1. Superconductivity: approaching the century jubilee Andrey Varlamov Institute of Superconductivity and Innovative Materials (SPIN) CNR, Italy 2nd International School on Nanophotonics and Photovoltaics Zakhadzor 15-22 September 2010

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. Superconductivity in alloys

7. 1933: Meissner-Ochsenfeld effect Ideal conductor! Ideal diamagnetic!

9. 1935: Brothers London theory H H=0

10. 1937: Superfluidity of liquid He 41913

11. Landau theory of 2 nd order phase transitions Order parameter? Hint: wave function of Bose condensate (complex!) 1913

12. 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

13. 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.

14. 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.

15. 1950: Isotopic effect

16. 1950:Electron phonon attraction

17. 1957: BCS- Microscopic theory of superconductivity1972

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

21. 1987: Nitrogen limit is overpassed YBa 2 Cu 3 O 7-x : T c =93 K

23. 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

24. Superconducting RF cavities for colliders

25. Energy transmission

26. Transformers for railway power supply

27. Powerful superconducting magnets

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

29. Medical NMR tomography equipment

30. Criogenic high frequency filters for wireless communications

31. Fluctuation Phenomena in Superconductors 2nd International School on Nanophotonics and Photovoltaics Zakhadzor 15-22 September 2010 Andrey Varlamov Institute of Superconductivity and Innovative Materials (SPIN), CNR, Italy

32. Smearing of the transition 0D super- conductor

33. In-plane resistance of HTS

34. Transversal resistance of HTS

35. Nernst effect in cuprates

36. Superconducting fluctuations near Tc: qualitative picture

38. Ginzburg-Landau formalism Fast (fermionic) and slow (bosonic) variables

39. Quadratic GL approximation

40. d ξ(T) 0D0D Exact solution for the 0D superconductor

41. Microscopic theory of fluctuations

42. Fluctuation propagator

44. Fluctuation thermodynamical potential Green function Diagrammatic presentation of the fluctuation corrections Fluctuation correction the Green function

45. Leading-order fluctuation propagator contributions to the electromagnetic response operator

47. Aslamazov-Larkin paraconductivity ~ When T=0 When T>>Tc When T-Tc<<Tc = =

48. Anomalous MT contribution ~ When T-Tc<<Tc When T=0

49. Density of States Renormalization Δσ (2) DOS = - 0.1e 2 /ħ ln(1/ε) When T-Tc<<Tc When T=0 -

50. Diffusion coefficient renormalization Δσ (2) DOS = - 0.1e 2 /ħ ln(1/ε) When T-Tc<<Tc When T=0

51. Exact solution

52. Asymptotic regimes in the phase diagram

53. Fluctuation conductivity surface as the function of temperature and magnetic field

54. Contours of constant fluctuation conductivity.

55. Temperature dependence of the FC at different fields close to H_{c2}(0) and comparison to experimental data for thin films of LaSCO with T_{c0}≈19K and B_{c2}(0)≈15T

56. Quantum fluctuations near Hc 2 (0): qualitative picture ~ Close to Tc: Close to Hc 2 (0):

57. Snapshot visible for times shorter than τ QF