Josephson effect through a quantum dot array

Abstract

We analyze the ground state properties of an array of quantum dots connected in series between superconducting electrodes. This system is represented by a finite Hubbard chain coupled at both ends to BCS superconductors. The ground state is obtained using the Lanczos algorithm within a low energy theory in which the bulk superconductors are replaced by effective local pairing potentials. We study the conditions for the inversion of the sign of the Josephson coupling ($\pi$-junction behavior) as a function of the model parameters. Results are presented in the form of phase diagrams which provide a direct overall view of the general trends as the size of the system is increased, exhibiting a strong even-odd effect. The analysis of the spin-spin correlation functions and local charges give further insight into the nature of the ground state and how it is transformed by the presence of superconductivity in the leads. Finally we study the scaling of the Josephson current with the system size and relate these results with previous calculations of Josephson transport through a Luttinger liquid.

9 pages, 8 figures

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• Correlated electron transport through double quantum dots coupled to normal and superconducting leads
• Signatures of nonlocal Cooper-pair transport and of a singlet-triplet transition in the critical current of a double-quantum-dot Josephson junction
• Equilibrium and time-dependent Josephson current in one-dimensional superconducting junctions
• Interplay between direct and crossed Andreev reflections in hybrid nano-structures
• Numerical sub-gap spectroscopy of double quantum dots coupled to superconductors
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Suppressed Josephson phase transition in one parallel double-quantum-dot junction
• Generalized transmon Hamiltonian for Andreev spin qubits
• Yu-Shiba-Rusinov states, the BCS-BEC crossover, and the exact solution in the flat-band limit
• Slave-spin approach to the Anderson-Josephson quantum dot