超导体中磁杂质的大 N$ 方法

Chen-How Huang, Alejandro M. Lobos, Miguel A. Cazalilla
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引用次数: 0

摘要

与超导体耦合的量子自旋杂质正受到人们的密切关注,因为它们不仅与基础研究相关,而且有望设计出新的物质量子相。在这里,我们发展了传统 $s$ 波超导体中强耦合自旋-$tfrac{1}{2}$ 量子杂质的大 $N$ 均场理论。该方法以威尔逊的数值重正化群(NRG)为基准。虽然大-N$方法不适用于Kondotemperature $T_K$小于超导间隙$\Delta$的弱耦合体系,但它在强耦合体系中的表现非常好,在强耦合体系中,$T_K \gtrsim \Delta$,从而可以获得对实验相关量子的合理精确描述。后者包括Yu-Shiba-Rusinov子间隙态的能量、它们的光谱权重以及连续态的局部密度。该方法提供了一种可靠的分析工具,是对其他扰动和非扰动方法的补充,并可扩展到 NRG 可能不易适用的更复杂的杂质模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Large-$N$ Approach to Magnetic Impurities in Superconductors
Quantum spin impurities coupled to superconductors are under intense investigation for their relevance to fundamental research as well as the prospects to engineer novel quantum phases of matter. Here we develop a large-$N$ mean-field theory of a strongly coupled spin-$\tfrac{1}{2}$ quantum impurity in a conventional $s$-wave superconductor. The approach is benchmarked against Wilson's numerical renormalization group (NRG). While the large-$N$ method is not applicable in the weak-coupling regime where the Kondo temperature $T_K$ is smaller than the superconducting gap $\Delta$, it performs very well in the strong coupling regime where $T_K \gtrsim \Delta$, thus allowing to obtain a reasonably accurate description of experimentally relevant quantities. The latter includes the energy of the Yu-Shiba-Rusinov subgap states, their spectral weight, as well as the local density of continuum states. The method provides a reliable analytical tool that complements other perturbative and non-perturbative methods, and can be extended to more complex impurity models for which NRG may be not easily applicable.
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