Bernoulli Potential in Superconductors

There are many monographs and textbooks addressing superconductivity from di? erent angles. In spite of a large variety of explored approaches, one problem is always left aside. It is the balance of forces acting on the sup- conducting condensate. In the present book this question is central. As the title suggests, there is a close analogy between the electrostatic ? eld in superconductors and the pressure in the ideal incompressible liquid. As one can easily imagine looking at swirling water, molecules of the inc- pressible liquid are accelerated by gradients of the pressure so that they can follow complicated trajectories often changing their directions and velocities. Electronsinthe superconductorbehavesimilarly, exceptthatthe electrostatic potential plays the role of the pressure. The pressure in any material develops when we reduce its volume. This leads us to the main puzzle. By de? nition, the incompressible liquid never changes its volume. Consequently, how can be any pressure there? Of course, one has the direct experience that there is a pressure in water and one would never deny it. The incompressible liquid is an ideal model which assumes that the pressure we feel has been achieved with a negligibly small change of the volume.

History of the Bernoulli Potential. - Basic Concepts. - Balance of Forces. - Thermodynamical Correction. - Phenomenological Description. - Non-local Corrections. - Extended Ginzburg Landau Theory. - Quasi-neutral Limit. - Diamagnetic Current at Surface. - Surfaces. - Matching of Electrostatic Potentials at Surfaces. - Diamagnetic Currents Deep in the Bulk. - Electrostatic Potential Above a Surface with Vortices. - Layered Structures. - Charge Transfer in Layered Structures. - Effect of the Electrostatic Field on the Superconductor. - Outlook and Perspectives.