Electric field in stationary superconductors

It is generally accepted that vortex core is charged, what illustrates that even in stationary superconductors electric field may be present. Vortex structure and other properties of superconductors are usually calculated in the framework of the Ginzburg-Landau theory, which does not cover electric field. We show that the generalization of the GL theory due to Bardeen allows one to derive a third GL equation for the electrostatic potential. Since the Bardeen theory applies to all temperatures, the presented theory enables one to calculate charge profiles of the vortex under quite general conditions. The theory is consistent with the BCS-Gorkov results.