Syllabus
1. Introduction to superconductivity (electrical resistance, critical parameters, ideal conductivity and Meissner effect, London theory, thermodynamic properties, isotope effect, interaction with electromagnetic radiation)
2. Bardeen-Cooper-Schrieffer microscopic theory (origin of attractive interaction, variation method, ground state energy, coherence coefficients, calculation of the critical temperature and critical thermodynamic field, temperature dependence of the gap, density of states, gap-less superconductivity, electron tunneling, coherence effects)
3. Ginzburg-Landau (GL) phenomenological theory (order parameter, energy, coherence length, GL equations, flux penetration length and coherence length, limits of validity of GL theory, surface energy, type 1 and type 2 superconductors, magnetic flux quantization and quantum vortices)
4. Spontaneous breaking of gauge symmetry
5. Properties of type 2 superconductors (intermediate state, mixed state, interaction energy of vortices, interaction of vortices with surface, vortex pinning, critical state, resistive state, critical current, magnetization loop, imaging of vortices)
6. Applications of superconductivity
7. Weak superconductivity (Josephson junction (JJ), Josephson effect, calibration transformation, influence of a static magnetic field on JJ, electrodynamics of JJ, voltage-current characteristics of JJ, macroscopic quantum interference)
8. Applications of weak superconductivity (tunnel junctions, SQUIDs, analog and digital circuits)
9. High temperature superconductivity (history, structural and chemical properties of materials, magnetic and transport properties, theory)
Annotation
General introduction to superconductivity and superfluidity, phenomenology of superconductivity, BSC theory of superconductivity, experimental proofs of validity of BCS theory, Ginzburg-Landau theory of superconductivity, type 1 and 2 superconductors, magnetic flux quantization and vortices, weak superconductivity - Josephson effect, applications of Josephson junctions, SQUID, high temperature superconductivity.