# Dissipative and nonequilibrium effects near a superconductor-metal quantum critical point - Condensed Matter > Strongly Correlated Electrons

Abstract: We present a microscopic derivation of the effect of current flow on a systemnear a superconductor-metal quantum critical point. The model studied is a 2ditinerant electron system where the electrons interact via an attractiveinteraction and are coupled to an underlying normal metal substrate whichprovides a source of dissipation, and also provides a source of inelasticscattering that allows a nonequilibrium steady state to reach. A nonequilibriumKeldysh action for the superconducting fluctuations on the normal side isderived. Current flow, besides its minimal coupling to the order parameter isfound to give rise to two new effects. One is a source of noise that acts as aneffective temperature $T {eff} = e E v F \tau {sc}$ where $E$ is the externalelectric field, $v F$ the Fermi velocity, and $\tau {sc}$ is the escape timeinto the normal metal substrate. Secondly current flow also produces a drift ofthe order-parameter. Scaling equations for the superconducting gap and thecurrent are derived and are found to be consistent with previousphenomenological treatments as long as a temperature $T \sim T {eff}$ isincluded. The current induced drift is found to produce additional correctionsto the scaling which are smaller by a factor of ${\cal O}\frac{1}{E F\tau {sc}}$, $E F$ being the Fermi energy.