^{1,a)}, Najmul Hassan

^{2}, Sana Nawaz

^{1}, Babar Shabbir

^{1}, Sajid Khan

^{1}and Azhar A. Rizvi

^{3}

### Abstract

High quality electrical resistivity versus temperature data of as-prepared and -annealed (, 0.25, 0.5, 0.75, 1.0, 1.25, and 1.5) superconductors has been studied for fluctuation-induced phenomena setting in at temperatures well above the critical temperature. The analysis of the data is done by using Aslamazov–Larkin (AL) and Lawrence–Doniach models for the excess conductivity. We have estimated several physical parameters, including coherence length, interplane coupling strength, exponents, and dimensionality of the fluctuations. The as-prepared and oxygen postannealed samples have shown a cross-over temperature associated with two distinct exponents and the excess conductivity data fits well with the two-dimensional and three-dimensional AL equations. The coherence length along the c-axis and the interlayer coupling strength (J) are found to decrease with increased Sn doping. These values are increased after annealing the samples in oxygen atmosphere, which is most likely associated with the approach of carrier concentration in the conducting planes to the optimum value. The and the peak temperature as determined from the versus temperature plots are also found to decrease with increased Sn substitution, however, these temperatures are improved to higher values after annealing the samples in oxygen atmosphere. The decreased values of and with increased Sn substitution in the as-prepared samples are most likely arising from the suppression of carrier’s density promoted by the increased volume of unit cell and the localization of the carriers at the sites.

The International Center for Theoretical Physic (ICTP) is acknowledged for their financial support through Project No. PRJ-27.

I. INTRODUCTION

II. EXPERIMENTAL

III. BRIEF THEORETICAL BACKGROUND

IV. RESULTS AND DISCUSSIONS

A. Fluctuations induce conductivities and dimensional exponents

B. Coherence length, cross over temperature, and interlayer coupling strength

V. CONCLUSION

### Key Topics

- Copper
- 22.0
- Electrical resistivity
- 15.0
- Coherence
- 13.0
- Superconductors
- 12.0
- Annealing
- 10.0

## Figures

X-ray diffraction pattern of (, 0.5, 1.0, and 1.5) superconductor samples.

X-ray diffraction pattern of (, 0.5, 1.0, and 1.5) superconductor samples.

(a) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown.(b) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown.(c) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown. (d) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown. (e) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown. (f) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown. (g) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown.

(a) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown.(b) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown.(c) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown. (d) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown. (e) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown. (f) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown. (g) vs plot of sample. The scattered points are experimentally found FIC of with the help of Eq. (1). In the inset of figure, the resistivity measurement of sample and its derivative curve are shown.

(a) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (b) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (c) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (d) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (e) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (f) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (g) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown.

(a) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (b) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (c) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (d) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (e) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (f) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown. (g) vs plot of oxygen annealed sample. The scattered points are experimentally found FIC of oxygen annealed with the help of Eq. (1). In the inset of figure, the resistivity measurement of oxygen annealed sample and its derivative curve are shown.

## Tables

Various parameters obtained from the resistivity versus temperature data and versus plots of (, 0.25, 0.5, 0.75, 1.0, 1.25, and 1.5) superconductor samples.

Various parameters obtained from the resistivity versus temperature data and versus plots of (, 0.25, 0.5, 0.75, 1.0, 1.25, and 1.5) superconductor samples.

Various regions obtained from the versus plots of (, 0.25, 0.5, 0.75, 1.0, 1.25, and 1.5) superconductor samples.

Various regions obtained from the versus plots of (, 0.25, 0.5, 0.75, 1.0, 1.25, and 1.5) superconductor samples.

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