Effect of Impurity on Inhomogeneous Vacuum and Interacting Vortices

TL;DR

This paper investigates how magnetic impurities affect the vacuum structure and vortex configurations in an inhomogeneous abelian Higgs model, revealing implications for superconductivity and flux pinning.

Contribution

It introduces a detailed analysis of inhomogeneous vacuum states and vortex solutions in the presence of impurities, connecting to superconductivity classifications.

Findings

Vacuum energy varies with coupling strength, indicating different superconductivity types.

Non-BPS vortex solutions suggest vortex-impurity composites in type II superconductors.

Impurity-induced vortex lattices provide insights into flux pinning mechanisms.

Abstract

We study the inhomogeneous abelian Higgs model with a magnetic impurity. The vacuum configuration of the symmetry-broken phase is not simply the constant Higgs vacuum but is a nontrivial function of spatial coordinates, satisfying the Euler-Lagrange equations. The vacuum of zero winding number has zero magnetic flux but its non-zero magnetic field depends on spatial coordinates. The corresponding vacuum energy is negative for weak coupling $(\lambda < 1)$, zero for critical BPS coupling $(\lambda = 1)$, and positive for strong coupling $(\lambda > 1)$ by an over-, exact-, and under-cancellation of the huge positive impurity energy. This distinct vacuum energies are consistent with classification of the type I and I$\!$I superconductivity in dirty conventional superconductors. Non-BPS vortex configurations are also obtained in the presence of inhomogeneity. Their rest energies favor energetically vortex-impurity composite in conventional type I$\!$I superconductivity, consistent with imperfect diamagnetism. The delta function limit of Gaussian type impurity suggests the formation of vortex-lattice composite which elucidates flux-pinning in the context of inhomogeneous field theory.