More remarks on the electromagnetic properties of a domain wall interacting with charged fermions

The response to a magnetic flux is considered of the vacuum state of charged Dirac fermions interacting with a domain wall made of a neutral spinless field in 3+1 dimensions with the fermion mass term having a phase variation across the wall. It is pointed out that as a result of simple C parity arguments the spontaneous magnetization for this system is necessarily zero, thus invalidating some claims to the contrary in the literature. The cancellation of the spontaneous magnetization is explicitly demonstrated in a particular class of models. The same calculation produces a general formula for the electric charge density induced by the magnetic flux-an effect previously discussed in the literature for axionic domain walls. The distribution of the induced charge is calculated in specific models.