Superconductivity of small metal grains  

作　　者：ZHENG Renrong1 CHEN Zhiqian2 & ZHU Shunquan1,3 1. Department of Physics, Shanghai Normal University, Shanghai 200234, China 2. Department of Physics, Southwest Normal University, Chongqing 400715, China 3. Department of Computer and Electric Technology, Shanghai Business School, Shanghai 201400, China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2005年第4期431-441,共11页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(NNSF)(Grant Nos.10147207 and 10375001);China Shanghai Foundation for Developing Science and Technology(Grant No.0252nm082);China Shanghai Foundation for Developing Science and Technology in Universities(Grant No.03DZ03);the Third Phase Foundation of Theoretical Center in China Lanzhou National Key Laboratory.

摘　　要：The formulas of the energy gap and superconducting critical temperature appropriate for systems with both odd and even number of electrons are derived; the bases of the derivations are BCS theory and energy level statistics. Numerical results qualitatively agree with the experimental phenomena. i.e., the superconductivity of small metallic grains will first enhance then decrease to zero when the grain are getting smaller and smaller. The calculations indicate that the above phenomena happen in the metallic grains belonging to Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary ensemble (GUE) with zero spin; The superconductivity of small metallic grains in Gaussian Symplectic Ensemble (GSE) will monotonically decrease to zero with the decreasing of the grain size. The analyses suggest that the superconductivity enhancements come from pairing and the balance of the strengths between spin-orbital coupling and external magnetic field. In order to take the latter into account, it is necessary to include the level statistics given by Random Matrix Theory (RMT) in describing small metallic grains.The formulas of the energy gap and superconducting critical temperature appropriate for systems with both odd and even number of electrons are derived; the bases of the derivations are BCS theory and energy level statistics. Numerical results qualitatively agree with the experimental phenomena. i.e., the superconductivity of small metallic grains will first enhance then decrease to zero when the grain are getting smaller and smaller. The calculations indicate that the above phenomena happen in the metallic grains belonging to Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary ensemble (GUE) with zero spin; The superconductivity of small metallic grains in Gaussian Symplectic Ensemble (GSE) will monotonically decrease to zero with the decreasing of the grain size. The analyses suggest that the superconductivity enhancements come from pairing and the balance of the strengths between spin-orbital coupling and external magnetic field. In order to take the latter into account, it is necessary to include the level statistics given by Random Matrix Theory (RMT) in describing small metallic grains.

关 键 词：SIZE effect  SUPERCONDUCTIVITY enhancements  SMALL METALLIC grains. 

分 类 号：O511[理学—低温物理]