Bernoulli potential in superconductors. How the electrostatic field helps to understand superconductivity. (Q2473784)

The book is devoted to statement of analogy between the electrostatic field in superconductors and the pressure in the ideal incompressible liquid on the base of force balance acting on the superconducting condensate. The book is divided into seventeen chapters and three appendixes. The history of the Bernoulli potential (BP) in the context of the development of the superconductivity research is presented in Chapter 1. Chapter 2 considers basic concepts of superconductivity, in particular Maxwell equations and the main material relations. In Chapter 3, it is taken the London condition, determining the trajectories of electrons, and discussed its consequences for deviations from the charge neutrality. It is shown that the London theory separates the electron velocity into the longitudinal and transverse motion. By this, the London theory deals with the transverse velocity only. Chapter 4 derives the thermodynamic correction from a phenomenological free energy following the Rickayzen approach. Then the experiments are considered and observed potentials are discussed. The Gorter-Cazimir (GC) two-fluid model of the superconducting phase transition is presented in Chapter 5. The kinetic energy of super-electrons, the magnetic energy and the Coulomb energy is added to the GC free energy. Due to, the BP is derived which includes the thermodynamic correction and applies to any magnetic field. Chapter 6 includes the healing distance into the two-fluid model because the superconducting fraction does not change abruptly but on a finite distance, and non-local corrections in superconductors are discussed. In Chapter 7, it is derived the complete set of equations which represent the Ginzburg-Landau (GL) theory. The obtained equations are the stability conditions of the free energy stated in Chapter 6. Chapter 8 shows that the BP has a very small effect on magnetic and thermodynamic properties of a superconductor and a quasi-neutral limit is stated. Chapter 9 estimates the diamagnetic current at the surface and a related electrostatic field into the framework of the GL theory. Chapter 10 considers a conflict between theory and experiment connected with effects of metal surfaces. The surface value of the electrostatic potential is given by the identity stated by the Budd-Vannimenus theorem. Chapter 11 shows how to match the BP valid only inside superconductor with the electrostatic potential observed outside. In Chapter 12, it is shown that the magnetic field can penetrate into the superconductor if the London penetration depth is larger than the GL coherence length. This characterizes the type II superconductors. The Abrikosov vortex lattice, generating an electric potential above the surface of the superconductor is discussed in Chapter 13, where it is made the theoretical prediction of the potential seen by a tip of electrode, does not interacting with the surface. Chapter 14 introduces a phenomenological theory of GL type for superconducting planes treated as 2-D subsystems. The hybrid model proposed by Lawrence and Doniach for layered superconductors is extended to cover the electrostatic field and the charge transfer. In Chapter 15, it is shown that for a magnetic field parallel to the main axis, the magnetic properties of the layered structure are described in analogy with metals. In particular, one can use the GL theory in the quasi-neutral approximation. Chapter 16 shows that a change of the electron density near the surface of the superconductor, caused by the applied electric field, locally increases or decreases the density of the condensation energy. This influences the formation of the local superconducting fraction with corresponding change of the phase transition temperature in thin layers. Outlook and perspectives are present in Chapter 17. The appendixes are devoted to some material properties, obtained numerical solutions and auxiliary theorems. In total, this sound and thorough book on the application of the electrostatic force approach to the superconductors, written in the sufficiently simple but strict mathematical level could be useful by creating of introductory courses on superconductivity, and also for students and engineers studying independently.