Supercurrent and multiple singlet-doublet phase transitions of a quantum dot Josephson junction inside an Aharonov-Bohm ring

Abstract

We study a quantum dot Josephson junction inside an Aharonov-Bohm environment. The geometry is modeled by an Anderson impurity coupled to two directly-linked BCS leads. We illustrate that the well-established picture of the low-energy physics being governed by an interplay of two distinct (singlet and doublet) phases is still valid for this interferometric setup. The phase boundary depends, however, non-monotonically on the coupling strength between the superconductors, causing the system to exhibit re-entrance behavior and multiple phase transitions. We compute the zero-temperature Josephson current and demonstrate that it can become negative in the singlet phase by virtue of the Coulomb interaction U. As a starting point, the limit of large superconducting energy gaps Δ=\infty is solved analytically. In order to tackle arbitrary Δ<\infty and U>0, we employ a truncated functional renormalization group scheme which was previously demonstrated to give quantitatively reliable results for the quantum dot Josephson problem.

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• The Anderson-Josephson quantum dot -- A theory perspective
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• Spectroscopy of spin-split Andreev levels in a quantum dot with superconducting leads
• Proximity effect on spin-dependent conductance and thermopower of correlated quantum dots
• Probing the exchange field of a quantum-dot spin valve by a superconducting lead
• Supercurrent through a serial quantum dot close to singlet-triplet degeneracy
• Magneto-electric spectroscopy of Andreev bound states in Josephson quantum dots
• Josephson response of a conventional and a noncentrosymmetric superconductor coupled via a double quantum dot
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• The Functional Renormalization Group for Zero-Dimensional Quantum Systems in and out of Equilibrium
• Andreev bound state spectroscopy of a quantum-dot-based Aharonov-Bohm interferometer with superconducting terminals
• Effects of electron-electron interaction and spin-orbit coupling on Andreev pair qubits in quantum dot Josephson junctions