Oscillations of the amplitude of the Cooper pair gap induced by interactions between Cooper pairs in the framework of BCS theory

According to BCS theory, superconductivity arises from the weak attraction between electrons. In particular, Cooper pairs are important in determining the properties of superconductivity; therefore, the theoretical description of Cooper pairs is based on the mean-field approximation used in the BCS theory. However, the mean-field approximation cannot estimate the contribution induced by the interactions between Cooper pairs, i.e., many-body terms , accurately. In this article, therefore, using simultaneous differential equations derived from time-dependent Schrödinger equation, we show the detailed description of the Cooper pairs including such interactions, which has not been mentioned in BCS theory so far. We reveal that the time dependence oscillates when interactions between Cooper pairs are accurately considered. Based on theses calculations, the coupling of the Cooper pair gap can become zero, suggesting that the Cooper pairs can be switched on and off in real superconductors in the framework of BCS theory.