Self-dual vortices in Abelian Higgs models with dielectric function on the noncommutative plane

We show that Abelian Higgs Models with a dielectric function defined on the noncommutative plane enjoy self-dual vorticial solutions. By choosing a particular form of the dielectric function, we provide a family of solutions whose Higgs and magnetic fields interpolate between the profiles of the noncommutative Nielsen–Olesen and Chern–Simons vortices. This is done both for the usual U(1) model and for the SU(2)×U(1) semilocal model with a doublet of complex scalar fields. The variety of known noncommutative self-dual vortices which display a regular behavior when the noncommutativity parameter tends to zero results in this way considerably enlarged