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

TL;DR

This paper develops a many-body perturbation theory for superconducting quantum dots, emphasizing the crucial role of magnetic fields in understanding phase transitions and magnetic responses beyond weak correlations.

Contribution

It introduces a thermodynamically consistent, two-particle self-consistent perturbation approach that accurately captures magnetic effects and phase transitions in superconducting quantum dots.

Findings

Magnetic field controls the $0$-$ ext{$ ext{ extpi}$}$ transition behavior.

Magnetic susceptibility vanishes in the $0$-phase and diverges in the $ ext{ extpi}$-phase.

The approach suppresses spurious transitions in Hartree-Fock solutions.

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 $0-\pi$ quantum transition, 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 of the Curie type and diverges in the $\pi$-phase at zero temperature.