Failed theories of SC

In one of my previous entries, I mentioned the failed theories that were briefly reviewed in a preprint. Here in Nature Physics [Nature Physics, 6: 715, 2010], another one based on this review came out. I especially like this story about Laudau:

Yet it turns out that Landau first proposed these ideas in the context of superconductivity, thinking not of magnetization but of electrical current. He expanded the free energy F around the state of zero current, j = 0, and argued that as the direction of the current shouldn't affect F, the odd terms should vanish. This gives an equation of the form F(j) = F(0) + aj² + bj⁴. Assuming b > 0 and that a passes through zero at a critical temperature T_c, he showed that there could be an abrupt transition from zero to non-zero current below T_c.

This early theory conflicted with observations — it erroneously predicted j ~ (T_c − T)^1/2 just below the critical temperature — and Landau went back to the drawing board. Yet here already were the seeds of the later Ginzburg–Landau theory of phase transitions. And Landau's introduction of the notion of an 'order parameter' as a convenient handle on order and how it changes has influenced physics ever since, even if it did appear in a failed theory.

This idea is crazy: when one expands free energy in current, one has in his mind that he is dealing with an equilibrium state. However, current usually exists in a non-equilibrium state. This gives a glimpse of the aberration of superconductivity !