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

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

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)

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."

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

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

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)

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

Nobel Prize Winning

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, (2002)

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

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

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

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

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

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

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

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

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

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

Solution Prevent flux from moving Tarp (or pin) flux

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)

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

Experiment Evidence Rectangular array of antidots

Reside in the area between pinning sites Trapped by other vortices (due to mutual repulsion) More mobile Energy Dissipation!! Interstitial Vortices

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

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

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