Characteristic length scales and formation of vortices in the Abelian   Higgs model in the presence of a uniform background charge
  In this brief report we consider a non-local Abelian Higgs model in the presence of a neutralizing uniform background charge. We show that such a system possesses vortices which key feature is a strong radial electric field. We estimate the basic properties of such an object and characteristic length scales in this model. 
Egor Babaev