SciPost Submission Page
A Large-$N$ Approach to Magnetic Impurities in Superconductors
by Chen-How Huang, Alejandro M. Lobos, Miguel A. Cazalilla
Submission summary
| Authors (as registered SciPost users): | Chen-How Huang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00023v1 (pdf) |
| Date submitted: | 2024-09-19 22:43 |
| 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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Report
The authors present a large-N mean field approach to the Kondo model for a magnetic impurity in a superconductor. They show results for the subgap states position and the local density of states which compare reasonably well with NRG calculations in the limit of large Kondo temperature.
In my opinion the approach and the results presented in this manuscript are sound and deserve to be published in Scipost. The manuscript is written in a rather pedagogical way, which I find very valuable.
The only point which I find a bit obscure is the choice of the band-width for the comparison of large-N and NRG calculations. As indicated in Eq. (25), the authors require that the density of states at the Fermi level, \rho_0, should be the same in
both calculations, i.e. \rho_0 = 1/(\pi t) = 1/2D, where t is the hopping element in the effective TB model and D is the NRG band-width. Thus, I would have expected that for the comparison they choose a ratio D/t such that \rho_0\Delta is the same in both calculations. However, taking the values indicated in Fig. 4(a) I find \rho_0\Delta= 0.0005 in the NRG calculation, and \rho_0\Delta = 0.005/\pi for the large-N one. There might be some misunderstanding from my side but in any case it would be worth that the authors could clarify this issue in their manuscript.
The authors might also consider giving a reference to some recent STM experimental works where YSR were detected and correlated with the Kondo effect in the normal state (see Communications Physics 6, 214 (2023) and references there in).
Notice also a typo in the sentence "We speculate that this is feature...".
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)