On the Theory of Superconductivity

Abstract
Bardeen, Cooper and Schrieffer's theory of superconductivity is discussed by developing an exact treatment of strong coupling approximation. With respect to the thermal properties, their results are verified: The energy of the ground state and the magnitude of the energy gap are found to be identical with the exact answers in the strong coupling limit. However, the argument for the magnetic properties such as the Meissner effect seems to leave some questions. We have discussed the Meissner effect by means of the gauge invariant method presented in the previous paper. In order to maintain the invariance exactly the case of strong coupling between electrons is investigated. Then the “interaction current” plays an essential role and is shown to diverge with the size of the system. In view of the qualitative resemblance of the BCS variational solution to that of the strong coupling approximation, it may be inferred that the above conclusion seems to hold also in the weak coupling case. This will suggest the importance of the interaction current and the requirement of the exact gauge invariance contrary to Anderson's arguments.