Many-body perturbation theory for the superconducting quantum dot: Fundamental role of the magnetic field

Abstract

We develop the general many-body perturbation theory for a superconducting quantum dot represented by a single-impurity Anderson model attached to superconducting leads. We build our approach on a thermodynamically consistent mean-field approximation with a two-particle self-consistency of the parquet type. The two-particle self-consistency leading to a screening of the bare interaction proves substantial for suppressing the spurious transitions of the Hartree-Fock solution. We demonstrate that the magnetic field plays a fundamental role in the extension of the perturbation theory beyond the weakly correlated 0 phase. It controls the critical behavior of the 0−π quantum transition and lifts the degeneracy in the π phase, where the limits to zero temperature and zero magnetic field do not commute. The response to the magnetic field is quite different in 0 and π phases. While the magnetic susceptibility vanishes in the 0 phase it becomes divergent in the π phase at zero temperature.

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