A Large-$N$ Approach to Magnetic Impurities in Superconductors

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-$\frac{1}{2}$ 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.

14 pages, 5 figures

References in corpus (14)

• The numerical renormalization group method for quantum impurity systems
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Spectral properties of locally correlated electrons in a BCS superconductor
• Topological Superconductivity induced by Ferromagnetic Metal Chains
• Magnetic anisotropy effects on quantum impurities in superconducting host
• Scaling of Yu-Shiba-Rusinov energies in the weak-coupling Kondo regime
• Microscopic resolution of the interplay of Kondo screening and superconducting pairing: Mn-phthalocyanine molecules adsorbed on superconducting Pb(111)
• Yu-Shiba-Rusinov states in real metals
• Adaptive logarithmic discretization for numerical renormalization group methods
• The fate of the Kondo cloud in a superconductor
• Pair excitations of a quantum spin on a proximitized superconductor
• Universal scaling of tunable Yu-Shiba-Rusinov states across the quantum phase transition
• Theory of a Single Magnetic Impurity on a Thin Metal Film in Proximity to a Superconductor
• Probing Magnetic and Triplet Correlations in Spin-Split Superconductors with Magnetic Impurities