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.

17 pages, 15 figures

References in corpus (18)

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• Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure
• Tunable reentrant Kondo effect in quantum dots coupled to metal-superconducting hybrid reservoirs
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• Controllable odd-frequency Cooper pairs in multi-superconductor Josephson junctions
• Rigorous Wilsonian Renormalization Group for impurity models with a spectral gap
• Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models
• Effective low-energy models for superconducting impurity systems
• Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Generalized transmon Hamiltonian for Andreev spin qubits
• YSR Bond Qubit in a Double Quantum Dot with cQED Operation
• Andreev bound state spectroscopy of a quantum-dot-based Aharonov-Bohm interferometer with superconducting terminals
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• 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
• Quantum phase transition in a double quantum dot Josephson junction driven by electron-electron interactions