Can a perfect insulator, i.e. matter devoid of all electrons conduct electricity?

Question

Few weeks ago an article on Nautilus was published on Neutron stars. After reading that, a question was asked by a friend of mine. He asked if matter in neutron star would be able to transfer electricity as he thought that since neutron stars have no electrons, they should not be able to conduct electricity. My answer based on whatever little I know about it was as follows:

IIRC, by definition if there is no charge (electrons i.e.), there will be no electric current, so there won't be any electrical conduction, however, you could transport other quantities such as spin. At a given point you should have a fermi gas (if diluted enough) or a fermi liquid depending on the number of protons of electrons at that specific time. However, let's assume you can apply a voltage in order to induce a current. You'll have two problems, the charges will radiate and lose kinetic energy and they will interfere with each other via coulomb interaction. In a solid, the electrons are not the charge carriers. The charge carriers are quasi-particle electrons that only exists due to the presence of the lattice and there is screening due to the core electrons and that is why in many cases you can consider them as a non-interacting electron/hole gas. In a real electron gas the coulomb interaction is long range and there will be radiation due to the voltage. So, if you sum this with the fact that the mean time this proton-electron pair is probably very small I would say the conduction should be close to zero on a bulk scale. But again they transport neutrons. Although, for me it is quite interesting neutron transport, because it can be related to spin-transport which is something I am interested in.  That is what I think matters should be, unless I don't remember some details or/and have some fundamental misunderstandings in this regard. I think this paper should clear up some doubts regarding this.

I would like to know from experts at Physics StackExchange if what I have replied as an answer to him is correct, or are there some or fundamental misunderstandings on my part (if any). Have I missed some points which should have been stated with lucidity? I apologize in advance if this question has been asked here before me. Regards!

Answer 1

Neutron stars are electrically conductive because the neutrons are able to decay into protons and electrons. An equilibrium is setup so that the Fermi energy of the neutrons is equal to the sum of the Fermi energies of the protons and electrons. At typical neutron densities inside a neutron star, the n/p ratio is around 50-100 (the numbers of protons and electrons are equal). e.g. see What stabilizes neutrons against beta decay in a neutron star?

The protons in the deep interior are likely to be both superfluid and superconducting once the neutron star has cooled for a few hundred years or so.

Degenerate electrons also have a very high conductivity because, despite what you say in your post, they are not susceptible to long range interactions or scattering since there are no free states for them to scatter into. The long mean free paths mean both a high thermal and electric conductivity. Degenerate electrons are present both in the deep interior of the neutron star and the crust, right up to very close to the surface.

The very high electrical conductivity of neutron stars combined with their strong magnetic fields forms the basis of the original Julian & Goldreich (1969 ) model for the pulsar phenomenon.