Hydrodynamic theory of quantum fluctuating superconductivity

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.

1 + 44 pages. 2 figures. v2 discussion improved in places. v3 sign errors fixed in section 4

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• Absence of cyclotron resonance in the anomalous metallic phase in InO${}_x$
• Diffusion in inhomogeneous media
• Constraints on hydrodynamics from many-body quantum chaos
• Hydrodynamic sound modes and Galilean symmetry breaking in a magnon fluid
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