Metal-superconductor transition at zero temperature: A case of unusual scaling

TL;DR

This paper develops an effective field theory for the zero-temperature metal-superconductor transition, revealing unusual critical behavior and explaining experimental transition broadening in disordered thin films.

Contribution

It provides an exact critical behavior analysis for the transition in all dimensions greater than two, with a complete scaling description and insights into disorder effects.

Findings

Critical exponents  and  do not exist, but scaling relations still hold.

Disorder causes strong T_c-fluctuations, explaining transition broadening.

Unusual critical behavior is characterized and discussed.

Abstract

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 \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 T_c-fluctuations which are shown to explain the experimentally observed broadening of the transition in low-T_c thin films.