Microscopic Foundations of the Meißner Effect - Thermodynamic Aspects

We analyze the Meißner 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 Meißner 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 Meißner effect is not necessarily related to an effective magnetic susceptibility equal to $-1$.

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