关键词：
COOPER-SCHRIEFFER THEORY
CRITICAL-TEMPERATURE
摘要：
In this paper, we present a mathematical analysis for the phonon-dominated multiband isotropic and anisotropic BCS gap equations at any finite temperature T. We establish the existence of a critical temperature T-c so that, when T < T-c, there exists a unique positive gap solution, representing the superconducting phase;when T > T-c, the only nonnegative gap solution is the zero solution, representing the normal phase. Furthermore, when T = T-c, we prove that the only gap solution is the zero solution and that the positive gap solution depend on the temperature T < T-c monotonically and continuously. In particular, as T --> T-c, the gap solution tends to zero, which enables us to determine the critical temperature T-c. In the isotropic case where the entries of the interaction matrix K are all constants, we are able to derive an elegant T-c equation which says that T-c depends only on the largest positive eigenvalue of K but does not depend on the other details of K. In the anisotropic case, we may derive a similar T-c equation in the context of the Markowitz-Kadanoff model and we prove that the presence of anisotropic fluctuations enhances T-c as in the single-band case. A special consequence of these results is that the half-unity exponent isotope effect may rigorously be proved in the multiband BCS theory, isotropic or anisotropic. (C) 2004 Elsevier B.V. All rights reserved.
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中文科技期刊
详细信息
Wiley期刊
