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A Large-$N$ Approach to Magnetic Impurities in Superconductors
by Chen-How Huang, Alejandro M. Lobos, Miguel A. Cazalilla
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Submission summary
| Authors (as registered SciPost users): | Miguel A. Cazalilla · Chen-How Huang · Alejandro Lobos |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00023v2 (pdf) |
| Date accepted: | Feb. 11, 2025 |
| Date submitted: | Jan. 21, 2025, 2 p.m. |
| Submitted by: | Huang, Chen-How |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
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 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 not be easily applicable.
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- Provide a novel and synergetic link between different research areas.
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- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We thank you for forwarding the referee reports on our manuscript entitled "A Large-N Approach to Magnetic Impurities in Superconductors."
We are resubmitting a revised version of the manuscript with minor modifications, as suggested by the referees. We appreciate the positive feedback and constructive criticisms from both reviewers. Below we have addressed the points raised by them.
Given the ongoing effort in the Physics community to achieve a deeper understanding of the quantum phases of magnetic impurities in superconductors, we believe our paper is both timely and relevant to the field. We kindly ask that you consider it for publication in SciPost.
Sincerely,
Chen-How Huang, Alejandro M. Lobos, and Miguel A. Cazalilla
List of changes
In the paragraph between Eq.24 and Eq. 25, on page 5 of the revised manuscript. We have included an extended explanation of our parameter choices together with a citation to the work of Huang et al. and to Phys. Rev. Res. 6, 033022 (2024), as examples of the universal scaling.
Published as SciPost Phys. 18, 087 (2025)
Reports on this Submission
Report
(Although the presentation issues due to different densities of states in NRG and large-N approach could have been easily avoided by performing NRG calculations with the cosine DOS, which is not difficult to do.)
Recommendation
Publish (meets expectations and criteria for this Journal)