Hydrodynamic theory of quantum fluctuating superconductivity

          @misc{ pirsa_PIRSA:16080051,
            doi = {10.48660/16080051},
            url = {https://pirsa.org/16080051},
            author = {},
            keywords = {Condensed Matter, Quantum Fields and Strings},
            language = {en},
            title = {Hydrodynamic theory of quantum fluctuating superconductivity},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {aug},
            note = {PIRSA:16080051 see, \url{https://pirsa.org}}
          }
          

Abstract

A hydrodynamic theory of transport in quantum mechanically phase-disordered superconductors is possible when supercurrent relaxation can be treated as a slow process. We obtain general results for the frequency-dependent conductivity of such a regime. With time-reversal invariance, the conductivity is characterized by a Drude-like peak, with width given by the supercurrent relaxation rate. Using the memory matrix formalism, we obtain a formula for this width (and hence also the dc resistivity) when the supercurrent is relaxed by short range Coulomb interactions. This leads to a new -- effective field theoretic and fully quantum -- derivation of a classic result on flux flow resistance. With strong breaking of time-reversal invariance, the optical conductivity exhibits what we call a `hydrodynamic supercyclotron' resonance. We obtain the frequency and decay rate of this resonance for the case of supercurrent relaxation due to an emergent Chern-Simons gauge field. The supercurrent decay rate in this `topologically ordered superfluid vortex liquid' is determined by the conductivities of the normal component of the liquid. Our work gives a controlled framework for low temperature metallic phases arising from phase-disordered superconductivity.