We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-$s$-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this asymptotic region is very narrow. It is preempted by a wide crossover regime with mean-field critical behavior and, in the $p$-wave case, logarithmic corrections to scaling in all dimensions.

• Received 20 October 2003

DOI:https://doi.org/10.1103/PhysRevB.70.104514