Emergent Chern-Simons Interactions in 3+1 Dimensions

TL;DR

This paper explores how parity-violating superconductors can support emergent Chern-Simons interactions in 3+1 dimensions, leading to novel physical phenomena and connections to microscopic interactions.

Contribution

It introduces a new class of emergent Chern-Simons interactions in 3+1D superconductors and analyzes their physical implications and microscopic origins.

Findings

Solutions to generalized London equations with complex penetration depth

Flux exclusion involving anapole moments

Current configurations around vortices and wires

Abstract

Parity violating superconductors can support a low-dimension local interaction that becomes, upon condensation, a purely spatial Chern-Simons term. Solutions to the resulting generalized London equations can be obtained from solutions of the ordinary London equations with a complex penetration depth, and suggest several remarkable physical phenomena. The problem of flux exclusion by a sphere brings in an anapole moment, the problem of current-carrying wires brings in an azimuthal magnetic field, and the problem of vortices brings in currents along the vortices. We demonstrate that interactions of this kind, together with a conceptually related dimensionally reduced Chern-Simons interaction, can arise from physically plausible microscopic interactions.