Vortices in Maxwell-Chern-Simons-Higgs models with nonminimal coupling

Abstract

We investigate the presence of vortex configurations in generalized Maxwell-Chern-Simons models with nonminimal coupling, in which we introduce a function that modifies the dynamical term of the scalar field in the Lagrangian. We first follow a route already considered in previous works to develop the Bogomol'nyi procedure, and, in this context, we use the first-order equations to obtain a vortex with a novel behavior at its core. We then go further and introduce a novel procedure to develop the Bogomol'nyi methodology. It supports distinct first-order equations, and we then investigate another model, in which the vortex may engender inversion of the magnetic flux, an effect with no precedents in the study of vortices within the nonminimal context.

Electrically charged localized structures

“…This function W is inspired in the work [34] and it has been used before in several distinct situations as, for instance, in Refs. [15,17,19]. Notice the presence of the factor 1/r in the last term; it is important since, under integration to get the energy, the line element dx dy = r dr dθ makes dW/dr be a surface term after integration.…”

“…The use of a field-dependent function coupled with the gauge field dynamical term has also been recently considered in [14] in the electric context, that is, in the presence of an electric charge fixed at the origin; there, we showed that the electric field has a behavior that captures the basic feature of asymptotic freedom, an effect that is usually associated to quarks and gluons. It was also considered, for instance, in [15][16][17][18][19] to describe vortex configurations with internal structures in the plane in the magnetic context. Moreover, very recently, in [20] the authors studied the dielectric Skyrme model, that is, the Skyrme model where both the kinetic and Skyrme terms are multiplied by field-dependent functions, leading to new results of current interest.…”

“…The field-dependent function can be used to modify the magnetic properties of the medium to study vortices, as in [7][8][9][15][16][17][18][19], but it can also be considered to modify electrical properties of the medium, as in [3,4] and in [14], for instance.…”

Topological structures in a non-canonical perturbative dynamics of a cuscuton-like model

“…Looking at (24) and ( 25), we can clearly see that at the limit of λ → 0, the gauge field assumed a constant behavior, i. e., a(r) = a 0 . Meanwhile, we have f (r) ∝ r a 0 , which gives us non-topological field configurations.…”

“…As a motivation for the study of these structures we have some applications such as: in the study of vortices in topological superconductors [3], the study of topological structures in twodimensional quantum gravity [21], topological solutions describing the multivortex dynamics in Abelian theories [22], structures in models with k-defects [23], study of generalized models [24][25][26][27][28][29] and non-generalized ones [30][31][32][33].…”