Magnetic Vortex Lattices in Finite Isospin Chiral Perturbation Theory

TL;DR

This paper investigates magnetic vortex lattices in finite isospin chiral perturbation theory, revealing differences from Ginzburg-Landau theory due to derivative interactions and neutral pion effects, near the upper critical magnetic field.

Contribution

It extends vortex lattice analysis to $ ext{chi}$PT, highlighting the impact of derivative interactions and neutral pions on vortex structure and condensation energy.

Findings

Vortex lattice is hexagonal, similar to GL vortices.

Condensation energy is smaller in magnitude compared to GL theory.

Neutral pions do not condense near the upper critical field.

Abstract

We study finite isospin chiral perturbation theory ($\chi$PT) in a uniform external magnetic field and find the condensation energy of magnetic vortex lattices using the method of successive approximations (originally used by Abrikosov) near the upper critical point beyond which the system is in the normal vacuum phase. The difference between standard Ginzburg-Landau (GL) theory (or equivalently the Abelian Higgs model) and $\chi$PT arises due to the presence of additional momentum-dependent (derivative) interactions in $\chi$PT and the presence of electromagnetically neutral pions that interact with the charged pions via strong interactions but do not couple directly to the external magnetic field. We find that while the vortex lattice structure is hexagonal similar to vortices in GL theory, the condensation energy (relative to the normal vacuum state in a uniform, external magnetic field) is smaller (larger in magnitude) due to the presence of derivative interactions. Furthermore, we establish that neutral pions do not condense in the vortex lattice near the upper critical field.