Local Lattice Instability and Superconductivity in La1.85_{1.85}Sr0.15_{0.15}Cu1−x_{1-x}Mx_xO4_4 (M=Mn, Ni, and Co)

Local lattice structures of La$_{1.85}$Sr$_{0.15}$Cu$_{1-x}$M$_x$O$_4$ (M=Mn, Ni, and Co) single crystals are investigated by polarized extended x-ray absorption fine structure (EXAFS). The local lattice instability at low temperature is described by in-plane Cu-O bond splitting. We find that substitution of Mn for Cu causes little perturbation of local lattice instability while Ni and Co substitution strongly suppresses the instability. The suppression of superconductivity by Cu-site substitution is related to the perturbation of lattice instability, indicating that local lattice instability (polaron) plays an important role in superconductivity

Once again: Instanton method vs. WKB

A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lam${\acute e}$ potential (derived from representations of a finite dimensional matrix expressed in terms of $su(2)$ generators) with the results of the tight--binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lam${\acute e}$ potential as well as others the WKB--related method of matched asymptotic expansions yields the exact instanton result as a result of boundary conditions imposed on wave functions which are matched in domains of overlap.Comment: 10 pages, no figures. References list revised according to JHE