局域排斥相互作用对s波超导体的影响
Effect of a Locally Repulsive Interaction on s-wave Superconductors
摘要：
通过对强耦合BCS-Hubbard哈密顿量的平衡态和基态的严格研究，分析了库仑排斥对s波超导体的热力学影响。我们发现，在化学势不变的情况下，通过提高临界温度和（或）库珀对凝聚密度，单格点电子排斥可以促进超导性.如果单位点排斥力不太大，则在低温下可出现一级或二级超导相变。迈斯纳效应是相当普遍的，但超导和铁磁相的共存也被证明是可行的，例如接近半填充和强排斥。我们对超导体-莫特绝缘体相变的证明意味着对掺杂绝缘体以产生超导体的必要性的严格解释。这些数学结果是“量子大偏差”论点的结果，结合了Størmer定理的证明对CAR代数上的偶态的适应。
英文摘要：
The thermodynamic impact of the Coulomb repulsion on s-wave superconductors is analyzed via a rigorous study of equilibrium and ground states of the strong coupling BCS-Hubbard Hamiltonian. We show that the one-site electron repulsion can favor superconductivity at fixed chemical potential by increasing the critical temperature and/or the Cooper pair condensate density. If the one-site repulsion is not too large, a first or a second order superconducting phase transition can appear at low temperatures. The Meißner effect is shown to be rather generic but coexistence of superconducting and ferromagnetic phases is also shown to be feasible, for instance near half-filling and at strong repulsion. Our proof of a superconductor-Mott insulator phase transition implies a rigorous explanation of the necessity of doping insulators to create superconductors. These mathematical results are consequences of "quantum large deviation" arguments combined with an adaptation of the proof of Størmer's theorem to even states on the CAR algebra.
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