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

Abstract

We consider a three dimensional lattice U͑1͒ ϫ U͑1͒ and ͓U͑1͔͒ N superconductors in the London limit with individually conserved condensates. The U͑1͒ ϫ U͑1͒ 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 U͑1͒ ϫ U͑1͒ superconductor which includes both of these interactions. We study phase transitions and two types of competing paired phases which occur in this general model: ͑i͒ a metallic superfluid phase ͑where there is order only in the gauge-invariant phase difference of the order parameters͒, ͑ii͒ 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 U͑1͒ ϫ U͑1͒ 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 U͑1͒ transitions into a single U͑1͒ ϫ U͑1͒ discontinuous phase transition. We also report a general form of vortexvortex bare interaction potential and possible phase transitions in an N-component London superconductor with individually conserved condensates.

Pair superfluid and supersolid of correlated hard-core bosons on a triangular lattice

“…Secondly, there is a pair superfluid (PSF) phase, where b i = 0 while b i b i+α = 0. This pair superfluid phase is an analogue of the charge-4e superconductor that was discussed lately [13][14][15] . Thirdly, we show that there is a continuous quantum phase transition between the supersolid and the pair superfluid phase.…”

Current loops, phase transitions, and the Higgs mechanism in Josephson-coupled multicomponent superconductors

“…This is because of the multiple connectedness of the physical space, fluctuations in a single individual phase induce fluctuations in N − 1 composite neutral modes, as well as in the charged mode. In the present form, with λ = 0 and e sufficiently large, this model is known to have one phase transition in the inverted 3dXY -universality class, and N − 1 transitions in the 3dXY -universality class at a higher temperature 17,19 . These transitions correspond to proliferations of the composite charged mode and the composite neutral modes, respectively.…”

“…Consequently, the N phase transitions collapse into a single first-order transition. This interplay between the charged and neutral sector has been coined a preemptive phase transition 25 , and has been verified numerically in two-component systems in the absence of intercomponent Josephson-coupling in several detailed large-scale Monte Carlo simulations 18,19,25 . In the following Section, we reformulate the model in terms of integer-valued current fields, considering first the case with zero Josephson-coupling and then move on to include Josephson coupling.…”

“…In the preemptive scenario for λ = 0, fluctuations in the neutral and charged sectors increase as T is increased from below in the fully ordered state. The charged sector influences the fluctuations in the neutral sector and vice versa, such that the putative continuous transitions in these sectors are preempted by a common first order phase transition 17,19 . The important point to realize is that neither of the sectors actually reach criticality, since there are no critical fluctuations at the preemptive first-order phase transition.…”

“…This causes the N -component model without Josephson interactions to have N − 1 superfluid phase transitions and a single superconducting phase transition 17 . For certain values of the gauge charge these transitions will interfere in a non-trivial way, causing the transitions to merge in a single first-order transition 18,19 . The question of the nature of the phase transitions present in Josephson-coupled multiband superconductors is of considerable interest.…”