Would superconductors made from heavy radio-isotopes transition at higher temperatures?

Question

I read somewhere that heavier variants of water (using deuterium or hydrogen) melt at higher temperatures compared to normal water.

A simple argument for why this is could be the following: heavier water has more mass per molecule than normal water. So in an ice crystal if the transition from ice to water is a function of the "velocities" of the vibrating water molecules, then the heavier water will need MORE energy to get to the same "vibrational state" as the regular water (before the ice starts to melt), this manifests as the heavier water requiring a higher temperature before it melts.

So assuming that line of logic makes sense (and if it doesn't I guess the question just dies here), then would it be the case that superconductors made from radio-isotopes achieve their transition temperature at higher temperatures?

One could argue from our water-thought-experiment that a superconductor (say YBCO) made from heavy variants of its constituent elements should be able to absorb a lot more energy before its vibrational state breaks superconductivity. Would this difference in temperature be significant from an engineering standpoint? In the case of ice melting the difference is not very large (just a few degrees).

Answer 1

Your line of logic regarding water melting sounds reasonable to me, however I believe it is not applicable to superconductors. Primarily because in superconductivity it is more about electrons than atoms (it is the electrons that get into broken-symmetry state). Hence, at the $0^{th}$ level of approximation changing the nuclear content of the surrounding ions should not do anything. In the next approximation you can remember that electrons interact with lattice ions. When this interaction is important for the formation of SC state, you get the isotope effect. But here your analogy with waters breaks down, as ions here are not the ones that "vibrate out of the ordered positions" (that would be electrons in SC), but instead contribute to the "glue" that holds electrons "in place" so to speak. Consequently heavier ions reduce T$_c$ rather than increase it (typically $\sqrt{M_{ion}}\, T_C=$const). In other cases (like YBCO and other cuprate superconductors) isotopic masses does not do anything and hence it is believed it has no role in the "glue" keeping the electrons together.

However you question would make more direct sense if you have asked what would happen if one had replaced electrons in YBCO with, say, muons (assuming the lattice structure had miraculously remained the same). Then your reasoning could be applied more directly although I don't know the answer.