1. Vortices in Classical Systems

2. Vortices in Superconductors  = B  da = n hc e*  e i  wavefunction Superconducting flux quantum e*=2e   = 20.7 Gauss-  m 2 supercurrent magnetic vector potential Phase gradient magnetic flux quantization if J s = 0 B    vortices in type II superconductors Abrikosov lattice

3. Nanoscale Characterization of Single Vortex Motion Stanford O. Ausleander J.E. Hoffman N. Koshnick E.W.J. Straver E. Yenilmez McMaster R.A. Hughes J. Preston Vancouver, May 12, 2005 Stanford University IBM D. Rugar Vortices in Nb Film Cooled to 5.3K in 100G  f=2.01Hz 1m1m

4. Experimental Goal quantitative description of dynamics of a single vortex Aside 1: Two Possible Meanings for “Quantum Vortex” 1.a vortex in a superfluid 2.a vortex whose macroscopic degrees of freedom can be shown to obey quantum mechanics Aside 2: Vortices aren’t this simple: B   

5. Cuprate Superconductors conducting CuO planes stuff complex structure surface pancake vortex c-axis vortex core interlayer Josephson vortex John Clem Lawrence-Doniach model c-axis

6. Vortex Interactions and Pinning Images from CUNY web site

7. 10 1 10 2 10 3 10 4 10 5 020406080100 first-order transition second magnetization peak H c2 T [ K ] B [ G ] depinning disordered liquid / gas quasi-ordered-lattice (Bragg glass) Vortex Matter in High-Tc Superconductors Zeldov & co-workers Nature 2001 layered structure, disorder, and high-T combine to give a rich phase diagram model system for phase transitions determines the critical current phase diagram in Bi 2 Sr 2 CaCu 2 O 8 Nelson and Seung 1989

8. Theoretical Proposals for Single-Vortex Manipulation

9. Previous Single-Vortex Manipulation with Transport Current Finnemore and coworkers ongoing work (1988-present) Cabrera and coworkers 1992

10. What a vortex looks like to a surface magnetic probe: z ab SC r c ab plane B For r 2 +z 2 » 2, a vortex looks like a monopole one penetration depth ( ab ) below the surface where = ab, r = (x, y), k = (k x, k y ) London model of the field from a vortex above a bulk superconductor:

11. Single-Vortex Manipulation with a micro-SQUID shielded leads Gardner et al. 2001, 2002 Current applied to field coil pulls/pushes vortex with ~0.5pN Create and observe vortex-antivortex pair:

12. Magnetic Sensors for sub-Flux-Quantum Imaging representative 4 Kelvin data from the literature and from the Moler Lab 10 -2 10 Moler RSI 2001 Kirtley APL 1995 Hasselbach RSI 2001 (0.5 K) Chen Phys C 2002 Bending APL 1996 Bending APL 2001 2002 Hess APL 1992 Sensor Size (  m) Flux Sensitivity(  0 /Hz 1/2 ) SQUIDs Hall Probes MFM 2003  0 =20.7G  2 2004 1000  B /Hz 1/2 10  B /Hz 1/2

13. Previous Single-Vortex Manipulation with Magnetic Force Microscopy

14. Magnetic Force Microscopy Disadvantages of MFM: Imperfect knowledge of tip geometry Signal-to-noise Advantages of MFM: Signal-to-noise can be good enough Good spatial resolution Tip exerts force on vortex => manipulation capability Simultaneous topography possible Image cantilever resonant frequency  f 0 = dF z /dz better signal-to-noise Force between tip and sample:

15. Vortices in Nb film field cooled to 5.3K in 100G external field 1m1m 300 nm thick Onset Tc = 8.9K Midpoint Tc = 8.6K  Tc = 0.57K

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17. Next generation: Improved spatial resolution and interpretability with metal-coated carbon nanotube tips 1 m1 m typical metal-coated carbon nanotube tips Z. Deng et al., APL, Dec. 2004. conventional tip image nanotube tip image cantilever with carbon nanotube tip 100 nm

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19. Students and Postdocs Eric Straver Jenny Hoffman Nick Koshnick Ophir Ausleander Not shown: summer student Andrew Whitehead

20. Mesoscopic magnetism toolbox Magnetic Force Microscopy SQUID Magnetometry & Susceptometry Hall Probe Microscopy Measures F or  F Sensitivity: difficult to quote Spatial resolution: <30 nm goal = 10nm Broad field and temp range Measures Sensitivity: 1  0 /Hz 1/2 (~0.3  G/Hz 1/2 ) Spatial resolution: 4  m (goal = 0.5  m) B<100 G and T<10 K Measures Sensitivity: ~1-50 mG/Hz 1/2 (flux HF: 10  0 /Hz 1/2 ) (flux DC: 1 m  0 /Hz 1/2 ) Spatial resolution: 0.5  m ( goal = 30 nm) Broad field and temp range V I cantilever magnetic tip