Bernoulli potential in type-I and weak type-II superconductors: II. Surface dipole

Abstract

The Budd-Vannimenus theorem is modified to apply to superconductors in the Meissner state. The obtained identity links the surface value of the electrostatic potential to the density of free energy at the surface which allows one to evaluate the electrostatic potential observed via the capacitive pickup without the explicit solution of the charge profile.

Bernoulli potential in type-I and weak type-II superconductors. III. Electrostatic potential above the vortex lattice

“…6 Here n is the total density of pairable electrons ͑the total density͒ and f el is the density of the electronic part of the free energy. The surface potential ͑1͒ follows from general thermodynamic assumptions and it can be implemented within different approximations of the free energy, compare Ref.…”

“…The surface potential ͑1͒ follows from general thermodynamic assumptions and it can be implemented within different approximations of the free energy, compare Ref. 6 with Ref. 18.…”

“…5 In this paper we show that close to the critical temperature the electrostatic potential above the sur-face is strongly reduced by the surface dipole, which arises due to unbalanced pairing forces. 6 At lower temperatures the surface dipole is not so effective and the electrostatic field reaches observable amplitudes.…”

The Concept of Correlated Density and Its Application

“…This force has to balance the centrifugal force by the electrons rotating around the vortex center, the outward push of the magnetic field via the Lorentz force and the outward force coming from the fact that the energy of Cooper pairs is lower than the one of free electrons such that unpaired electrons in the vortex core are attracted towards the condensate around the core. 22 (ii) The surface dipole which cancels all contributions of pairing forces 23 resulting in an observable surface potential of…”

“…The full theory and the inertial/Lorentz forces even result in different profiles and sign. This illustrates the delicate balance between the three contributions in (23). It is not justified to neglect just one of them.…”