BCS Superconductivity Development and Controversy

Recently there have been a number of attempts to give a quantum-
mechanical explanation of superconductivity. We mention work by
Heisenberg,28 Tisza,29 Slater,30 Born and Cheng,»1 Frohlich,32 and
Bardeen.32 At the present time all these theories are highly contro-
versial, and the difficulties do not lend themselves to analysis in an
introductory textbook.

In every theory the apparent contradiction between the Bloch theorem and the observed persistence of currents in a superconducting ring is explained by the presumed metastable nature of the current distribution.

Did you know that the BCS theory of superconductivity wasn't fully developed until 1957? It is covered in later editions such as the 3rd (1967), but lightly since this book is an Introduction to solid state physics. For full coverage, see Kittel's Quantum Theory of Solids, or these excellent books: Harrison, Solid State Theory, or Tinkham, Introduction to Superconductivity.
Also, note that the mechanisms of high temperature superconductivity (HTS) are still being worked out.

These include the prediction that the Knight shift in superconductors vanishes, that higher transition temperatures exist, and that the isotope effect, with a value of M(-1/2) is general; in addition, the theory has also incorrectly predicted the electronic heat conductivity.
Unfortunately, one question remained almost totally ignored in most theories and experiments; namely, What are the critical conditions for the occurrence of superconductivity itself? Derivations of a criterion were first attempted by Frohlich and Bardeen, and later by Bardeen, Cooper, and Schrieffer. The latter group actually gave an equation for the transition temperature itself; this equation, however, contained an interaction constant that cannot be calculated at present Apart from this difficulty, the critical condition* for superconductivity could not be predicted by this equation either. Fог example, асcording to the equation, yttrium and lanthanum should have (the same transition temperature, that of yttrium being possibly a liltle higher, since both have the same N(0) and almost the same V and Debye temperature. However, yttrium is not superconducting down to 0.07'K and alfa lanthanum is superconducting at about 5K. This difference is discussed later. Moreover, this formula, cited by Anderson, is not only crude, as he says, but also incorrect for the transition elements, since the dependence of Tc on N (0) is in most cases the exact opposite of that stated in the formula. For example, the T, of yttrium, rhodium, and platinum decreases with an increase in N{0). Since the formula was proposed it seems to have been discarded completely because it does not present the criteria for the occurrence of superconductivity which, on the other hand, are easily given by a simple empirical rule (9).

Discussion between Bernd Matthias and P.W. Anderson about validity of BCS, published in Science 144, 373 (1964). See "A career in theoretical physics" by Philip W. Anderson.