Microscopic Foundations of the Mei\ss ner Effect - Thermodynamic Aspects

TL;DR

This paper derives the microscopic quantum mechanical basis of the Meissner effect, demonstrating the existence of superconducting states that minimize magnetic free energy and expel magnetic fields, advancing understanding of its fundamental origins.

Contribution

It provides a first-principles analysis showing superconducting states with surface currents that eliminate magnetic induction, moving towards a complete microscopic explanation of the Meissner effect.

Findings

Superconducting states minimize magnetic free energy in BCS-like models.

Surface currents in these states expel magnetic fields from the bulk.

The Meissner effect is not necessarily linked to magnetic susceptibility of -1.

Abstract

We analyze the Mei\ss ner effect from first principles of quantum mechanics. We show in particular the existence of superconducting states minimizing the magnetic free-energy of BCS-like models and carrying surface currents which annihilate the total magnetic induction inside the bulk in the thermodynamic limit. This study is a step towards a complete explanation of the Mei\ss ner effect from microscopic models. It remains indeed to prove that those states are dynamically stable, i.e., quasi-stationary at low temperatures. Note that our analysis shows that the Mei\ss ner effect is not necessarily related to an effective magnetic susceptibility equal to $-1$.