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Andrey Varlamov Institute of Superconductivity and Innovative Materials (SPIN) CNR, Italy

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

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Andrey Varlamov Institute of Superconductivity and Innovative Materials (SPIN) CNR, Italy

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

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

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

  4. Superconductivity in alloys

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

  6. 1935: Brothers London theory H H=0

  7. 1913 1937: Superfluidity of liquid He4

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

  9. 1950: Ginzburg-Landau Phenomenology Ψ-Theory of Superconductivity 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 Order parameter? Hint: wave function of Bose condensate (complex!)

  10. Thus the Gibbs free energy acquires the form Ginzburg-Landau functional 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.

  11. 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.

  12. 1950: Isotopic effect

  13. 1950:Electron phonon attraction

  14. 1957: BCS- Microscopic theory of superconductivity 1972

  15. 1957: Discovery of the type II superconductivity 2003

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

  17. 1987 1986: Discovery of the High Temperature Superconductivity in Oxides

  18. 1987: Nitrogen limit is overpassed YBa2Cu3O7-x: Tc=93 K

  19. MAGLEV:flying train 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.

  20. Superconducting RF cavities for colliders

  21. Energy transmission

  22. Transformers for railway power supply

  23. Powerful superconducting magnets

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

  25. Medical NMR tomography equipment

  26. Criogenic high frequency filters for wireless communications

  27. 2nd International School on Nanophotonics and Photovoltaics Zakhadzor 15-22 September 2010 Fluctuation Phenomena in Superconductors Andrey Varlamov Institute of Superconductivity and Innovative Materials (SPIN), CNR, Italy

  28. Smearing of the transition 0D super- conductor

  29. In-plane resistance of HTS

  30. Transversal resistance of HTS

  31. Nernst effect in cuprates

  32. Superconducting fluctuations near Tc: qualitative picture

  33. Ginzburg-Landau formalism Fast (fermionic) andslow (bosonic) variables

  34. Quadratic GL approximation

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

  36. Microscopic theory of fluctuations

  37. Fluctuation propagator

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

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

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

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

  42. Density of States Renormalization When T-Tc<<Tc Δσ(2)DOS= - 0.1e2/ħ ln(1/ε) - When T=0

  43. Diffusion coefficient renormalization When T-Tc<<Tc When T=0 Δσ(2)DOS= - 0.1e2/ħ ln(1/ε)

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