PORTALE DELLA DIDATTICA

PORTALE DELLA DIDATTICA

PORTALE DELLA DIDATTICA

Elenco notifiche



Physics of superconductivity

02MLUKG

A.A. 2020/21

Course Language

Inglese

Degree programme(s)

Doctorate Research in Fisica - Torino

Course structure
Teaching Hours
Lezioni 20
Lecturers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Ummarino Giovanni Professore Associato PHYS-04/A 20 0 0 0 12
Co-lectures
Espandi

Context
SSD CFU Activities Area context
*** N/A ***    
The course is divided into three parts. The longest part is the first about the classical macroscopic theory of superconductivity and BCS theory (microscopic). The second part is on Eliashberg theory and not all results are demonstrated for the difficulties of the theory. The third part is the shortest and it is a very quick overview of the application of superconductivity
Physics I, Physics II, Quantum Mechanics, Foundaments of Solid State Physics
FIRST PART: CLASSICAL SUPERCONDUCTIVITY AND BCS THEORY 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, order parameter, 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. SECOND PART: ELIASHBERG THEORY Eliashberg theory in general. Eliashberg equations on the real axis. The equations Eli-ashberg at T = 0 K. The tunnel effect for reversing the Eliashberg equations to calcu-late the spectral function and the Coulomb pseudopotential. Working on the imaginary axis. Calculation of the critical temperature. Pade approx-imants. BCS limit. Calculation of the critical temperature in the BCS limit. Intermedi-ate 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, coher-ence 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: HTCS and PuCoGa. Multiband Eliashberg theory (magnesium diboride: the perfect superconductor), ef-fect 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 theory of superconductivity. THIRTH PART: APPLICATIONS OF SUPERCONDUCTIVITY Power applications. Applications of perfect diamagnetism. Macroscopic quantum properties applications (small scale applications).
On site
Oral presentation
P.D.1-1 - January