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Abstract The discovery of superconductivity has been recognized as one of the greatest scientific achievements of twentieth century. Superconductivity phenomenon, at which the current can flow in material without noticeable energy dissipation and is accompanied by a sudden DROP of the electrical resistance to zero by cooling below a critical temperature called the superconducting transition temperature Tc, see figure 1.1(a). Superconductivity was first discovered in mercury by Onnes [1] in 1911. The temperature at which mercury becomes superconducting was found to be close to the boiling point of liquid helium (4.2 K). Subsequently, many metals, alloys and intermetallic compounds were exhibited superconductivity. Besides the lack of resistance, another characteristic of superconductivity is the ”Meissner effect”, discovered by Meissner and Ochsenfeld in 1933 [2]. Superconductor can always expel the applied magnetic fields completely except for a very thin layer at the surface (penetration depth l ), as shown in figure 1.1(b). Therefore, superconductivity can not be understood simply as a classical perfect conductor that will keep a fixed magnetic flux since it loses electric resistivity regardless of the change in external field. The superconductor indeed acts as a perfect diamagnet, which always creates magnetization in opposition to the applied field to cancel the interior field for temperature below Tc. |