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 $T=0\mathrm{}$. The critical behavior is determined exactly for all dimensions $d>\mathrm{}2\mathrm{}$. Although the critical exponents $\beta$ and $\nu$ 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.