A superconductor is defined as "An element, inter-metallic alloy, or compound that will conduct electricity without resistance below a certain temperature." 1
The idea is that resistance causes energy that is flowing through the material to be lost.
The theory is that electrical current will flow forever in a closed loop of superconducting material in what is called a "macroscopic quantum phenomenon", or perhaps the closest thing that we will ever have to natural perpetual motion.
Type I, or "soft" superconductors are metals that have a bit of conductivity at room temperature, but actually require extreme cooling in order to provide the conditions for electrons to flow without resistance.
Type II, or "hard" superconductors work through a variety of stages and with complications that are not all understood! There is a transition temperature, or tc, where the free flow of electrons occurs, and the higher the tc, the better the superconductor. As a result, "hard" superconductors are supposed to require far less extreme measures in cooling the materials.
Lately, scientists are finding that using the properties of certain rare earth metals to "dope" or to affect the complex arrangements of magnetic fields, ions, electrons and so on in metal alloys, will not raise the temperature required for free and unrestricted flow of electricity in superconducting, but create additional conditions that are conducive to permanent electrical current in a closed system.
Various rare earth metals are tested in these complex constructions of metal alloys including: yttrium, erbium, neodymium, samarium, Europium, and Dysprosium.
All but Yttrium are lanthanoids on the periodic table of elements. Yttrium is the most desirable of the rare earths in some testing. Yttrium Barium Copper Oxide has been historically good for higher temperature conductivity. Neodymium has the highest magnetic properties. Erbium has magnetic and superconductivity properties. Lutetium is extremely difficult to extract and is rare.
In summary, the goal in superconductor development is to get to the higher temperatures (Tc) required to produce maximum conductivity, eliminating or reducing the need for supercooling. The rare earth metals are showing promise, in alloy with other metals and elements, in getting closer to that goal, but not always in ways that are understood, and with more of "less supercooling" than of "no supercooling at all" as the results.
1. Superconductor Information For The Beginner
"US Patent 4857504 - Melt-produced high temperature rare earth barium copper oxide superconductor and processes for making same"
Yttrium Barium Carbon Oxide (YBCO)