Some Chaotic Points in Cuprate Superconductors

The aim of this chapter is to determine the chaotic points of cuprate layered superconductors by means of magnetization data and the concept of the Josephson penetration depth based on Bean Critical State and Lawrance-Doniach Models, respectively. In this chapter, the high temperature mercury based cuprate superconductors have been examined by magnetic susceptibility (magnetization) versus temperature data, X-Ray Diffraction (XRD) patterns and Scanning Electron Microscope (SEM) outputs. Thus by using these data, a new method has been developed to calculate the Josephson penetration depth precisely, which has a key role in calculating various electrodynamics parameters of the superconducting system. The related magnetization versus temperature data have been obtained for the optimally oxygen doped virgin (uncut) and cut samples with the rectangular shape. By means of the magnetization versus temperature data of the superconducting sample, taken by Superconducting Quantum Interference Device (SQUID), the Meissner critical transition temperature, Tc, and the paramagnetic Meissner temperature TPME, called as the critical quantum chaos points, have been extracted. In superconductors, the second order phase transition occurs at Meissner transition temperature, Tc, that is considered as the first chaotic point in the system, since the normal state of being is transformed into another state of being called as “superconducting state” that has been driven by temperature. The XRD measurements have been performed in order to calculate the lattice parameters of the system. The crystallographic lattice parameters of superconducting samples, determined by the XRD patterns, have been used to estimate the extent of the Josephson penetration depth. The SEM outputs have been used to determine the grain size of the optimally oxygen doped polycrystalline superconducting samples. The average grain size of the HgBa2Ca2Cu3O8+x (Hg-1223) samples, t, is a crucial parameter, since the critical current density value, Jc, is inversely proportional to “t”, whereas it is directly proportional to the difference in magnetization. It has been concluded that the grain size of the superconductors and the length of the c-axis of the unit cell of the system are highly effective on both of the first and second chaotic points of the superconducting system.