磁性杂质扰动下的4-费米子吸引超导体
A superconductor with 4-fermion attraction perturbed by magnetic impurities
摘要：
本文对Maenkowiak和Tarasewicz提出的具有4-费米子吸引的超导体的哈密顿量进行了修正，在哈密顿量中加入了导电费米子与自旋为1/2的磁性杂质之间的长程磁相互作用$V$。$V$具有简化的s-d相互作用的形式。系统的自由能量密度$f(H,β)$的上限和下限推导和两个边界合并的热力学极限。由此产生的平均场方程的间隙$Δ$和一个参数$y$，表征杂质子系统的解决方案，并找到最小化$f$的磁耦合常数$g$和杂质浓度的各种值。系统的相图被描述为五个不同的相：正常相、未扰动超导相、在激发谱中具有非零能隙的扰动超导相、扰动无能隙超导相和具有完全抑制的超导性的杂质相。
英文摘要：
A superconductor with 4-fermion attraction, considered by Maćkowiak and Tarasewicz is modified by adding to the Hamiltonian a long-range magnetic interaction $V$ between conduction fermions and localized distinguishable spin 1/2 magnetic impurities. $V$ has the form of a reduced s-d interaction. An upper and lower bound to the system's free energy density $f(H,β)$ is derived and the two bounds are shown to coalesce in the thermodynamic limit. The resulting mean-field equations for the gap $Δ$ and a parameter $y$, characterizing the impurity subsystem are solved and the solution minimizing $f$ is found for various values of magnetic coupling constant $g$ and impurity concentration. The phase diagrams of the system are depicted with five distinct phases: the normal phase, unperturbed superconducting phase, perturbed superconducting phase with nonzero gap in the excitation spectrum, perturbed gapless superconducting phase and impurity phase with completely suppressed superconductivity.
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