UNIVERSITÀ DEGLI STUDI DI GENOVA

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1 UNIVERSITÀ DEGLI STUDI DI GENOVA

2 Outline Story of superconductivity phenomenon going through the discovery of its main properties. Microscopic theory of superconductivity and main parameters which characterize the superconducting state. Magnetic properties and main mechanisms which allow a superconductors to carry superconducting current. Main superconducting materials. Peculiarities and issues of novel superconducting materials.

resistivity of Hg to investigate the behavior of resistivity at low

3 Kammerlingh Onnes, Leiden 1908: Liquefaction of Helium 1911: discovery of superconductivity 1913: Nobel price 1913 He was measuring the resistivity of Hg to investigate the behavior of resistivity at low temperature He noticed that the electrical resistance dropped to zero at 4.2K

4 The consequences of the Zero Resistance State (R =0) R= 0 implies no Joule dissipation in cable conducting current R= 0 implies that current can flow in a loop without decay R= 0 implies that large magnetic field can be realized through solenois with large current flowing in persistent mode

Kammerlingh Onnes s Visions Construction of a 10 T Magnet with Hg und Pb Wires Presented at 3 International Congress on Refrigeration, Chikago 1913 Superconducting Magnet Coil Experiments with Hg-and

5 Kammerlingh Onnes s Visions Construction of a 10 T Magnet with Hg und Pb Wires Presented at 3 International Congress on Refrigeration, Chikago 1913 Superconducting Magnet Coil Experiments with Hg-and Pb wires failed The coil lost superconducting properties already at small Current densities and at Magnetic Fields of several 100 Gauss. Superconductivity can be destroyed also by an external magnetic field, which is called critical field, H c (Kamerlingh Onnes 1914)

6 Critical Field Empirically :

7 1933: Meissner-Ochsenfeld effect Magnetic field does not penetrated the superconductor Ideal conductor! Ideal diamagnetic!

8 Campo magnetico T > Tc T < Tc superconduttività Temperatura T c

The consequences of the perfect diamagnetisms

large masses like the coaches of a train

maglev train between Tokyo and Osaka will be

9 The consequences of the perfect diamagnetisms c=-1 B m MAGNET SUPERCONDUCTORS The expulsion of the magnetic field, generates great magnetic moments, able to levitate extremely large masses like the coaches of a train ELECTRODINAMIC LEVITATION The future (2025) maglev train between Tokyo and Osaka will be the fastest train in the world with a speed approximately 1000 km/h.

10 The quantum coherence 1950: Ginzburg-Landau Phenomenology Ψ-Theory of Superconductivity

11 T > Tc T < Tc A macroscopic wave function describes the system as a whole Macrscopic quantum effects

1962: Josephson effect Super electrons cross the

superconductors as a consequence of the phase

Levitazione magnetica 1973 SQUID superconducting

presence of two superconductive junctions and on

12 1962: Josephson effect Super electrons cross the insulanting junction between the two superconductors as a consequence of the phase difference between the two superconductors Levitazione magnetica 1973 SQUID superconducting quantum interference device it is based on the presence of two superconductive junctions and on the interference due to the phase difference across the two junctions

13 SQUID for biomagnetisms SQUID sensitivity Heart magn. field Brain magn. field Earth magn. field Fridge magnet T T T 10-5 T 10-2 T

14 1957: Microscopic theory of superconductivity (Bardeen, Cooper, Schrieffer) 1972

15 1950: Isotopic effect Isotopic effect suggests that the ion lattice plays a crucial role

impulse and spin: the Cooper pairs Cooper pair K -K An energy gap opens in

16 BCS- Theory of superconductivity in the presence of an attractive interaction provided by the lattice electrons form pairs of opposite impulse and spin: the Cooper pairs Cooper pair K -K An energy gap opens in the energy spectrum which stabilizes the supercoducting state Normal E g superconductor

17 Energy Energy gap electrons Normal state BCS state

18 ħω < A T< Tc Phonons don t have energy enough to breack the Cooper pairs = 0

19 0 A T Tc Interaction with phonons break the Cooper pairs 0

20 Electron pairing mechanisms

21 BCS theory predictions Interaction strength Energy Gap - w D -g w D E w D exp 1 g Critical temperature T c ~1-20 K T c 1 D exp g Debye Temperature D T cmax ~ K D ~ K

22 Coherence length For the superconducting elements the coherence length can be as large as hundreds nm, much larger than the lattice spacing. between the two electrons of a pair, there may be thousands of electrons belonging to other pairs. size of the Cooper pair

23 MAGNETIC PROPERTIES 2 classes of superconductors with different properties TYPE I (elements) TYPE II (alloys, composites,...)

24 London penetration depth 1935: Brothers London theory B=m 0 H B=0 M=-H B=0 I s B 0 B 0 I s The magnetic field does not change abruptly to zero within the superconducting material. In the superficial thickness where the superconduncting currents flow, the magnetic field goes progressively to zero

B = μ 0 (M+H) Magnetization curves H c2 > H c Type II superconductors can be high field

expelled thank to a negative A- Pb; B Pb+2%In; Afterthat C- magnetic Pb+8%In; flux D- enters

25 B = μ 0 (M+H) Magnetization curves H c2 > H c Type II superconductors can be high field superconductors For Type I, the magnetic fields is Type II behaves like Type I till to H c1. expelled thank to a negative A- Pb; B Pb+2%In; Afterthat C- magnetic Pb+8%In; flux D- enters Pb+20%In the magnetization which grows sample and magnetization decreases linearly up to H c where the progressively. At H c2 themagnetization magnetization falls to zero as in becomes zero end the seperconductor Areas below the curve remain the same normal conductors becomes normal.

26 Meissner state Meissner state

27 Type II Type I Who is of I or II type? 1 2 Ginzburg - Landau parameter 1 Type I ; Type 2 II With disorder Type II m 2 2 e m0n s 1/ 2 n 1/ 3 s T c MgB SmFeAsO 0.7 F KBaFe2As Fe(Se,Te)

28 1957: What the mixed state is (Abrikosov) Quantized flux lines 2003 Quantized flux lines (fluxons/vortices) enter the superconductor Φ 0 = h 2e Wb Fluxons form an exagonal lattice Abrikosov solution near Hc2 Contours of B

14, 729 (2001) Scanning SQUID Microscopy of

29 U. Essmann and H. Trauble Max-Planck Institute, Stuttgart 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) 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)

Normal electrons Dissipation in the mixed state Applied current Lorenz Force acting on the flux lines an applied current exerts a force on the vortices the motion of the fluxons whose core is made up

30 Normal electrons Dissipation in the mixed state Applied current Lorenz Force acting on the flux lines an applied current exerts a force on the vortices the motion of the fluxons whose core is made up of normal electrons causes dissipation The system is superconducting but it is resistive and dissipates Resistenza B = 0 T B = 0.02 T B = 1 T B = 2 T B = 4 T B = 6 T Temperatura (K)

31 Vortex pinning The flux motion reduces the current that the superconductor can curry without dissipation. SOLUTION: to introduce defects which pinn the vortices Critical current I c : the maximum current that the superconductors can curry without dissipation

32 The region in which a superconductors can work without dissipation is limited by the three parameters: The criticat temperature; The critical field; The critical current.

33 The superconducting materials

34 Above Future Now 1997? Record Pressure: 250 GPa 2,500,000 atmospheres

35 Story of the superconducting materials 250 Hydrides series LaH 10 T C =260 K P>1.7GPa 200 H 3 S T C =203 K P>1.5 GPa Hidride Liquid N Liquid H Liquid He

High Temperature superconductors (HTS) 1986 Bednorz and Müller 1986 1987 YBa 2 Cu 3 O 7 T c =92 K Ceramic materials charactized by CuO 2 layers

36 High Temperature superconductors (HTS) 1986 Bednorz and Müller YBa 2 Cu 3 O 7 T c =92 K Ceramic materials charactized by CuO 2 layers spaced by a reservoir block Conduction (and superconductivity ) occurring in the CuO 2 layers Maximum T c = 165 K in HgBa 2 Ca 2 Cu 3 O 8+d under pressure

The increasing of CuO 2 layer increases T c T c (K) 10-40 65-85

CuO 2 planes The coupling between electron is determined by

37 The increasing of CuO 2 layer increases T c T c (K) Complex phase diagram as a function of the doping in the CuO 2 planes The coupling between electron is determined by unconventional mechanism (not mediated by the phonons) not yet completely clarified

optical mode of B ions Conventional superconductivity T

38 MgB2 Akimitzu (2001) T c = 39 K Layered structure Metallic system Electron pairing mediated by the optical mode of B ions Conventional superconductivity T c = 39 K is too near the maximum T c predicted by the BCS theory!!

39 MgB 2 first example of a two-gap superconductor

40 Iron based superconductors Gennaio 2008 Tc=25 K in LaFeAs(OF) Ba(CoFe) 2 As LiFeAs Fe(SeTe) FeSe SrNi 2 As 2

41 F O RE Fe As REFeAsO 1111 T c,max = 58 K AEFe 2 As T c,max = 40 K Fe(Se,Te) 11 T c,max = 21 K

42 Phase diagram as a function of doping Temperature Sanna et al., PRB 80, SmFeAsO 1-x F x T m msr T c SQUID T c msr AF Analogies with HTS and with MgB 2 superconductivity occurs upon doping proximity with magnetic ordering Anisotropic structure two-gap superconductivity

43 C. Tarantini et al., PRB 84, (2011)

44 IBS HTS MgB 2 C. Tarantini et al., PRB 84, (2011)

45 Peculiarities and issues of novel superconducting materials 1: Not conventional order parameter (Cooper pair wave function) LTS s-wave HTS d-wave MgB 2 s++ Fe-S s+- What does it imply a not conventional oder parameter? Wheak coupling between grains

Peculiarities and issues of novel superconducting materials 2: Small coherence length n 1/ 2 s 3: Large structural anisotropy ab d c T c d Small and large anisotropy: What does

46 Peculiarities and issues of novel superconducting materials 2: Small coherence length n 1/ 2 s 3: Large structural anisotropy ab d c T c d Small and large anisotropy: What does it imply? Giant dissipation in presence of an applied magnetic field Resistenza Bi-Sr-Ca-Cu-0 B=0T B=0.02T B=1T B=2T B=4T B=6T Temperatura(K)

Strongly Correlated Systems:

M.N.Kiselev Strongly Correlated Systems: High Temperature Superconductors Heavy Fermion Compounds Organic materials 1 Strongly Correlated Systems: High Temperature Superconductors 2 Superconductivity: