The Solid State 381
10.10 BOUND ELECTRON PAIRS
The key to superconductivityThe origin of superconductivity remained a mystery until the Bardeen-Cooper-Schrieffer
(BCS) theory of 1957. An earlier hint of the direction such a theory should take was
the discovery that the critical temperatures Tcof the isotopes of a superconducting
element decrease with increasing atomic mass. For instance, in mercury Tcis 4.161 K
in^199 Hg but only 4.126 K in^204 Hg. This isotope effectsuggests that the current-
carrying electrons in a superconductor do not move independently of the ion lattice
(as we might think when we recall that the resistance of ordinary conductors arises
from the scattering of these electrons by lattice defects and vibrations) but instead are
somehow interacting with the lattice.
The nature of the interaction became clear when Leon Cooper showed how two
electrons in a superconductor could form a bound state despite their coulomb repul-
sion. What happens is that the lattice is slightly deformed as an electron moves through
it, with the positive ions in the electron’s path being displaced toward it. The defor-
mation produces a region of increased positive charge. Another electron moving through
this polarized region will be attracted by the greater concentration of positive charge
there. If the attraction is stronger than the repulsion between the electrons, the elec-
trons are effectively coupled together into a Cooper pairwith the deformed lattice as
the intermediary.
The electron-lattice-electron interaction does not keep the electrons a fixed distance
apart. In fact, the theory shows that they must be moving in opposite directions, and
their correlations may persist over lengths as great as 10^6 m. The binding energy ofMagnetic levitation. A small permanent mag-
net is floating freely above a high-temperature
superconductor cooled with liquid nitrogen.
The magnetic field of the magnet induces
electric currents in the superconductor which
lead to a zero resultant field inside the super-
conductor. The magnetic field of these cur-
rent outside the superconductor repels the
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