**d. Impurity model**

The impurity model deals with the superconductivity for nanoscale systems that have impurity magnetic moments with localized spins as magnetic superconductors [14], in which there is a strong Zeeman effect. According to this model, superconductivity is enhanced with the quenching of pair-breaking magnetic spin fluctuations by the applied magnetic field.

These are major theoretical models for the explanation of the anti-proximity effect in nanoscale systems. Their validity needs more experimental evidence.
