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Disordered Superconductors
The well known BCS theory, describes properties of clean superconductors. Clean means the superconducting material has a perfect lattice structure. But the reality is, there are no material in nature which has perfect lattice structure in large scale. A few number of metals, behaves very closely as clean superconductors but a large number of superconducting materials do not follow exact BCS theory but approximately. On the other hand, one can intentionally make a perfect material to a poor material, whose lattice structure is imperfect, these are called disordered materials, and if they are also superconducting, we call them disordered superconductors.

Properties
The small disordered superconductor more or less follow the BCS theory, but when disorder (lattice imperfection) is large, behaviours of superconductors deviate from predictions of BCS theory, such as the decrease in transition temperature $$T_c$$, pair-amplitude Δ and superconducting gap $$E_g$$. At very large disorder superconductivity may destroyed, but the gap $$E_g$$ may persist. In this situation the material behaves like an insulator, although the superconducting gap is non-zero and hence cooper pairs are there. This transition is called Superconductor Insulator Transition(SIT).

Theory
The first step of the theoretical understanding of disordered superconductors is made by P. W. Anderson, L. P. Gor'kov and A. A. Abrikosov in 1959. The main outcome of this theory is, there will be no effect of disorder in the superconductivity in small disorder limit. When disorder is increased a dramatic situation can happens due to the localization of electrons.