Professor Giovanni Ummarino

Politecnico di Torino, Italy

Lecture: "The theory and application of superconductivity"


A brief history of superconductivity.
The main experimental evidence of superconductivity, types and classes of
superconductors: an exhaustive landscape. Difference between perfect conductor and superconductor. London equations. Pippard theory.
Superconductors of type I and II.
 Intermediate state. Magnetic flux quantum.
Ginzsburg_Landau theory.
Calculation of the upper critical magnetic field. Upper critical surface magnetic field. Calculation of the lower critical magnetic field. Mixed state. Abrikosov solution.
Josephson effect. RSJ model. SQUID. Model of Lawrence-Doniach.
Time-dependent Ginzsburg-Landau equations.
Granular superconductors.
Electron-phonon interation. Cooper pairs.
BCS equation. Approximations of the BCS theory.
Calculation of the critical temperature. Calculation of the order parameter.
Rate 2delta/Tc, jump of the specific heat.
Superconducting density of states and other physical observables.
The BCS tunnel effect and theAndrev reflection.
BCS theory in two bands. Proximity effect.
Limits of the BCS theory.

Eliashberg theory in general. Eliashberg equations on the real axis. The equations Eliashberg at T=0 K. The tunnel effect. The Andrev reflection.
Reversing the Eliashberg equations to calculate the spectral function and the Coulomb pseudopotential.
Working on the imaginary axis. Calculation of the critical temperature. Pade approximants.
BCS limit. Calculation of the critical temperature in the BCS limit. Intermediate coupling: formula Rowell-Mac Millan.
Calculation of the critical temperature in the extreme strong coupling limit.
Mixed formulation of the Eliashberg equations
Eliashberg equations for the critical magnetic field.
Calculation of physical observables via numerical solution of Eliashberg equation: critical temperature, gap, temperature dependence of gap
penetration lenght, coherence length  jump of specific heat and temperature dependence of specif heat, NMR, isotope effect ect.
Effect of magnetic impurities and disorder.
Eliashberg equations in d-wave and effect of impurities in d-wave: HTCS and PuCoGa.
Multiband Eliashberg theory (magnesium diboride: the perfect superconductor), effect of magnetic impurities and disorder on a two-band superconductor. Three bands superconductor: the iron-picnitides, the interband superconductivity and the sign-reversal of the gap.
The proximity effect in Eliashberg theory.
Limits of Eliashberg equations and possible generalizations. Eliashberg equations in not half filling and normal density of states energy-depending. Migdal theorem breakdown.
Brief overview of other approaches to the theory of superconductivity.

Power applications.
Applications of perfect diamagnetism.
Macroscopic quantum properties applications (small scale applications).