Analytical BPS Maxwell-Higgs vortices

Abstract

We have established a prescription for the calculation of analytical vortex solutions in the context of generalized Maxwell-Higgs models whose overall dynamics is controlled by two positive functions of the scalar field. We have also determined a natural constraint between these functions and the Higgs potential allowing the existence of axially symmetric Bogomol'nyi-Prasad-Sommerfield (BPS) solutions possessing finite energy. Furthermore, when the generalizing functions are chosen suitably, the nonstandard BPS equations can be solved exactly. We have studied some examples, comparing them with the usual Abrikosov-Nielsen-Olesen (ANO) solution. The overall conclusion is that the analytical self-dual vortices are well-behaved in all relevant sectors, strongly supporting the generalized models they belong themselves. In particular, our results mimic well-known properties of the usual (numerical) configurations, as localized energy density, while contributing to the understanding of topological solitons and their description by means of analytical methods.

8 pages, 4 figures

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• Topological vortices in generalized Born-Infeld-Higgs electrodynamics
• Analytic vortex solutions in generalized models of the Maxwell-Higgs type
• Some exact BPS solutions for exotic vortices and monopoles
• Self-dual configurations in Abelian Higgs models with $k$-generalized gauge field dynamics
• Long range vortex configurations in generalized models with the Maxwell or Chern-Simons dynamics
• Self-dual effective compact and true compacton configurations in generalized Abelian Higgs models
• Lorentz Violation and Topologically Trapped Charge Carriers in 2D Materials