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Abstract Discovery of superconductivity is recognized as one of the greatest scientific achievements of twentieth century. Superconductivity was first discovered by Onnes [1] in mercury in 1911. He observed a sudden DROP of the electrical resistance to zero when cooling mercury to a temperature close to the boiling point of liquid helium (4.2 K). Subsequently, many metals, alloys and intermetallic compounds have exhibited superconductivity. Superconductivity is a phenomenon which is characterized by zero resistivity at a certain temperature Tc, called superconducting transition temperature, Figure 1.1(a). Another characteristic of superconductivity is the ”Meissner effect” which was discovered by Meissner and Ochsenfeld in 1933 [2]. Superconductors can always expel the applied external magnetic fields completely, except for a very thin layer at the surface, Figure 1.1(b). Therefore, superconductivity cannot 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. So, the superconductor indeed acts as a perfect diamagnet, which always creates internal magnetization opposite to the external applied field to cancel the interior one. |