LEVEL STATISTICS AND PARITY EFFECT ON SMALL SUPERCONDUCTING SYSTEMS
Chen Zhi-qian (陈志谦)a, Zheng Ren-rong (郑仁蓉)b
a Department of Physics, Southwest China Normal University, Chongqing 400715, China; b Department of Physics, Shanghai Teachers University, Shanghai 200234, China
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. Solids11 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.
Received: 31 May 2000
Revised: 12 July 2001
Accepted manuscript online:
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