Abstract
In this chapter we explore the main models of superconductivity that have emerged in the last century. In the early classical models of superconductivity, the magnetic vector potential was found to be directly proportional to the supercurrent. For the sake of completeness, we briefly elaborate on the semi-classical Ginzburg-Laundau theory, microscopic BCS theory, BdG formalism, superfluidity and the Anderson-Higgs mechanism. Our aim in this chapter is to give a concise mathematical and historical overview of the theory, having the magnetic vector potential in the foreground as much as possible.
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