  We demonstrate for the first the existence of electrically charged BPS
vortices in a Maxwell-Higgs model supplemented with a parity-odd
Lorentz-violating (LV) structure belonging to the CPT-even gauge sector of the
standard model extension and a fourth order potential (in the absence of the
Chern-Simons term). The modified first order BPS equations provide charged
vortex configurations endowed with some interesting features: localized and
controllable spatial thickness, integer flux quantization, electric field
inversion and localized magnetic flux reversion. This model could possibly be
applied on condensed matter systems which support charged vortices carrying
integer quantized magnetic flux, endowed with localized flipping of the
magnetic flux.
