Superconductivity and dephasing in a two-dimensional disordered non-Fermi liquid

We study superconductivity and dephasing in a two-dimensional disordered marginal Fermi liquid. We consider a system with N flavors of fermions coupled to SU(N) critical bosons. At the saddle point level, the bosonic propagator acquires a quantum relaxational form, which consequently induces a marginal Fermi liquid self-energy for the fermions that destroys quasiparticles. Although quasiparticles are no longer well-defined, quantum coherence can surprisingly survive and manifest itself through interference of collective excitations. Motivated by the survival of phase coherence, we explore the interplay between Cooperons and critical bosons on superconductivity. At the semiclassical level, the transition temperature Tc is suppressed because of the marginal Fermi liquid self-energy. Interestingly, interactions between Cooperons and the critical bosons can nevertheless enhance Tc through quantum interference. We also examine the effect of dephasing. We find that the dephasing rate saturates very quickly as temperature increases due to the quantum relaxational bosons and that weak localization is therefore strongly suppressed.