Fourier Transform Inelastic Tunneling Spectroscopy of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$

Jinho Lee$^{1}$, K. McElroy$^{1,2}$, James Slezak$^{1}$, H. Eisaki$^{3}$, {\&} S. Uchida$^{4}$ \newline \newline Inelastic electron tunneling spectroscopy (IETS) played a central role in determining that phonons were responsible for conventional superconductivity[1]. Since STM-based IETS can reveal local vibrational modes[2], and STM-based Fourier transform scanning tunneling spectroscopy (FT-STS) [3] can reveal momentum-space structure of elastic scattering processes[4], a combination of these techniques might be used to elucidate the momentum-space structure of electron-boson inelastic processes in cuprates[5]. Here we introduce this new STM technique, FT-IETS, in which we map the derivative of the differential conductance, d$^{2}$I/dV$^{2}$, with atomic resolution in the high-T$_{c}$ superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta {\rm g}}$. Fourier analysis is then used to search for the momentum-space structure of electron-boson interactions in this system [6]. 1. J.R. Schrieffer, D.J. Scalapino {\&} J. Wilkins, \textbf{\textit{Phys. Rev. Lett}} . \textbf{10}, 336 (1963); W.L. McMillan {\&} J.M. Rowell \textbf{\textit{Phys. Rev. Lett.}} \textbf{14}, 108 (1965). 2. B.C. Stipe \textit{et al }\textbf{\textit{Science}} \textbf{280}, 1732 (1998) 3. J.E. Hoffman \textit{et al }\textbf{\textit{Science 266}}, 455 (2002)~; J.E. Hoffman \textit{et al }\textbf{\textit{Science}} \textbf{297, }1148 (2002). 4. K. McElroy \textit{et al }\textbf{\textit{Nature}} \textbf{\textit{422}}$, $520 (2003). 5. J.-X. Zhu, J. Sun, Q. Si, and A. V. Balatsky \textbf{\textit{Phys. Rev. Lett.}} \textbf{92}, 017002 (2004) 6. Jinho Lee \textit{et al}, Submitted. \newline \newline $^{1}$\textit{ Department of Physics, Cornell University, Ithaca NY 14850, USA.}$^{ 2}$\textit{Department of Physics, University of California, Berkeley, CA 94720-7300, USA. }$^{3}$\textit{AIST, 1-1-1 Central 2, Umezono, Tsukuba, Ibaraki, 305-8568 Japan. }$^{4}$\textit{Department of Physics, University of Tokyo, Tokyo, 113-8656 Japan.}