Superconducting multi-vortices and a novel BPS bound in chiral perturbation theory

TL;DR

This paper derives a new BPS bound in chiral perturbation theory, revealing magnetic multi-vortices with quantized flux and a maximum magnetic field, connecting topological charge to magnetic flux in a superconducting context.

Contribution

It introduces a novel BPS bound and explicit solutions for magnetic vortices in chiral perturbation theory at finite isospin chemical potential.

Findings

Derived a new BPS bound in chiral perturbation theory.

Found magnetic multi-vortex solutions with quantized flux.

Estimated the maximum magnetic field of these vortices.

Abstract

We derive a novel BPS bound from chiral perturbation theory minimally coupled to electrodynamics at finite isospin chemical potential. At a critical value of the isospin chemical potential, a system of three first-order differential field equations (which implies the second-order field equations) for the gauge field and the hadronic profile can be derived from the requirement to saturate the bound. These BPS configurations represent magnetic multi-vortices with quantized flux supported by a superconducting current. The corresponding topological charge density is related to the magnetic flux density, but is screened by the hadronic profile. Such a screening effect allows to derive the maximal value of the magnetic field generated by these BPS magnetic vortices, being $B_{max}=2,04 \times 10^{14}G$. The solution for a single BPS vortex is discussed in detail, and some physical consequences, together with the comparison with the magnetic vortices in the Ginzburg-Landau theory at critical coupling, are described.