Application of the Coherent Potential Approximation to Impurity Problems in Superconductor. I : Resonance Scattering

概要

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The effect of the resonance scattering on superconductivity is investigated in the coherent potential approximation. The depression of the transition temperature and the density of states in the energy gap are calculated. Compared with the result in the usual approximation, the depression of the transition temperature is shown to be smaller. The critical concentration c_0 at which the transition temperature becomes zero is given by c_0(1-c_0)=πρΓΔ/Δ_d, which is slightly different from that in the usual approximation. The value of Δ_d/Δ is calculated with and without the cut off procedure of Kaiser. With the cut off procedure, the value of Δ_d/Δ is shown to be slightly smaller in the CPA than in the usual approximation. Without using this procedure, the expression for Δ_d/Δ is expanded in powers of the concentration. The first-order correction to the usual approximation is calculated, and is shown to be negative, and large if πρΓ>>1. From the density of states calculated, we obtain the condition for the superconductor to become gapless. It is shown that the concentration at which the gapless situation begins coincides with the critical concentration, and the gapless superconductor is not realized.
理論物理学刊行会の論文
1973-04-25