ 70-90 meV.~Origins and implications of these excitations will be discussed.