Model of relativistic superconductivity

We propose a simplified 2D effective scalar electrodynamics model of relativistic type-II superconductivity. Within this framework, we discuss possible electromagnetic (EM) behaviors of superconductivity along the lines of the nonrelativistic Ginzburg-Landau (GL) theory. This model may be of significance to study very diverse physical phenomena such as a nonlinear version of the electron-hole conversion by a superconductor and electron-positron dynamics around neutron stars. We briefly comment on extending the model to study the 3D dynamics of vortex-vortex interactions and Abrikosov fluxonics.