THEORY OF IMPURE SUPERCONDUCTORS - ANDERSON VERSUS ABRIKOSOV AND GORKOV

The influence of ordinary (nonmagnetic) impurities on the transition temperature of a traditional singlet-pairing superconductor is revisited. The theory of Anderson is juxtaposed with that due to Abrikosov and Gor'kov (AG). Whereas Anderson's treatment leads to no substantial decrease of T(c) with impurity substitution, the Abrikosov-Gor'kov theory predicts a large decrease of T(c), linear in the impurity concentration. This latter result is not well known because an unallowed mathematical manipulation canceled a large T(c) decrease required by a correct evaluation of the AG theory. The controversy that arises is herein settled in favor of Anderson. The Green's functions employed in the AG method are not appropriate for an impure Bardeen-Cooper-Schrieffer superconductor. It is shown that if the required projected Green's functions (not derivable from a Dyson equation) are employed, Anderson's theorem is recovered.