超导临界温度理论(Ⅱ)

THEORY OF THE SUPERCONDUCTING CRITICAL TEMPERATURE (Ⅱ)

在文献[1]中,我们导出了超导临界温度T_c的一个严格级数表式。本文讨论这个级数的收敛范围,以及通过解析延拓来扩展收敛范围的可能性。结论是:我们的T_c级数(指文献[1]原来的级数,或者经过延拓后的级数)在∞>λ>λ_0的整个范围内,都是收敛的。这里λ_0是Matsubara表象中使决定T_c的方程具有正实数解的最小的λ值。实际上,就是库仑赝势。因此,这就是说,也许除了少数非常弱耦合的超导体以外,我们的T_c级数,能适用于一切超导体。

In a previous paper (I), we have derived a rigorous series expression for the superconducting critical temperature Tc. Here we discuss the region of convergence of this series, and the possibility of its extension through analytical continuation. Our conclusion is that the above mentioned series or its analytical extension is convergent within the whole region ∞ > λ > λ0. By λ0 we mean the smallest value of λ which can be taken such that the equation determining Tc in the Matsubara representation has a real positive solution. It is in fact the Coulomb pseudopotential. Therefore, ex-cluding possibly a few very weakly coupled ones, our Tc formula is applicable to all superconductors.