### Session V1: Collective Modes, Phonons in Cuprates

 Thursday, March 24, 2005 11:15AM - 11:51AM V1.00001: Fourier Transform Inelastic Tunneling Spectroscopy of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ Invited Speaker: J.C. Seamus Davis 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.} Thursday, March 24, 2005 11:51AM - 12:27PM V1.00002: Electron-Phonon Coupling in the t-J Model Invited Speaker: Andrei Mishchenko We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for single hole in $tt't''-J$ model coupled to optical phonons. The systematic-error free diagrammatic Monte Carlo [1,2] is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonons variables. It is found that interplay of electron-phonon interaction with intrinsic to the holes in Mott insulator interaction with magnons can explain the main puzzles encountered in ARPES experimental studies: anomalous damping in underdoped and moderately doped regime, kink,'' anomalous universal velocity,'' and giant anomalous isotope effect. Crucial discussions with N.\ Nagaosa and Z.-X.\ Shen are acknowledged. ([1] A.\ S.\ Mishchenko {et.\ al}.\ Phys.\ Rev.\ B {\bf 62} 6317 (2000); [2] A.\ S.\ Mishchenko and N.\ Nagaosa\ Phys.\ Rev.\ Lett.\ {\bf 93} 036402 (2004).) Thursday, March 24, 2005 12:27PM - 1:03PM V1.00003: Unconventional isotope effects in cuprate high-temperature superconductors Invited Speaker: Hugo Keller A brief review on unconventional oxygen-isotope ($^{16}$O/$^{18}$O) effects (OIE) in cuprate high-temperature superconductors (HTS) is presented. First the doping dependence of the OIE on the superconducting transition temperature $T_{c}$ in various H TS is discussed. For all cuprate HTS families the OIE exponent of $T_{c}$ ($\alpha_{\rm O}$) shows a generic trend: In the underdoped regime $\alpha_{\rm O}$ is large ($\alpha_{\rm O} > 0.5$) and becomes small in the optimally doped and overdoped re gime. Magnetization, magnetic torque, and muon-spin rotation ($\mu$SR) studies of the OIE on the in-plane penetration depth $\lambda_{ab}(0)$ in La$_{2-x}$Sr$_{x}$CuO$_{4}$ and Y$_{1-x}$Pr$_{x}$Ba$_2$Cu$_3$O$_{7-\delta}$ indicate a substantial oxygen-mass dependence of $\lambda_{ab}(0)$ which increases with reduced doping. It is remarkable that even in optimally doped YBa$_2$Cu$_3$O$_{7-\delta}$ and La$_{2-x}$Sr$_{x}$CuO$_{4}$ a substantial OIE on $\lambda_{ab}(0)$ is observed, although the OIE o n $T_{c}$ is rather small. The oxygen-isotope shifts of $T_{c}$ and $\lambda_{ab}(0)$ exhibit a correlation that appears to be generic for various families of HTS. Furthermore, site-selective OIE investigations of Y$_{1-x}$Pr$_{x}$Ba$_2$Cu$_3$O$_{7-\ de lta}$ clearly reveal that the planar oxygen atoms mainly contribute to the total OIE on $T_{c}$ as well as on $\lambda_{ab}(0)$ at all doping levels. These unusual OIE, which are beyond the scheme of BCS theory, may be explained with a polaron theory.$^{1}$ It is found that the coupling of the electronic degrees of freedom to the Jahn-Teller $Q_{2}$-type mode is the origin of these isotope effects. ~\\ $^{1}$~A.~Bussmann-Holder and H.~Keller, cond-mat/0409738. Thursday, March 24, 2005 1:03PM - 1:39PM V1.00004: An Isotope Dependent Study of the Quasiparticle Dynamics in High Temperature Superconductors Invited Speaker: Alessandra Lanzara The effect of oxygen isotope substitution on the electronic properties of double layer Bi2212 high temperature superconductor is studied by means of angle resolved photoemission spectroscopy (ARPES). This new approach allows us to unambiguously and directly extract information on the role and the nature of the electron-lattice interaction in these highly correlated materials. Data as a function of temperature, momentum and doping are presented. The isotope-induced changes of the electron spectral function together with their energy, momentum, and temperature dependences, as well as the \textit{local} nature of the electron-lattice interaction are discussed. A dynamic spin-Peierls picture [1,2], where the singlet pairing of the electrons and the electron-lattice coupling mutually enhance each other is presented. This work was done in collaboration with G. --H. Gweon, T. Sasagawa, H. Takagi and D. H. Lee. This work was supported by DOE, Contract No. DE-AC03-76SF00098, NSF Grant No. DMR-0349361 and Sloan Foundation. [1] G. H. Gweon \textit{et al}. Nature \textbf{430}, 187 (2004) [2] A. Seidel \textit{et al}. cond-mat/0408665 (2004) Thursday, March 24, 2005 1:39PM - 2:15PM V1.00005: Polaronic behavior and electron-phonon interaction in cuprates Invited Speaker: Olle Gunnarsson Photoemission and neutron scattering indicate a substantial electron-phonon coupling in high-$T_c$ cuprates. To address the associated anomalous softening of a half-breathing Cu-O bond-stretching phonon, we derive a $t$-$J$ model with electron-phonon coupling.$^1$ Using input parameters from band structure calculations and solving the model by exact diagonalization, we obtain a good description of the phonon softening.$^1$ We study the interplay of the electron-phonon and Coulomb interactions for a (weakly) doped Mott-Hubbard insulator. Using sum-rules, we find that that the effect of the electron-phonon interaction on the phonon self-energy is strongly suppressed, while there is no corresponding suppression for the electron self-energy or the phonon-induced carrier-carrier interaction.$^2$ Photoemission suggests polaronic behavior in undoped cuprates. Calculating the electron-phonon interaction in a shell model of an undoped cuprate, we find sufficiently strong coupling to give polaronic behavior. Using an adiabatic approximation, we discuss the dispersion and width of the corresponding phonon side-band. {}$^1$O. R\"osch and O. Gunnarsson, Phys. Rev. Lett. {\bf 92}, 146403 (2004); {}$^2$O. R\"osch and O. Gunnarsson, Phys. Rev. Lett. (in press), cond-mat/0407064.