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.

arXiv comment14 pages, 5 figures

References in corpus (29)

• The numerical renormalization group method for quantum impurity systems
• Majorana fermions in chains of magnetic atoms on a superconductor
• Topological Superconductivity and Majorana Fermions in RKKY Systems
• Topological superconducting phase in helical Shiba chains
• Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: toward a self-sustained topological Majorana phase
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Kondo effect in a magnetic field and the magnetoresistivity of Kondo alloys
• Josephson Current through a correlated quantum level: Andreev states and Pi-junction behavior
• Single magnetic adsorbates on s-wave superconductors
• Spectral properties of locally correlated electrons in a BCS superconductor
• Topological Superconductivity induced by Ferromagnetic Metal Chains
• Tunneling processes into localized subgap states in superconductors
• The Interacting Impurity Josephson Junction: Variational Wavefunctions and Slave Boson Mean Field Theory
• Mapping the orbital structure of impurity bound states in a superconductor
• Loss of Pi-Junction Behaviour in an Interacting Impurity Josephson Junction
• Magnetic anisotropy effects on quantum impurities in superconducting host
• Spin and charge gaps in the one-dimensional Kondo-lattice model with Coulomb interaction between conduction electrons
• 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)
• Numerical renormalization group calculation of near-gap peaks in spectral functions of the Anderson model with superconducting leads
• 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
• Local moment physics in heavy electron systems
• 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
• Influence of Rashba spin-orbit coupling on the 0-$\pi$ transition and Kondo temperature in 1D superconductors
• Probing Magnetic and Triplet Correlations in Spin-Split Superconductors with Magnetic Impurities