The theory of electrostatic potential in superconductors

The problem of electrostatic potential distribution in superconductors is studied based on the microscopic theory of superconductors. Local chemical potential of the superconductor is introduced, and an approximation is made to BG theory, which is similar to the Thomas-Fermi (TF) method used in quantum mechanics. The electrostatic potential and charge distribution around an isolated vortex in type-II superconductors is discussed within the approximation. A correction to GL theory considering the electrostatic potential distribution is suggested.