Failure of the mean-field description of magnetic fluctuations in the superconducting quantum dot

TL;DR

This paper demonstrates that static mean-field approaches fail to accurately describe magnetic fluctuations in superconducting quantum dots at non-zero temperatures, revealing the importance of dynamical corrections and the instability of spin-symmetric states.

Contribution

It shows that static mean-field approximations are inadequate at non-zero temperatures due to magnetic fluctuations causing dynamical effects and state broadening.

Findings

Mean-field approximation fails at non-zero temperatures.

Magnetic fluctuations induce dynamical corrections.

Spin-symmetric state is unstable at finite temperature.

Abstract

The zero-temperature physics of interacting quantum dots attached to superconducting leads is now well understood. The overall qualitative picture is obtained from the static mean-field approximation. The situation drastically changes at non-zero temperatures. No reliable solutions apart from numerical simulations exist there. We show that any static mean-field approximation fails at non-zero temperatures since magnetic fluctuations induce dynamical corrections that lead to broadening of the in-gap state energies to energy bands. Spin-symmetric equilibrium state at non-zero temperatures is unstable with respect to magnetic fluctuations and the zero magnetic field can be reached only as a weak limit of the spin-polarized solution like in a magnetically ordered phase.