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

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

2008-10-21

arxiv.org/abs/0810.3847v2

Phys. Rev. B 79, 045110 (2009)

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

10.1103/PhysRevB.79.045110

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 \Delta=\infty is solved analytically. In order to tackle arbitrary \Delta<\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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