Significance of Phonon Modes and Excess Conductivity of (Cu_0.5Tl_0.5)Ba₂Ca₃(Cu_4−x Ti _x )O_12−δ (x = 0, 0.25, 0.50, 0.75, 1.0) Superconductors

Abstract

We have synthesized (Cu_0.5Tl_0.5)Ba₂Ca₃(Cu_4−x Ti _x )O_12−δ (x = 0, 0.25, 0.50, 0.75, 1.0) superconductors by two-step solid-state reaction method at 880 °C. The a-axis length of tetragonal unit cell increases, whereas the c-axis decreases with doping of Ti in the final compound revealed by X-ray diffraction measurements. Moreover, the magnitude of superconductivity suppresses with increased Ti doping. The Fourier transform infrared spectrometer (FTIR) absorption measurements have shown that the peak position of the apical oxygen modes at 480 and 540 cm ⁻¹ remains unchanged, whereas the CuO₂/TiO₂ planar oxygen modes is softened with increased Ti doping. We explained the softening of planar oxygen mode to be arising due to the difference in the atomic masses of Ti (47.90 amu) and Cu (63.54 amu) atoms. The suppression of superconductivity magnitude is suggested to be originating from an-harmonic oscillations induced by doped Ti atoms which in turn suppress the density of phonon population. These studies show the importance of density of phonon population in mechanism of high- T _c superconductivity and hence the electron-phonon interactions. The excess conductivity analyses (FIC) of conductivity data of these samples have shown that with increased Ti doping, the mean field critical temperature T _cmf is shifted to lower temperatures. The increase in the coherence length along the c-axis, interlayer coupling, and the Fermi velocity is suggested to be arising from the decrease in the c-axes length. We attribute the suppression in B _c, B _c1, J _c(0), and τ _ϕ with Ti doping to the free energy difference between the normal and superconducting state. The idea of suppression in the density of phonon modes induced by Ti doping is supported by excess conductivity analyses.