Inelastic tunneling spectroscopic imaging study of electron-lattice interactions in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$.

We investigated impact of oxygen isotope effect on d$^{2}$I/dV$^{2}$ spectroscopy on $^{16}$O and $^{18}$O substituted Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta ,}$respectively, with the same doping level (nearly optimally doping. $^{16}$O$\to ^{18}$O: Tc=89K$\to $88K), using the newly developed inelastic spectroscopic imaging technique (Jinho Lee \textit{et al.}, \textit{Nature} \textbf{422},546 (2006)) . We found that oxygen isotope effect ($^{16}$O$\to ^{18}$O) leads to reduction of mode energy from 52meV to 49meV, while superconducting gap remained unchanged. Oxygen isotope re-substitution shifted mode energy back to the original energy ($^{18}$O$\to ^{16}$O) as well as $T_{c}$ back to 89K, completing the series of isotope effect probed by STM/S. We concluded that renormalization effect seen in dI/dV spectra is caused by strong electron-lattice interaction from a mode near 52meV. We will also discuss about relevance of this lattice vibration mode as a pairing glue in the talk.