Superconductivity Of Small Metal Particles

In recent years,the study on the superconductivity of the small metal particles has attracted much attention.Though the BCS theory established in 1957 can explain the superconductivity of macroscopic superconductors very well,but it cannot be directly used to explain the superconductivity of the small metal particle superconductors.Therefore,a new theory is needed to solve this problem.In 1963,Richardson proposed a model(called Richardson Model)to study the physics properties of the limited size atomic nucleus;subsequently,it was found that the slightly modified Richardson model can be used to study physics properties of the small metal particle superconductors.In this paper,we have generalized the one-band Richardson model to the two-band case,and the superconductivity of small metal particles have been studied by the random matrix method.Our work can be classified into two parts.In the first part,we have studied the superconductivity of the small metal particle systems with the Gauss unitary electron energy level distribution.The entropy,specific heat jump and critical magnetic have been calculated.The obtained results show that the superconductivity increases with the increase of the interband interaction Vsd.The large ground state spin S is unfavorable to the superconductivity of the system.With the decrease of particle size l,there is only the superconducting attenuation phenomenon for S? 0,but for S=0,there is not only the superconducting enhancement phenomenon but also the superconducting attenuation phenomenon.Our results are in agreement with the experiments.In the section part,we have studied the superconductivity of the systems(GOE-Gauss orthogonal ensemble,GUE-Gauss unitary ensemble,GSE-Gauss symplectic ensemble)with different electron energy level distributions.For ground state spin S = 0?S? 0 and changing S cases,we have calculated the relation between the superconductivity energy gap and the temperature T and energy level space d.The obtained results show that,For the case of S?O,superconducting energy gap of the different system gradually decreases with the increasing temperature T,the superconducting energy gap of the GOE system is highest and the superconducting energy gap of the GSE system is smallest;with the increase of the energy level space d,the superconducting energy gap first increases and then decreases,i.e.,the superconductivity increases first and then decreases;the critical superconducting energy space dc of GOE system is the highest,and the critical superconducting energy space dc of GSE system is smallest.For the case of S? 0,the relation of superconducting energy gap with T has the same tendency to the case of S = 0,with the increase of d,there is only the superconducting attenuation phenomenon,the critical superconducting energy space dc of the GOE system is highest,and the critical superconducting energy space dc of GSE system is smallest.In summary,GOE system is most favorable to the superconductivity,and GSE system is most unfavorable to the superconductivity.The large ground state spin S is unfavorable to the superconductivity of the systems.