Effective low-energy models for superconducting impurity systems

Abstract

We present two complementary methods to calculate the Andreev bound state energies of a single-level quantum dot connected to superconducting leads described by the superconducting impurity Anderson model. The first method, which is based on a mapping to a low-energy model, can be utilized to extract the Andreev bound state energies from finite-temperature, imaginary-time quantum Monte Carlo data without the necessity of any analytic continuation technique. The second method maps the full model on an exactly solvable superconducting atomic limit with renormalized parameters. As such, it represents a fast and reliable method for a quick scan of the parameter space. We demonstrate that after adding a simple band correction this method can provide predictions for measurable quantities, including the Josephson current, that are in a solid quantitative agreement with precise results obtained by the numerical renormalization group and quantum Monte Carlo.

arXiv comment16 pages, 7 figures

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• Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions
• Nonlocal Andreev transport through a quantum dot in a magnetic field: Interplay between Kondo, Zeeman, and Cooper-pair correlations
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Properties of multiterminal superconducting nanostructure with double quantum dot
• Three-body Fermi-liquid corrections for Andreev transport through quantum dots