Generalized atomic limit of a double quantum dot coupled to superconducting leads

Abstract

We present an exactly solvable effective model of a double quantum dot coupled to superconducting leads. This model is a generalization of the well-known superconducting atomic limit approximation of the paradigmatic superconducting impurity Anderson model. However, in contrast to the standard atomic limit and other effective models, it gives quantitatively correct predictions for the quantum phase transition boundaries, subgap bound states as well as Josephson supercurrent in a broad range of parameters including experimentally relevant regimes. The model allows fast and reliable parameter scans important for the preparation and analysis of experiments which are otherwise inaccessible by more precise but computational heavy methods such as quantum Monte Carlo or the numerical renormalization group. The scans also allowed us to identify and investigate new previously unnoticed phase diagram regimes. We provide a thorough analysis of the strengths and limitations of the effective model and benchmark its predictions against numerical renormalization group results.

arXiv comment17 pages, 15 figures

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• Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models
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• Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions
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• Generalized transmon Hamiltonian for Andreev spin qubits
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• Andreev bound state spectroscopy of a quantum-dot-based Aharonov-Bohm interferometer with superconducting terminals
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• Kondo Screening and Indirect Magnetic Exchange through a Conventional Superconductor Studied by the Density-Matrix Renormalization Group
• Slave-spin approach to the Anderson-Josephson quantum dot
• Magnetic flux controlled current phase relationship in double Quantum Dot Josephson junction
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