Temperature and magnetic-field dependence of the conductivity of YBaCuO films in the vicinity of superconducting transition: Effect of Tc-inhomogeneity

TL;DR

This study analyzes how temperature and magnetic fields affect the conductivity of YBaCuO films near the superconducting transition, considering spatial inhomogeneity in Tc, and provides a method to quantify and measure these effects.

Contribution

The paper develops a theoretical model for superconducting conductivity considering Tc-inhomogeneity and introduces a high-resolution measurement technique for spatial Tc distribution.

Findings

Tc-inhomogeneity causes over 30% error in conductivity measurements at low fields.

The spatial Tc distribution in YBaCuO microbridges has a dispersion of about 1K.

Experimental resistance data align well with the resistor network model based on Tc distribution.

Abstract

Temperature and magnetic field dependences of the conductivity of YBaCuO films in the transition region are analyzed taking into account spatial inhomogeneity in transition temperature, Tc. (i) An expression for the superconducting contribution to conductivity, \sigma_s(T,H,Tc), of a homogeneous superconductor for H<<Hc2(T=0) is obtained using the solution of the Ginzburg-Landau equation in form of perturbation expansions [S.Ullah, A.T.Dorsey, PRB 44, 262 (1991)]. (ii) The error in \sigma_s(T,H,Tc) occurring due to the presence of Tc-inhomogeneity is calculated and plotted on an H-T plane diagram. These calculations use an effective medium approximation and a Gaussian distribution of Tc. (iii) Measuring the temperature dependences of a voltage, induced by a focused electron beam, we determine spatial distributions of the critical temperature for YBaCuO microbridges with a 2 micron resolution. A typical Tc-distribution dispersion is found to be approximately 1K. For such dispersion, error in \sigma_s(T,H,Tc) due to Tc-inhomogeneity exceeds 30% for magnetic fields H < 1 T and temperatures |T-Tc| < 0.5 K. (iv) Experimental R(T,H) dependences of resistance are well described by a numerical solution of a set of Kirchoff equations for the resistor network based on the measured spatial distributions of Tc and the expression for \sigma_s(T,H,Tc).