Shortcut to Superconductivity: Superconducting Electronics via COMSOL Modeling

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?

5. SQUIDs

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:

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