TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.3.087
TI  - A large-$N$ approach to magnetic impurities in superconductors
PY  - 2025/03/10
UR  - https://www.scipost.org/SciPostPhys.18.3.087
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 3
SP  - 087
A1  - Huang, Chen-How
AU  - Lobos, Alejandro M.
AU  - Cazalilla, Miguel A.
AB  - 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 us to obtain a reasonably accurate description of experimentally relevant quantities. The latter include 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 not be easily applicable.
ER  -

@Article{10.21468/SciPostPhys.18.3.087,
	title={{A large-$N$ approach to magnetic impurities in superconductors}},
	author={Chen-How Huang and Alejandro M. Lobos and Miguel A. Cazalilla},
	journal={SciPost Phys.},
	volume={18},
	pages={087},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.3.087},
	url={https://scipost.org/10.21468/SciPostPhys.18.3.087},
}