Page 65 - Materials Chemistry, Second Edition

52 2 Solid-State Chemistry

Figure 2.29. Illustration of Cooper pair formation by electron–phonon coupling, and experimental
evidence for their formation (“the isotope effect”). Data taken from Maxwell, E. Phys. Rev. 1950, 78,
477, and Reynolds, C. A. et al. Phys. Rev. 1950, 78, 487.

within the conduction band, centered about the Fermi level. The energy of this
bandgap (ca. 7/2 kT c ) corresponds to the minimum energy required to break up a
Cooper pair and release the electrons into the vacant quantum levels. The energy gap
may be measured by microwave absorption spectroscopy, and represents another
key experimental finding that supports the BCS theory. As the critical temperature is
approached, the energy gap decreases; at 0 < T < T c , the superconductor metal is in
an excited state, wherein a number of electrons, primarily from broken Cooper pairs,
have been promoted across the bandgap into vacant energy states. This indicates that
the binding energy of the Cooper pairs is decreased as the temperature increases,
caused by greater phonon vibrations that interrupt electron correlation. At T > T c ,
the binding energy of the Cooper pairs has been exceeded and the electrons behave

as discrete carriers, resulting in bulk resistivity due to e /e collisions. According to
this theory, a superconductor’s electrical resistance will be zero because the Cooper
pair condensate moves as a coherent quantum mechanical entity, which lattice