高斯正交系综中金属小粒子的超导电性

利用推广的BCS场理论，考虑随机矩阵理论的能级统计，得到了适合奇偶两种电子数的金属小粒子能隙和超导转变温度的统一公式．计算结果表明，对于总自旋为零的、服从高斯正交系(GOE)的金属小粒子，可以从理论上定性再现其随其尺寸变小，所出现的超导电性先增强后衰减到零、连续变化的实验现象，说明了此类现象与库仑堵塞和能谱统计有关。

Superconductivity for ultra-small metallic grains belonging to gaussian orthogonal ensemle

Based on generalized BCS theory, considering energy level statistics from Random Matrices Theory, we have derived the unified formulas of energy gap and superconductor critical temperature suitable for ultra-small metallic grains with both odd and even number of electrons . The numerical results reproduce the experimental phenomena qualitatively, i. e. the superconductivity will be first enhanced then decreasing gradually until disappearing when the size of the metal particle belonging GOE ensemble with spin zero getting smaller and smaller. This tells us the Coulomb blockade and the level statistics are necessary in describing small metal grains.