This accessible textbook offers a novel, concept-led approach to superconducting electronics, using the COMSOL Multiphysics software to help describe fundamental principles in an intuitive manner.
Based on a course taught by the author and aimed primarily at engineering students, the book explains concepts effectively and efficiently, uncovering the "shortcut" to understanding each topic, enabling readers to quickly grasp the underlying essence. The book is divided into two main parts; the first part provides a general introduction to key topics encountered in superconductivity, illustrated using COMSOL simulations based on time-dependent Ginzburg-Landau equations and avoiding any deeply mathematical derivations. It includes numerous worked examples and problem sets with tips and solutions.
The second part of the book is more conventional in nature, providing detailed derivations of the basic equations from first principles. This part covers more advanced topics, including the BCS-Gor'kov-Eliashberg approach to equilibrium properties of superconductors, the derivation of kinetic equations for nonequilibrium superconductors, and the derivation of time-dependent Ginzburg-Landau equations, used as the basis for COMSOL modeling in the first part.
Supported throughout by an extensive library of COMSOL Multiphysics animations, the book serves as a uniquely accessible introduction to the field for engineers and others with a less rigorous background in physics and mathematics. However, it also features more detailed mathematical background for those wishing to delve further into the subject.
Dr. Armen Gulian is Senior Research Scientist and Director of Chapman University's Advanced Physics Laboratory, located in Burtonsville, Maryland. His scientific career began with a Ph.D. and postdoctoral research on non-equilibrium phenomena in superconductors and superfluids within the group of Nobel Laureate Vitaly Ginzburg.
Before setting up the Advanced Physics Laboratory for Chapman, Dr. Gulian founded the Laboratory of High-Temperature Superconductivity at the Physics Research Institute, Armenia - overseeing the world's first observation of phase-slip centers in high-temperature superconductors. Dr. Gulian has also worked on the development of quantum detectors at the US Naval Research Laboratory, where he proposed a theoretical design and performed experimental demonstration of novel cryogenic detector prototypes for X-ray/UV single-photons.
Dr. Gulian's many publications include those on prediction of the "phonon deficit" effect (important for development of electronic coolers); the theory of superconducting quantum generators (potential application for terahertz radiation imaging and high-resolution acoustic imaging); and the prediction of interference current at the description of superconductivity based on time-dependent Ginzburg-Landau equations (important for superconducting electronics).
Chapter 1. What is superconductivity
1. How to handle zero resistance/infinite conductivity?
2. Londons' approach
Problems in Section 2 (all problems here and below with solutions, almost all of them also have hints):
1. Describe penetration of magnetic field into superconductor.
2. Prove that screening of magnetic field in superconductors occurs at shortest possible distance.
3. Estimate the characteristic length of magnetic field penetration into the bulk superconductor.
3. Ginzburg-Landau approach
Problem in Section 3:
1. Find out what is the difference between Cooper condensate and Bose condensate.
4. Josephson effects
Problem in Section 4:
1. What will happen if constant voltage is applied to superconducting junctions?
Problems in Section 5:
1. Consider a hollow superconducting cylinder, and prove that magnetic flux is quantized in it.
2. When the flux is not quantized?
6. Time-dependent Ginzburg-Landau theory
Problems in Section 5:
1. Using COMSOL Multiphysics, consider penetration of magnetic field into a thin superconducting disk.
2. Explore this phenomenon Using COMSOL and realize existence of two types of superconductors.
3. Using COMSOL, consider the flow of current through a thin superconducting wire: discover oscillatory regime of the current flow and explore it.
4. Using COMSOL, consider the flow of current through a thin superconducting strip: observe annihilation of Abrikosov vortices and anti-vorticies.
Chapter 2. BCS-Gor'kov approach to equilibrium properties of superconductors
Chapter 3. Green's function formalism in nonequilibrium case
Chapter 4. Derivation of kinetic equations for nonequilibrium superconductors
Chapter 5. Superconducting lasers
Chapter 6. Cooling by heating
Chapter 7. Derivation of time-dependent Ginzburg-Landau equations