Metal-Superconductor Transition at Zero Temperature: A Case of Unusual Scaling

An effective field theory is derived for the normal metal-to-superconductor quantum phase transition at T = 0. The critical behavior is determined exactly for all dimensions d>2. Although the critical exponents β and ν do not exist, the usual scaling relations, properly reinterpreted, still hold. A complete scaling description of the transition is given, and the physics underlying the unusual critical behavior is discussed. Quenched disorder leads to anomalously strong fluctuations in T_c which are shown to explain the experimentally observed broadening of the transition in low- T_c thin films.