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We have performed a complete study of BPS vortex solutions in the Abeliansector of the standard model extension (SME). Specifically, we have coupled theSME electromagnetism with a Higgs field which is supplemented with aLorentz-violating CPT-even term. We have verified that Lorentz violation (LV)belonging to the Higgs sector allows to interpolate between some well knownmodels like, Maxwell-Higgs, Chern-Simons-Higgs and Maxwell-Chern-Simons-Higgs.We can also observed that the electrical charged density distribution isnonnull in both CPT-even and CPT-odd models; however, the total electric chargein the CPT-even case is null, whereas in the CPT-odd one it is proportional tothe quantized magnetic flux. The following general results can be establishedin relation to the LV introduced in the Higgs sector: it changes the vortexansatz and the gauge field boundary conditions. A direct consequence is thatthe magnetic flux, besides being proportional to the winding number, alsodepends explicitly on the Lorentz-violation belonging to the Higgs sector.

Topological charged BPS vortices in Lorentz-violating Maxwell-Higgs electrodynamics