Spatial Chern-Simons Interactions and Complex Magnetic Penetration Depth

TL;DR

This paper explores how spatial Chern-Simons interactions in Weyl semimetals alter magnetic field behavior in superconductors, leading to complex penetration depths and oscillations, with potential experimental implications.

Contribution

It introduces the effect of purely spatial Chern-Simons terms into Landau-Ginzburg theory, revealing new magnetic phenomena in Weyl semimetal superconductors.

Findings

Complex magnetic penetration depth due to Chern-Simons term

Surface magnetic field exhibits spatial oscillations

Vortex solutions with magnetic field inversion can occur

Abstract

This paper examines the Landau-Ginzburg theory in the presence of spatial Chern-Simons interactions, which typically emerge in Weyl semimetals due to domain-wall motion. We demonstrate that the incorporation of a purely spatial Chern-Simons term, which violates parity, into the Landau-Ginzburg free energy leads to a complex magnetic penetration depth. This characteristic indicates that, aside from possessing an effective penetration depth, the magnetic field on the surface of the superconductor experiences periodic spatial oscillations, which significantly deviates from the conventional Meissner effect. In particular, we observe that as the degree of parity breaking, quantified by the strength of the spatial Chern-Simons term, increases, a vortex solution with magnetic field inversion may emerge. With the discovery of superconductivity in certain Weyl semimetals, we anticipate the possibility of experimentally observing this phenomenon in these materials.