Anti-Jahn-Teller effect and d-wave phonon mechanism in cuprates

Undoped cuprates are Jahn-Teller (JT) Materials [1] and Mott AF insulators [2]. When holes are doped, the octahedrons or pyramids elongated by the JT effect shrink. We call such distortion against the JT effect ``\textbf{\textit{anti-Jahn-Teller effect}}''[3]. By the interplay of the \textit{anti-Jahn-Teller effect }and \textit{Mott physics}, the two multiplets, the Zhang-Rice singlet and the Hund's coupling triplet, become nearly degenerate, and thus the hole-carriers in the underdoped regime form a metallic state, by taking the two multiplets alternately in the presence of the local AF order without destroying it [3,4]. On the basis of this two-component K-S model with small Fermi surfaces, the mechanism of superconductivity is discussed by the interplay of the electron-phonon interactions and local AF order [5,3]. It is shown that (1) the phase difference of wave functions between up- and down-spin carriers leads to the gap of dx$^{2}$-y$^{2}$ symmetry, and (2) the calculated concentration dependences of Tc and of isotope effects for LSCO are consistent with recent experimental results including anomalous isotope effects [6]. Finally the origin of the high-energy pseudogap is discussed based on the K-S model [3]. \newline \newline [1] J.G. Bednorz and K.A. Mueller, \textit{Z. Phys}. \textbf{B64}, 189 (1986). \newline [2] P.W. Anderson, \textit{Science} \textbf{235}, 1196 (1987). \newline [3] H. Kamimura \textit{et al}., \textit{in Theory of Copper Oxide Superconductors} (Springer, Heidelberg, 2005). \newline [4] H. Kamimura and Y. Suwa, \textit{J. Phys. Soc. Jpn.}\textbf{ 62,} 3368 (1993). \newline [5] H. Kamimura \textit{et al.} \textit{Phys. Rev. Lett.}\textbf{ 77,} 723 (1996). \newline [6] A.R. Bishop \textit{et al}., \textit{J. Supercond}., to be published (2006).