Phase transitions in a three dimensional U(1)×U(1) lattice London superconductor: Metallic superfluid and charge-4e superconducting states

Abstract

We consider a three dimensional lattice U(1)×U(1) and [U(1)]N superconductors in the London limit with individually conserved condensates. The U(1)×U(1) problem, generically, has two types of intercomponent interactions of different characters. First, the condensates are interacting via a minimal coupling to the same fluctuating gauge field. A second type of coupling is the direct dissipationless drag represented by a local intercomponent current-current coupling term in the free-energy functional. In this work, we present a study of the phase diagram of a U(1)×U(1) superconductor which includes both of these interactions. We study phase transitions and two types of competing paired phases which occur in this general model: (i) a metallic superfluid phase (where there is order only in the gauge-invariant phase difference of the order parameters), (ii) a composite superconducting phase where there is order in the phase sum of the order parameters which has many properties of a single-component superconductor but with a doubled value of electric charge. We investigate the phase diagram with particular focus on what we call “preemptive phase transitions.” These are phase transitions unique to multicomponent condensates with competing topological objects. A sudden proliferation of one kind of topological defects may come about due to a fluctuating background of topological defects in other sectors of the theory. For U(1)×U(1) theory with unequal bare stiffnesses where components are coupled by a noncompact gauge field only, we study how this scenario leads to a merger of two U(1) transitions into a single U(1)×U(1) discontinuous phase transition. We also report a general form of vortex-vortex bare interaction potential and possible phase transitions in an N-component London superconductor with individually conserved condensates.

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