Statistic Ensemble Theory Of Superconductivity In Small Metallic Grains

The conventional BCS theory is generalized using random matrices theory, and a new approach is obtained to explain superconductivity in small metallic grains. Superconductivity in different small metallic grains has been deeply and carefully explored in Gauss orthogonal ensemble, Gauss unitary ensemble and Gauss sympletic ensemble. The following results- arc- obtained:1.Critical level spacings are found for all small metallic grains, at which superconductivity would vanish. In the spin-state of.s0, enhancement of superconductivity appears initially but finally superconductivity would break down. When external magnetic fields are imposed, there is possible enhancement for all spin-states in some regions, and their strength is determined by those of magnetic fields. It is until now that the approach is obtained, which contains both enhancement and attenuation of superconductivity.2.The basic relationship of superconductivity in bulk: the ratio of gap to transition temperature is a constant, is also true for small superconducting grains.3.Superconductivity between the state s0 and s>O is quite different. This is due to both parity of electrons in small metallic grains and mainly the distribution of electrons among Fermi levels.Chen Zhiqian (Condensed Matter Physics)Directed by Prof. Dr. Zheng Renrong...