1. Superconductivity: approaching the century jubilee A.A.Varlamov Institute of Superconductivity and Innovative Materials SPIN-CNR, Italy

2. 1911: discovery of superconductivity Whilst measuring the resistivity of “pure” Hg he noticed that the electrical resistance dropped to zero at 4.2K Discovered by Kamerlingh Onnes in 1911 during first low temperature measurements to liquefy helium In 1912 he found that the resistive state is restored in a magnetic field or at high transport currents 1913

5. The superconducting elements Transition temperatures (K) Critical magnetic fields at absolute zero (mT) Transition temperatures (K) and critical fields are generally low Metals with the highest conductivities are not superconductors The magnetic 3d elements are not superconducting Nb (Niobium) T c =9K H c =0.2T Fe (iron) T c =1K (at 20GPa) Fe (iron) T c =1K (at 20GPa)...or so we thought until 2001

6. Transition temperatures (K) Critical magnetic fields at absolute zero (mT) Li (Lithium) T c <0.4mK Li (Lithium) T c <0.4mK Helsinki University of Technology Low Temperature Laboratory, 2007

7. Superconductivity in alloys

8. 1933: Meissner-Ochsenfeld effect Ideal conductor! Ideal diamagnetic!

10. 1935: Brothers London theory H H=0

11. 1937: Superfluidity of liquid He 41913

12. Landau theory of 2 nd order phase transitions Order parameter? Hint: wave function of Bose condensate (complex!) 1962

13. 1950: Ginzburg-Landau Phenomenology Ψ-Theory of Superconductivity Order parameter? Hint: wave function of Bose condensate (complex!) Inserting and using the energy conservation law How one can describe an inhomogeneous state? One could think about adding. However, electrons are charged, and one has to add a gauge-invariant combination 2003

14. Ginzburg-Landau functional Thus the Gibbs free energy acquires the form To find distributions of the order parameter Ψ and vector–potential A one has to minimize this functional with respect to these quantities, i. e. calculate variational derivatives and equate them to 0.

15. Minimizing with respect to Minimizing with respect to A: Maxwell equation The expression for the current indicates that the order parameter has a physical meaning of the wave function of the superconducting condensate.

16. 1950: Isotopic effect

17. 1950:Electron phonon attraction

18. 1957: Discovery of the type II superconductivity2003

19. U. Essmann and H. Trauble Max-Planck Institute, Stuttgart Physics Letters 24A, 526 (1967) Physics Letters 24A, 526 (1967) Magneto-optical image of Vortex lattice, 2001 P.E. Goa et al. University of Oslo Supercond. Sci. Technol. 14, 729 (2001) Supercond. Sci. Technol. 14, 729 (2001) Scanning SQUID Microscopy of half-integer vortex, 1996 J. R. Kirtley et al. IBM Thomas J. Watson Research Center Phys. Rev. Lett. 76, 1336 (1996)BM Thomas J. Watson Research Center Phys. Rev. Lett. 76, 1336 (1996)

20. 1957: BCS- Microscopic theory of superconductivity1972

21. 1958: Lev Gorkov formulates elegant equations of the microscopic theory of superconductivity and demonstrates the equivalence between the microscopic BCS theory and GL phenomenology at temperatures close to the critical one.

22. Extensions of the BCS theory

23. BCS Superconductivity: no gap – no supercurrent ! The order parameter Ψ has a physical meaning of the wave function of the superconducting condensate and the gap in the quasi-particle spectrum determines its modulus: supercurrent

24. 1959: Abrikosov & Gorkov: Gapless Superconductivity there is no gap but supercurrent exists In the interval of concentrations Superconductor with paramagnetic impurities

25. BCS Superconductivity: long-range order In superconducting state In normal state, due to fluctuations 3D case Due to fluctuations:

26. 2D Superconductivity: Wegner - Mermin - Hohenberg theorem (1968): destruction of the long-range order by the phase fluctuations 1972-1973: Berezinsky–Kosterlitz–Thouless transition

27. 1973: Superfluidity in liquid He 3 David M. Lee, Douglas Dean Osheroff and Robert C. Richardson 1996 2003 Antony Legget

28. Superconductivity with nontrivial symmetry of the order parameter: Kirtley: Phase sensitive pairing symmetry tests. Observation of thehalf-flux quantum effect in a tricrystal geometry, showed that the gap has predominantly d-wave symmetry in a number of the cuprate high-T c superconductors

29. 1962: Josephson effect SS Amplitude 1973

31. Link Since the energy gain depends on the phase difference, the finite phase difference must create persistent current transferring Cooper pairs between the leads

32. 1986: Discovery of the High Temperature Superconductivity in Oxides 1987

33. 1987: Nitrogen limit is overpassed YBa 2 Cu 3 O 7-x : T c =93 K

35. Two band superconductor: MgB 2

36. The linear motor car experiment vehicles MLX01-01 of Central Japan Railway Company. The technology has the potential to exceed 4000 mph (6437 km/h) if deployed in an evacuated tunnel.evacuated MAGLEV: flying train

37. Superconducting RF cavities for colliders

38. Energy transmission

39. Transformers for railway power supply

40. Powerful superconducting magnets

41. Scientific and industrial NMR facilities 900 MHz superconductive NMR installation. It is used For pharmacological investigations of various bio-macromolecules. Yokohama City University

42. Medical NMR tomography equipment

43. Criogenic high frequency filters for wireless communications