Order parameter symmetry and mode coupling effects at dirty superconducting quantum phase transitions

TL;DR

This paper develops a theoretical framework for quantum phase transitions between disordered metals and exotic superconductors, highlighting mode coupling effects and their influence on critical behavior.

Contribution

It introduces an order-parameter field theory incorporating mode coupling effects, revealing the impact of long-range interactions on disorder fluctuations and critical scaling.

Findings

Long-range interactions cause singularities in free energy.

Disorder fluctuations are not suppressed by these interactions.

Critical behavior shows mean-field characteristics with logarithmic corrections in p-wave cases.

Abstract

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.