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

Understand

We consider a three-dimensional lattice $U(1) \times U(1)$ and $[U(1)]^N$ superconductors in the London limit, with individually conserved condensates.

• The $U(1) \times U(1)$ 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.