1. Why Make Holes in Superconductors? Saturday Morning Physics December 6, 2003 Dr. Sa-Lin Cheng Bernstein

2. Type I Superconductors Two Conditions: 1. Zero resistivity 2. Meissner effect Superconducting state: T < Tc H < Hc Normal State Superconducting State T Hc Tc H

3. Theoretical Understanding 1930s – quantum model could not explain superconductivity 1950 – phenomenological theory by Vitaly Ginzburg and Lev Landau GGGGinzburg-Landau equation DDDDescribe superconductivity near Tc 2003 – Ginzburg wins Nobel Prize in physics (Nobel Lectures will be held on December 8)

4. Vitaly L. Ginzburg: The New York Times, October 8, 2003 "They have been nominating me for about 30 years, so in that sense it didn't come out of the blue. But I thought, `Well, they're not giving it to me, I guess that's it.' After all, there are a lot of contenders. So, you know, I had long ago forgotten to think about this."

5. BCS Theory BCS = John Bardeen, Leon Cooper, and Robert Schrieffer 1957 – explain why superconductivity occurs Cooper pairs = Pairing of electrons 1972 – Nobel Prize in physics http://superconductors.org

6. Critical Fields in Type II Lower critical field Upper critical field vortices Incomplete Meissner Effect

7. Mixed State in Type II H c1 < H < H c2 Also called “ vortex state ” Magnetic field can penetrate but not completely Flux lines D. J. Bishop et al., © Scientific American, 48 (Feb. 1993)

8. Abrikosov Vortex Lattice 1953 – Abrikosov Vortex Lattice  Based on Ginzburg – Landau equation  Flux lines repel each other  Triangular vortex lattice 2003 – Nobel Prize in physics A. A. Abrikosov © AT&T, 1995

9. Nobel Prize Winning

10. Abrikosov Lattice Images First image of Vortex lattice, 1967 Bitter Decoration Pb-4at%In rod, 1.1K, 195G U. Essmann and H. Trauble © Physics Letters 24A, 526 (1967) Vortices in MgB2, 2002 Scanning Tunnel Spectroscopy MgB2 crystal, 2K, 2000G M. R. Eskildsen et al. © Phys. Rev. Lett. 89, 187003 (2002)

11. What is a vortex? Photo courtesy of the National Severe Storms Laboratory

12. Vortex (flux line) in superconductor Has a core, circled by supercurrents Inside the core: normal electrons Outside the core: superconducting electrons (Cooper pairs)

13. Examples of Type II Mostly compounds Record holder: Tc =138 K High Hc2: Hc2 > 1000 000 G (YBCO) Element Tc (K) Tc7.80 Nb9.25 La 1.85 Ba.15 CuO 4 30 YBa 2 Cu 3 O 7+ 93 Ca 1-x Sr x CuO 2 110 Tl 2 Ba 2 Ca 2 Cu 3 O 10 128 Hg 0.8 Tl 0.2 Ba 2 Ca 2 Cu 3 O 8.33 138

14. See the Light... More useful higher Tc higher Tc higher Hc2 higher Hc2 Easily cooled: He (4.22 K): $5/liter N (77.36 K): 10 ¢ /liter whole milk: 66 ¢ /liter whole milk: 66 ¢ /liter Columbia Pictures The Fifth Element

15. The “but”... Dilemma of Type II superconductors Solutions?

16. Magnetic Force on Current Thumb = current Fingers = magnetic field Palm = magnetic force Lorentz force © John Wiley & Sons, Inc.

17. Superconducting Wires Top View force Magnetic field: out of page D. J. Bishop et al., © Scientific American, 48 (Feb. 1993)

18. Resistance in Superconductors Lorentz force pushes vortices (Flux motion) Dissipation of energy Resistance Increase of temperature Quench!!!

19. Critical Surface Phase Diagram Superconducting state: T < Tc H < Hc J < Jc

20. Dilemma For practical applications, high Tc high Tc high Hc high Hc high Jc high JcDilemma: highest Jc is at Tc=0 and Hc=0

21. Solution Prevent flux from moving Tarp (or pin) flux

22. Flux Pinning Defects in crystalline structure Impurities Impurities Grain boundaries Grain boundaries Artificial pinning centers: Holes (antidots) Holes (antidots) Magnetic dots Magnetic dots Arrays of dots Arrays of dots Single defect in a YBa 2 Cu 3 O 7 film (magneto-optical imaging) http://www.fys.uio.no/super/mo/

23. Energy Surface Potential energy drops discontinuously when the vortex enters the defect zone

24. Experiment Evidence Rectangular array of antidots http://www.fys.kuleuven.ac.be/vsm/nsm/research/lieve2.html

25. Reside in the area between pinning sites Trapped by other vortices (due to mutual repulsion) More mobile Energy Dissipation!! Interstitial Vortices http://www.physics.colostate.edu/groups/fieldgroup/Holes.html

26. Solution Large defects C. Reichhardt et al. © Phys. Rev. B 64, 052503 (2001) A.Bezryadin et al. © Phys. Rev. B 53, 8553 (1996)

27. Solution2 Magnetic pinning centers Ag Dots Ni Dots A. Hoffmann et al., © Phys. Rev. B 61, 6958 (2000)

28. Summary Type II superconductor: Incomplete Meissner effect in vortex state (H c1 < H < H c2 ) Superconducting state: T < T c T < T c H < H c2 H < H c2 J < J c J < J c Flux consists of whirlpools supercurrent called vortex Abrikosov vortex lattice = triangular array Interstitial vortices are mobile  energy lost Effective pinning centers: Larger size Magnetic dots Summary