Research On The Superconductivity Of Small Metal Particles

The superconductivity of macroscopic samples has been explored more than one hundred years since it was discovered by Onnes in 1911. The superconductivity of conventional superconductors based on electron-phonon mechanism can be successfully explained by the BCS theory established in 1957. The theory for the high-temperature copper oxide superconductors, iron-based superconductors, et al. discovered after 1986 has still not been established. With the development of nano-science and technology, the relevant problem of superconductivity of metal nanoparticles has caused great attention of scientists in various fields. However, when the size of metal material is about nanoscale, the superconductivity of the system is very difficult to be explained by the previous BCS theory. For this reason, physicists tried to use a variety of theories and models, and much progress has been made on the research of superconductivity of metallic nanoparticles.In this paper, the two-band Richardson model and random matrix method are used to study the superconductivity of small metallic grains. The energy gap equations of the small metal particles with both even and odd number of electrons for different spin states have been obtained. Through Fortran program, the superconductivity of Gauss unitary ensemble of small metallic grains have been studied in the following two aspects.1. The effect of interband interaction on the superconductivity of small metallic particles. The obtained results show that, if no interband interaction, the relationship between the gap and temperature is BCS like. If interband interaction is not zero, there are l two energy gaps, and the relationship between the gap and temperature is also BCS like, but the two gaps vanish at the same transition temperature. Specifically, we have discussed the relationship between the energy gap and temperature, and the relationship between the gap and level spacing for different interband interactionsdV.(1) There are different transition temperatures for different interband interactionsdV. The transition temperature cT increases with the increasing of sdV. For fixed temperature T, gap A? andB? of small metal particles increase with sdV.( 2) Superconducting attenuation phenomenon. There are different critical level spacings for different interband interactionsdV. At the critical level spacing cd, the superconductivity vanishes. cd increases with the increasing of sdV, and for fixed level spacing d, gap A? andB? of small metal particles increase with sdV.2. The effect of different spin-states on superconductivity of small metallic particles. We have discussed the relationship between the energy gap and temperature, and the relationship between the gap and level spacing for different spin-state S.(1) There are different transition temperatures for different spin-state S. The transition temperature cT gradually decreases with the increasing of S. For fixed temperature T, gap A? andB? of the small metal particles decrease with the increasing of S.(2) There are different critical level spacings for different spin-state S. The critical level spacing cd decreases with the increasing of S, and for fixed level spacing d, gap A? andB? of small metal particles decrease with the increasing of S. For S?0, gap A? andB? of small metal particles gradually decrease with the increasing of d(decreasing of metal particles size), and the superconductivity becomes weak, even to disappear. With the increasing of S, the energy gap decreases rapidly, i.e. the superconductivity disappears rapidly. But for S?0, gap A? andB? of small metal particles increase firstly to their maximum values, then decrease monotonously with the increasing of d. This is so called the superconducting enhancement phenomenon.