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

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-pi quantum transition and lifts the degeneracy in the pi 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 pi phases. While the magnetic susceptibility vanishes in the 0 phase it becomes divergent in the pi phase at zero temperature.

Automated summary

This study develops a general many-body perturbation theory for a superconducting quantum dot and shows the critical role of the magnetic field in the 0-π quantum transition.