Vortices in Classical Systems

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Vortices in Classical Systems
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Vortices in Superconductors
wavefunction
Y Yeif
vortices in type II superconductors
supercurrent
Y2
l
x
B
Abrikosov lattice
magnetic vector potential
Phase gradient
magnetic flux quantization if Js 0
Superconducting flux quantum e2e F0 20.7
Gauss-mm2
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Nanoscale Characterization of Single Vortex
Motion
Vancouver, May 12, 2005
Stanford O. Ausleander J.E. Hoffman N.
Koshnick E.W.J. Straver E. Yenilmez
McMaster R.A. Hughes J. Preston
IBM D. Rugar
Stanford University
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Experimental Goal

• quantitative description of dynamics of a single
  vortex
• Aside 1 Two Possible Meanings for Quantum
  Vortex
• a vortex in a superfluid
• a vortex whose macroscopic degrees of freedom can
  be shown to obey quantum mechanics
• Aside 2 Vortices arent this simple

Y2
l
x
B
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Cuprate Superconductors
c-axis
Lawrence-Doniach model
surface
c-axis
pancake vortex
interlayer Josephson vortex
vortex core
John Clem
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Vortex Interactions and Pinning
Images from CUNY web site
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Vortex Matter in High-Tc Superconductors

• 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 Bi2Sr2CaCu2O8
Zeldov co-workers Nature 2001
Nelson and Seung 1989
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Theoretical Proposals for Single-Vortex
Manipulation
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Previous Single-Vortex Manipulation with
Transport Current
Finnemore and coworkers ongoing work
(1988-present)
Cabrera and coworkers 1992
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What a vortex looks like to a surface magnetic
probe
London model of the field from a vortex above a
bulk superconductor
where ? ?ab, r (x, y), k (kx , ky)
For r2z2 ?2, a vortex looks like a monopole
one penetration depth (?ab) below the surface
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Single-Vortex Manipulation with a micro-SQUID
Create and observe vortex-antivortex pair
shielded leads
Current applied to field coil pulls/pushes vortex
with 0.5pN
Gardner et al. 2001, 2002
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Magnetic Sensors for sub-Flux-Quantum
Imagingrepresentative 4 Kelvin data from the
literature and from the Moler Lab
F020.7Gm2
-1
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MFM
SQUIDs
Hall Probes
-2
10
)
Hess APL 1992
1/2
/Hz
Hasselbach RSI 2001 (0.5 K)
0
2004
F
1000mB/Hz1/2
Bending APL 2001
2003
Chen Phys C 2002
2004
Flux Sensitivity(
2002
Bending APL 1996
10mB/Hz1/2
Moler RSI 2001
Kirtley APL 1995
2003
2004
m
Sensor Size (
m)
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Previous Single-Vortex Manipulation with
Magnetic Force Microscopy
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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 gt
• manipulation capability
• Simultaneous topography possible

Force between tip and sample
Image cantilever resonant frequency Df0 dFz/dz
better signal-to-noise
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Vortices in Nb film field cooled to 5.3K in 100G
external field
300 nm thick Onset Tc 8.9K Midpoint Tc
8.6K DTc 0.57K
1mm
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• More slides deleted

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Next generationImproved spatial resolution and
interpretabilitywith metal-coated carbon
nanotube tips
cantilever with carbon nanotube tip
typical metal-coated carbon nanotube tips
1 mm
conventional tip image nanotube tip image
Z. Deng et al., APL, Dec. 2004.
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• More slides deleted

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Students and Postdocs
Eric Straver
Nick Koshnick Ophir Ausleander
Jenny Hoffman
Not shown summer student Andrew Whitehead
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Mesoscopic magnetism toolbox
Magnetic Force Microscopy
SQUID Magnetometry Susceptometry
Hall Probe Microscopy

• Measures F or ?F
• Sensitivity difficult to quote
• Spatial resolution lt30 nm goal 10nm
• Broad field and temp range

• Measures
• Sensitivity 1 m?0/Hz1/2
• (0.3 mG/Hz1/2)
• Spatial resolution 4 mm
• (goal 0.5 mm)
• Blt100 G and Tlt10 K

• Measures
• Sensitivity 1-50 mG/Hz1/2
• (flux HF 10 m?0/Hz1/2)
• (flux DC 1 m?0/Hz1/2)
• Spatial resolution 0.5 mm
• (goal 30 nm)
• Broad field and temp range