中国物理B ›› 2001, Vol. 10 ›› Issue (12): 1149-1153.doi: 10.1088/1009-1963/10/12/313

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LEVEL STATISTICS AND PARITY EFFECT ON SMALL SUPERCONDUCTING SYSTEMS

郑仁蓉1, 陈志谦2   

  1. (1)Department of Physics, Shanghai Teachers University, Shanghai 200234, China; (2)Department of Physics, Southwest China Normal University, Chongqing 400715, China
  • 收稿日期:2000-05-31 修回日期:2001-07-12 出版日期:2001-12-15 发布日期:2005-06-12
  • 基金资助:
    Project support by the Chongqing Commission of Science and Technology, China.

LEVEL STATISTICS AND PARITY EFFECT ON SMALL SUPERCONDUCTING SYSTEMS

Chen Zhi-qian (陈志谦)a, Zheng Ren-rong (郑仁蓉)b    

  1. a Department of Physics, Southwest China Normal University, Chongqing 400715, China; b Department of Physics, Shanghai Teachers University, Shanghai 200234, China
  • Received:2000-05-31 Revised:2001-07-12 Online:2001-12-15 Published:2005-06-12
  • Supported by:
    Project support by the Chongqing Commission of Science and Technology, China.

摘要: In this paper we have calculated the variations of the gap Δ'(0,d) and transition temperature T'c in small metallic grains as functions of grain size (or the level spacing d between discrete electronic states) for the cases of odd and even numbers of electrons by applying the random matrix theory to the mean field theory. We find the presence of enhancement of superconductivity and critical dc, where the superconductivity of small grains breaks down. This agrees with Anderson's prediction (1959 J. Phys. Chem. Solids 11 28). We find that in the grains, as the size is lowered, the transition temperature T'c decreases and Δ'(0,d)/kBT'c≤πe in odd numbers of electrons, and for Gaussian orthogonal and unitary ensembles in some regimes Δ'(0,d)/kB T'c>πe in even numbers of electrons.

Abstract: In this paper we have calculated the variations of the gap $\Delta'(0,d)$ and transition temperature T'c in small metallic grains as functions of grain size (or the level spacing d between discrete electronic states) for the cases of odd and even numbers of electrons by applying the random matrix theory to the mean field theory. We find the presence of enhancement of superconductivity and critical dc, where the superconductivity of small grains breaks down. This agrees with Anderson's prediction (1959 J. Phys. Chem. Solids 11 28). We find that in the grains, as the size is lowered, the transition temperature T'c decreases and $\Delta'(0,d)/k_{B}T'_{\rm c}\leq \pi e^{-\gamma}$ in odd numbers of electrons, and for Gaussian orthogonal and unitary ensembles in some regimes $\Delta'(0,d)/k_{B}T'_{\rm c}> \pi e^{-\gamma}$  in even numbers of electrons.

Key words: superconductivity, level statistics, parity effect

中图分类号:  (Other effects)

  • 74.62.Yb
74.25.Jb (Electronic structure (photoemission, etc.)) 74.20.-z (Theories and models of superconducting state)