How planar superconductors cure their infrared divergences

TL;DR

This paper explores how planar superconductors, due to their unique infrared divergence issues, can be effectively described by a topological Chern-Simons gauge theory, revealing new insights into their phase structure and vortex behavior.

Contribution

It demonstrates that planar superconductors are governed by a topological Chern-Simons gauge theory, replacing the Ginzburg-Landau model, and connects their phases to mechanisms curing infrared divergences in (2+1)-dimensional QED.

Findings

Planar superconductors decompose into superconducting droplets.

They match phases of (2+1)D QED divergence cures: Chern-Simons mass or monopole instantons.

Vortex structure differs from bulk superconductors, lacking Abrikosov vortices.

Abstract

Planar superconductors, thin films with thickness comparable to the superconducting coherence length, differ crucially from their bulk counterparts. The Coulomb interaction is logarithmic up to distances exceeding typical sample sizes and the Anderson-Higgs mechanism is ineffective to screen the resulting infrared divergences of the resulting (2+1)-dimensional QED because the Pearl length is also typically larger than sample sizes. As a consequence, the system decomposes into superconducting droplets with the typical size of the coherence length. We show that the two possible phases of the system match the two known mechanisms by which (2+1)-dimensional QED cures its infrared divergences, either by generating a mixed topological Chern-Simons mass or by magnetic monopole instantons. The former is realized in superconductors, the latter governs mirror-dual superinsulators. Planar superconductors are thus described by a topological Chern-Simons gauge (TCSG) theory which replaces the Ginzburg-Landau model in two dimensions. In the TCSG model, the Higgs field is absent. Accordingly, in planar superconductors Abrikosov vortices do not form, and only Josephson vortices with no normal core can emerge.