A Study of Electrical Magnetoconductivity Paracoherent Transition of Granular YBCO Doped Superconductors: A Possible Evidence of an Inverted XY Transition

This communication reports an electrical magnetoconductivity fluctuation study in polycrystalline (granular) samples of YBa<sub>2</sub>Cu<sub>2.985</sub>Fe<sub>0.015</sub>O<inline-formula> <tex-math notation="LaTeX">$_{\mathrm {7-\delta}}$ </tex-math></inline-formula> and YBa<sub>1.75</sub>Sr<sub>0.25</sub>Cu<sub>3</sub>O<inline-formula> <tex-math notation="LaTeX">$_{\mathrm {7-\delta }}$ </tex-math></inline-formula> superconductors. The measurements were performed in magnetic fields <inline-formula> <tex-math notation="LaTeX">$H \le1000$ </tex-math></inline-formula> Oe applied parallel to the measurement density current. The samples were prepared by a standard solid-state reaction technique. The results were analyzed in terms of the temperature derivative of the electrical resistivity, <inline-formula> <tex-math notation="LaTeX">$d\rho $ </tex-math></inline-formula><italic>/dT</italic>, and of the inverse of the logarithmic derivative of the electrical conductivity with respect to temperature, <inline-formula> <tex-math notation="LaTeX">$\chi _{\sigma }^{-1}(T)$ </tex-math></inline-formula>. The results allowed the identification of power law divergences of the magnetoconductivity and show that the superconductivity transition in our samples is a two-stage process. The genuine superconductor state with zero resistance stabilizes at the coherence transition temperature, <inline-formula> <tex-math notation="LaTeX">$T_{\mathrm {C0}}$ </tex-math></inline-formula>, in which a long-range-ordered state for the phase of the order parameter is established in the whole granular array. The approach to the zero-resistance state is characterized by the critical exponent <inline-formula> <tex-math notation="LaTeX">$\lambda \sim ~3.5$ </tex-math></inline-formula> for our Sr doped sample and <inline-formula> <tex-math notation="LaTeX">$\lambda \sim ~4$ </tex-math></inline-formula> for our Fe doped sample. It indicates that the universality class for the coherence transition for our samples is that of the 3-D XY model where non-trivial disorder is relevant. At a temperature called <inline-formula> <tex-math notation="LaTeX">$T_{\mathrm {C}}^{\mathrm {IN}}$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$T_{\mathrm {C}}^{\mathrm {IN}} > T_{\mathrm {C0}}$ </tex-math></inline-formula>), we observed another exponent, <inline-formula> <tex-math notation="LaTeX">$\lambda ^{\mathrm {IN}} ~ \sim ~1.4$ </tex-math></inline-formula>, which suggests a crossover in the critical phenomenology dynamic nearby the coherence transition. The origin of this crossover may be related to a change in the universality class of the transition and the value of <inline-formula> <tex-math notation="LaTeX">$\lambda ^{\mathrm {IN}}$ </tex-math></inline-formula> is consistent with a true asymptotic inverted XY critical regime. The chemical doping generally enhances the YBa<sub>2</sub>Cu<sub>3</sub>O<inline-formula> <tex-math notation="LaTeX">$_{\mathrm {7-\delta }}$ </tex-math></inline-formula> superconductor granular character; however, its physical contribution to the <inline-formula> <tex-math notation="LaTeX">$\lambda ^{\mathrm {IN}}$ </tex-math></inline-formula> exponent is an open question.