Figure 164: The superconducting band gap versus temperature. Comparison between theoretical
(BCS) and experimental data for Ta.
whereΘis the Debyetemperature. This relation coincides qualitatively with experimental
observations. Note that this means, the higherV (means large resistance at room temperature),
the more likely the material will be superconductor when cooled belowTc.
(v) The magnetic flux through a superconducting ring is quantized (see Sec. 16.4.4) and since a
Cooperpair consists of two electrons, the unit of charge is 2 q. This can be accounted for in the
Londonequations and in theGinzburg - Landauequations when one replaces the quantities
accordingly (nsis now the density ofCooperpairs,q→ 2 q,... ).
(vi) There exists a BCS groundstate: In case of a non-interacting electron system one obtains the
Fermisea as the groundstate. Arbitrarily small excitations are possible. Within the frame-
work of the BCS theory, one obtains, that for an appropriate attractive interaction potential a
superconducting groundstate, which is separated from the excited states by an energy gapEg,
is formed. The most important property of the BCS groundstate is that orbitals are occupied
in pairs: for every orbital with wavevectorkand some spin occupied the orbital with opposite
spin and wavevector−kis also occupied. These pairs are referred to asCooperpairs; we give
a short discussion below.Cooperpairs are bosons.
(vii) The BCS theory states that superconducting band gap∆(T)as a function of temperature is
implicitly given through the solution of the following equation:∆(T)
∆(0)
= tanh[
TC
T∆(T)
∆(0)
]. (310)
Comparison with experimental data of Ta shows perfect agreement, see Fig. 164