Is there a theoretical ground for ionic superconductivity?

I've been wondering for a while if there's a possible theoretical ground for ionic superconductivity, or whether it is at all possible from a thermodynamic and condensed matter physics standpoint.

Ions are obviously much more massive than electrons. and they cannot form Cooper pairs, so the mechanisms are likely very different. But is there anything that prevents a material like this from existing?

• What exactly do you mean by an ionic superconductor here? – By Symmetry Jul 12 '19 at 13:23
• I mean a solid state electrolyte (or fast ion conductor, which is how some people refer to them) with zero resistance to the conduction of ions (or of a specific ion, think H+, Li+, etc), while being simultaneously an electronic insulator. – FBolst Jul 12 '19 at 13:40
• I'm not particularly interested in conventional superconductivity properties (Meissner, phase transition, etc) other than zero ionic resistance in the presence of a DC potential. – FBolst Jul 12 '19 at 13:50
• Having superconducting ions is not impossible, but the temperature scale for this to happen is $\sqrt{m_{electron}/m_{ion}}$ which is anywhere from about 40 times smaller than usual superconducting temperatures for protons, to over 300 times smaller for something like an iron nucleus at the very least. So you're looking at things like cold atom or cold ion traps instead of solids state systems. – KF Gauss Jul 12 '19 at 14:08