Page 393 - Electrical Properties of Materials

Microscopic theory 375

as well as at D. Thus, the distribution of the magnetic field at C depends on
the path we have chosen. If we go via B, the magnetic field is expelled; if we
go via D, the magnetic field is the same inside as outside. The conclusion is
that for a perfect conductor (meaning a material with no resistance) the final
state depends on the path chosen. This is quite an acceptable conclusion; there
are many physical phenomena exhibiting this property. What is interesting is
that superconductors do not behave in this expected manner. A superconductor
cooled in a constant magnetic field will set up its own current and expel the
magnetic field when the critical temperature is reached.
The discovery of this effect by Meissner in 1933 showed superconductiv-
ity in a new light. It became clear that superconductivity is a new kind of
phenomenon that does not obey the rules of classical electrodynamics.

14.3 Microscopic theory

The microscopic theory is well beyond the scope of an engineering under-
graduate course and, indeed, beyond the grasp of practically anyone. It is part
of quantum field theory and has something to do with Green’s functions and
has more than its fair share of various operators. We shall not say much about
this theory, but we should just like to indicate what is involved.
The fundamental tenet of the theory is that superconductivity is caused by
a second-order interaction between electrons and the vibrating lattice. This is
rather strange. After all, we do know that thermal vibrations are responsible for
the presence of resistance and not for its absence. This is true in general; the
higher the temperature the larger the electrical resistance. Below a certain tem-
perature, however, and for a select group of materials, the lattice interaction
plays a different role. It is a sort of intermediary between two appropriately
placed electrons. It results in an apparent attractive force between the two elec- Lattice distortion
trons, an attractive force larger than the repulsive force, owing to the Coulomb
interaction. Hence, the electron changes its character. It stops obeying Fermi– Electron
Dirac statistics, and any number of electrons (or more correctly any number of
electron pairs) can be in the same state. Besides the atom laser (Section 12.14)
this is another example of a Bose–Einstein condensation. (a)
Do we have any direct experimental evidence that superconductivity is Spin-wave Spins flip
caused by electron–lattice interaction? Yes, the so-called isotope effect. The attraction
critical temperature of a superconductor depends on the total mass of the nuc-
leus. If we add a neutron (that is, use an isotope of the material) the critical
temperature decreases.
A simple explanation of the interaction between two electrons and the lat-
tice is shown in Fig. 14.6(a). The first electron moving to the right causes the (b)
positive lattice ions to move inwards, which then attract the second electron.
Hence, there is an indirect attraction between the two electrons. Fig. 14.6
Interactions leading to Bose–Einstein
Are there any other kinds of interactions resulting in superconductivity?
condensation (a) between the lattice
Nobody knows for certain, but it may be worthwhile describing briefly one of
and electrons, (b) between spin waves
the mechanisms proposed to explain the behaviour of the recently discovered and electrons.
oxide superconductors. It is electron attraction mediated by spin waves. As
may be seen in Fig. 14.6(b), an electron with a certain spin disrupts the spin of
an ion, which causes the spin of its neighbouring ion to flip, which then attracts