Carsten Timm: Theory of superconductivity

Superconductivity with rather high T c has also been found in fullerites, i.e., compounds containing fullerene
anions. The record T c in this class is at present T c = 38 K for b.c.c. Cs 3 C 60 under pressure. Superconductivity
in fullerites was originally thought to be driven by phonons with strong molecular vibration character but there
is recent evidence that it might be unconventional (not phonon-driven).
2.2 Superfluid helium
In 1937 P. Kapiza and independently Allen and Misener discovered that helium shows a transition at T c = 2.17 K
under ambient pressure, below which it flows through narrow capilaries without resistance. The analogy to
superconductivity is obvious but here it was the viscosity instead of the resistivity that dropped to zero. The
phenomenon was called superfluidity. It was also observed that due to the vanishing viscosity an open container
of helium would empty itself through a flow in the microscopically thin wetting layer.
He
On the other hand, while part of the liquid flows with vanishing viscosity, another part does not. This was shown
using torsion pendulums of plates submerged in helium. For T > 0 a temperature-dependent normal component
oscillates with the plates.
He
Natural atmospheric helium consists of 99.9999 % He-4 and only 0.0001 % He-3, the only other stable isotope.
The oberserved properties are thus essentially indistinguishable from those of pure He-4. He-4 atoms are bosons
since they consist of an even number (six) of fermions. For weakly interacting bosons, A. Einstein predicted in
1925 that a phase transition to a condensed phase should occur (Bose-Einstein condensation). The observation
of superfluidity in He-4 was thus not a suprise—in contrast to the discovery of superconductivity—but in many
details the properties of He-4 were found to be different from the predicted Bose-Einstein condensate. The reason
for this is that the interactions between helium atoms are actually quite strong. For completeness, we sketch the
temperature-pressure phase diagram of He-4:
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