Georg,

We seem to be at cross purposes.

I did not mean that the charges in a conductor were not cancelled out, but that the moving of the charges was not cancelled out. Let us consider an example where both the negative and positive charges move together: A simple case would be movement of a metal wire in a zero net magnetic and electric field. Plenty of charge moves, both positive and negative, but they move together, so there is no electric current. Right? Move just a fraction of the negative charge independently within that wire though, and lo! we have a current! In a normal conductor, if the motion is too energetic the interaction between the static atoms and the moving electrons can heat the conductor, but in the superconductor such interactions are abolished. Almost as soon as any factor re-introduces interaction, the superconductivity fails, often catastrophically. As you rightly point out, they fail differently in the different classes of sperconductors. As you also point out, not all of the classes are well understood.

Beware what you say about  non-exclusion of magnetic fields though; one of the most convenient demonstrations of superconductivity in high-temperature superconductors was to take the test item out of liquid N2 and put it on a magnet. If it was superconducting it floated above the magnet.

Remember?

I did mention that the effect I described was only part of the story, but I am sure you will agree that with my loquacity I could not cover the whole field, even if I were an expert on the whole field!

I am not! ;-)