The Vortex Matter In High-Temperature Superconductors. Yosi Yeshurun Bar-Ilan University Ramat-Gan Israel

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1 The Vortex Matter In High-Temperature Superconductors Yosi Yeshurun Bar-Ilan University Ramat-Gan Israel

2 7,700 km

4 The Vortex Matter In High-Temperature Superconductors OUTLINE: Temperatures High-Temperatures Vortices in superconductors dynamics and thermodynamics Conductors Superconductors Applications Energy Transportation Medical Global and local magnetic measurements

5 Conductors Energy is carried by electrons Resistance A result of interaction with Other electrons Vibrating atoms Impurities Energy dissipation

6 High-Temperature Superconductos Temperature conductors Superconductors

7 How to reach low temperatures? Cooling gases down: Compress/expand the gas adiabatically. Part of the gas liquefies and collected. Oxygen, O 2 : 90K Nitrogen, N 2 : 77K Hydrogen, H 2 : 20K 1908: H. Kamerlingh Onnes Helium, He 4 : 2 4 K 1913: Nobel Prize

8 Discovery of Superconductivity Heike Kamerlingh Onnes liquefied helium (~4 K = C ) investigated low temperature resistance of mercury

9 High-Temperature Superconductos Temperatures High-temperatures conductors Superconductors

15 Hg-Ba-Ca-Cu-O at 136 K 164 K under pressure

16 What is so SUPER about superconductors? Large critical current (the maximum current that can be carried by th superconductor without energy dissipation)

17 What is so SUPER about superconductors? Large critical current (the maximum current that can be carried by th superconductor without energy dissipation) 1. High current applications Transferring energy without loss

18 Energy transfer

19 1. High current applications Transferring energy without loss Superconducting Magnetic Energy Storage (SMES)

20 Superconducting Magnetic Energy Storage (SMES) Motivation: (1) Storing energy (2) Improving energy quality Other solutions: Fly Wheels Batteries Capacitors

23 1. High current applications Transferring energy without loss Superconducting Magnetic Energy Storage (SMES) Fault Current Limiter (FCL)

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29 1. High current applications Transferring energy without loss Superconducting Magnetic Energy Storage (SMES) Fault Current Limiter (FCL) Medical applications - Magnetic Resonance Imaging (MRI)

30 Medical applications: Magnetic Resonance Imaging (MRI)

31 MRI - the most expensive equipment in the hospital

33 What makes superconductors SUPER? Insulator Conductor Superconductor

34 BCS Theory of Superconductivity By John Bardeen, Leon Cooper, and Robert Schrieffer A key conceptual element in this theory is the pairing of electrons close to the Fermi level into Cooper pairs through interaction with the crystal lattice.

35 Cooper Pairs

36 Animation of Cooper pairs: Source: superconductors.org and Ian Grant

37 What is a superconductor? 1) Zero electrical resistivity NO!!! Insufficient characterization!!! 1.May be a perfect conductor 2.A superconductor may exhibit non-zero resistance (due to vortex motion) 2) The Meissner effect

the interior of a superconductor As a result: (1)

38 Meissner Effect 1933: Walther Meissner & Robert Ochsenfeld T<T c : external magnetic field is perfectly expelled from the interior of a superconductor As a result: (1) Diamagnetism (2) Mag. Levitation

39 Perfect Diamagnetism M χ m = -1 H M=-H Means: B = µ o (H + M) B = µ o (H + χ m H) B = 0 Normal Metal Superconductor Flux is excluded from the bulk by supercurrents flowing at the surface to a penetration depth (λ) ~ nm

41 Magnetic Levitation

42 TRANSPORTATION Magnetic Levitation (MagLev)

43 Meissner (and Ochsenfeld) Effect [1933] T<T c : external magnetic field is perfectly expelled from the interior of a superconductor Strong external magnetic fields: Shielding is partial Stronger magnetic fields destroy superconductivity

44 H-T diagram of conventional superconductors

45 Thermodynamic H-T phase diagram of conventional superconductors

46 Thermodynamic H-T phasediagram of superconductors 1) Zero electrical resistivity Electrical current in a superconducting ring continues indefinitely 2) The Meissner effect Magnetic field inside a bulk sample is zero -- Current flows to shield the external field (the induced field opposes the applied field) The material is strongly diamagnetic as a result. Magnetic lavitation

47 Experimental confirmation of the Abrikosov Lattice Magnetic Decoration Magneto-Optical Imaging Low-Angle Neutron Scattering

48 Vortex in type II superconductor J superconducting normal 2 µm Flux quantum Φ 0 =hc/2e Magnetic decoration Magnetic decoration of vortex lattice in superconductor

49 Magneto-optical setup PC MATLAB CCD camera Hamamatsu C Hg\Mercury lamp Green Filter Analyser Microscope Leica DMRM Polarizer Bi:YIG indicator Coil Lipman PS Cryostat oxford Liquid He Heater Sample

50 Vortices in type II superconductor J superconducting normal Flux quantum Φ 0 =hc/2e Magneto-optical image of a quasi-abrikosov (quasi-ordered) vortex state [Johansen et al.]

51 Vortices in type II superconductor J superconducting normal Motion of vortices results in: Energy dissipation Irreversible phenomena T. Johanssen, U. Oslo

52 Lorentz force (~ B x I) moves the vortices at all fields. As a result: A superconductor with resistance that increases with H How to prevent/minimize energy dissipation? Answer: Pin vortices by, e.g. defects Pinned vortices Magnetic irreversibility Larger critical currents

53 Width ~ j Max current that can be carried by the SC without dissipation. j reflects vortex pinning in defects and hence a disorder in the vortex lattice

54 Flux penetration sample B x MO images Bean Profile J ~ db/dx

55 Vortex instabilities and pattern formation Niobium film LaSCO film YBCO film Duran et al., 1995 MgB 2 film Y.Y. (unpublished) BSCCO crystals Wijngaarden et al.,1999. YBCO film Johansen et al., Barness, Y.Y. et al. (2008) P. Leiderer, 2000.

positive feedback Unstable if loop gain > 1 easier for vortices

56 Thermo-magnetic instability f = J Φ 0 vortex motion dissipates energy J E E ~ db/dt motion local temperature increases J positive feedback Unstable if loop gain > 1 easier for vortices to overcome pinning barriers +kt more vortices move After Galperin et al.

57 Novel vortex instabilities [NOT thermomagnetic mechanism] Thermodynamic vortex matter phase-diagram Found only in the proximity of vortex phase transition line

58 Magnetic phase diagram of conventional superconductors

59 Thermodynamic vortex phase diagram in BSCCO Disordered solid high j liquid B ss B m Quasi-ordered solid low j Low-angle neutron scattering (Cubit et al., Nature) Magneto-optical measurements (Johansen et al.)

60 Manifestation of the vortex order-disorder phase transition in magnetic measurements Second Magnetization Peak (SMP) Width ~ j Khaykovich et al., PRL 76 (1996).

61 Problems in identifying the solid-solid transition The SMP exhibits dynamic behavior: SMP is absent at short times Onset and peak shift with time As temperature is lowered, the second magnetization peak is gradually smeared, until below a certain temperature it disappears altogether

62 1000 B [Oe] Disordered Solid? Ordered Solid Liquid T [K] Termination of transition-line at low temperature? Y. Y. et al. (1994), Paltiel et al. (2000), Konczykowski et al. (2000), van der Beek et al. (2000), Giller et al. (2000), Kupfer et al. (2001), Li and Wen (2002), Kalisky et al. (2003)

63 Vortex instabilities near vortex phase transitions Transient disordered vortex state (in a vortex ordered phase)

64 Magneto-optical imaging during field sweep up Vortex injection through the sample edges contanimation Paltiel, Zeldov et al., Nature 403, 398 (2000). Edge contamination Disorder is induced by inhomogeneous surface barriers Transient disordered vortex state

65 Evidence for Transient Disordered Vortex States (TDVS) t=29 s t=0 time = 29 s break Time evolution of induction profiles at a constant applied field High j phase disappears with time time = 0.04 s transient disordered vortex state

66 Evaluation of τ(b,t) Relaxation at constant H ext Field Seep Up: Field Seep Down: Direct measurement τ 1 = B dh dt B= Bf0 τ (B ) = f0 B ext od f0 dh ext B dt (B) diverges as B B od Disorder state is thermodynamically favored above B od

67 Lifetime of TDVS - τ(b,t) 21 K 23 K 30 K As T decreases τ(b) increases

68 Termination of the transition line at low temperatures - artifact caused by long living transient states 1000 Transition masked by TDVS B [Oe] Disordered Solid Ordered Solid Liquid T [K]

69 Transient Disordered Vortex States are injected through inhomogeneous surface barriers during field increase The rush-hour-train model

70 Vortex instabilities near vortex phase transitions Transient disordered vortex state (in a vortex ordered phase) Spontaneous generation of vortex oscillations in B(x,t) Flux waves

71 Disordered solid high j liquid ontaneous Transient Oscillations states B ss B m Quasi-ordered solid low j

MO images at 24 K after application of 430 Oe 700 600

72 MO images at 24 K after application of 430 Oe [G] left edge Region of waves right edge

73 Induction [Gauss]

Induction profiles 340 320 24 K 430 Oe 732 ms 1099 ms 1246

74 Induction profiles K 430 Oe 732 ms 1099 ms 1246 ms 1392 ms 1539 ms B [G] x [µm]

75 Induction profiles

76 Temporal oscillations Hall-probe images (23 K) J. Moore et al. Imperial College, London Waves are clearly related to order-disorder phase transition

77 Experimental conditions for the appearance of flux waves 1. Proximity to the vortex order-disorder phase transition line 2. A nearly flat induction profile (low-j phase)

78 Theoretical analysis Working hypothesis: Origin of flux waves in diffusion processes in the vortex matter Flux waves belong to the general category of spatiotemporal pattern formation (For a review, see Cross and Hohenberg, Rev. Mod. Phys. (1993) Two COUPLED Nonlinear Diffusion Equations

79 1 st diffusion equation B Annealing of injected transient states disorder order T Landau-Khalatnikov Ψ t δf = Γ δψ 3 F = D( Ψ) -a Ψ + γ 0 Ψ 2 d r α=α (1 B/B ), D, γ (1) Free energy 0 od 0 Landau coefficients for the field-driven vortex phase transition high J Ψ c Ψ=0 low J Ψ c Ψ=Ψ 0 (B) Ψ is defined as the Fourier component of the vortex density at the minimal vector of the reciprocal lattice

80 2nd diffusion equation Relaxation of magnetic induction B/ = t c E/ x 2 B c B D = f t 4π x x (2) E= R electric field FJexp(-U/kT) R =R (B/B ) flux flow resistivity U U=U0ln(J c / J) J F n c2 c pinning potential U(J) logarithmic critical current density D f diffusion coefficient for flux creep σ=u /T 0 σ J Df = RF J c [ Ψ]

81 Coupling between the two nonlinear diffusion equations via Jc [ Ψ] Linear Stability Analysis predicts possibility for oscillatory instability characterized by a period and wavelength in accordance with the experimental results

82 Scenario for waves Injection: Ψ=0 Left: fast annealing Ψ > 0 (Eq. 1) lower J c larger D f (Eq. 2) faster relaxation Right: Ψ = 0 high J c low D f (Eq. 2) slow relaxation (regular creep) High B od Low B od gradient in D f accumulation of vortices higher B lower Ψ (Eq. 1) higher J c lower D f (Eq. 2) accumulation stops inverted slope flux moves to lower B B decreases (Eq. 1) anneals the disorder higher Ψ lower J c larger D f

Summary of spontaneous oscillations phenomena Oscillations in time B Oscillations in space B 24 K 430 Oe time 732 ms 1099 ms 1246 ms 1392 ms 1539 ms location Observed near the vortex

83 Summary of spontaneous oscillations phenomena Oscillations in time B Oscillations in space B 24 K 430 Oe time 732 ms 1099 ms 1246 ms 1392 ms 1539 ms location Observed near the vortex order-disorder phase transition Two coupled nonlinear diffusion equations instability phase diagram Instabilities associated with proximity to phase transition NOT with thermomagnetic processes

84 Summary and Conclusions High-temperature superconductors Fascinating fundamental physics Applications are around the corner

What s so super about superconductivity?

What s so super about superconductivity? Mark Rzchowski Physics Department Electrons can flow through the wire when pushed by a battery. Electrical resistance But remember that the wire is made of atoms.