# Constraining forces causing the Meissner effect

## TL;DR

This paper proposes a quantum mechanical constraining force mechanism for Cooper pair formation that explains the Meissner effect in superconductors, aligning with experimental observations across different types.

## Contribution

It introduces a novel nonadiabatic Heisenberg model mechanism for Cooper pairing that accounts for the Meissner effect under magnetic fields.

## Key findings

- Constraining forces produce Cooper pairs with non-zero momentum in magnetic fields.
- The resulting electric current obeys London equations, explaining the Meissner effect.
- Experimental evidence supports the universal presence of the Meissner effect in all superconductors.

## Abstract

As shown in former papers, the nonadiabatic Heisenberg model presents a novel mechanism of Cooper pair formation which is not the result of an attractive electron-electron interaction but can be described in terms of quantum mechanical constraining forces. This mechanism operates in narrow, roughly half-filled superconducting bands of special symmetry and is evidently responsible for the formation of Cooper pairs in all superconductors. Here we consider this new mechanism within an outer magnetic field. We show that in the magnetic field the constraining forces produce Cooper pairs of non-vanishing total momentum with the consequence that an electric current flows within the superconductor. This current satisfies the London equations and, consequently, leads to the Meissner effect. This theoretical result is confirmed by the experimental observation that all superconductors, whether conventional or unconventional, exhibit the Meissner effect.