Transcript Condensed Matter and Materials Physics (Experiment)

Vortices in Classical Systems
Vortices in Superconductors
wavefunction
Y = |Y|eif
vortices in type II superconductors
supercurrent
|Y|2
*2

e *
e
2 
*
Js =
     *  A
2im*
mc
*


B
*

e*  
2 e 
 f  A 
Js = 
* 
m 
c 
Phase
gradient
x
magnetic
vector potential
l
Abrikosov lattice
magnetic flux quantization if Js = 0
F = Bda = n hc
e*
Superconducting flux quantum e*=2e
F0 = 20.7 Gauss-mm2
Nanoscale Characterization of
Single Vortex Motion
Vancouver, May 12, 2005
Stanford
McMaster
O. Ausleander
J.E. Hoffman
N. Koshnick
E.W.J. Straver
E. Yenilmez
R.A. Hughes
J. Preston
Vortices in Nb Film Cooled to 5.3K in 100G
Df=2.01Hz
IBM
D. Rugar
1mm
Stanford University
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:
|Y|2
B
x
l
Cuprate Superconductors
conducting CuO planes
complex structure
stuff
c-axis
Lawrence-Doniach model
surface
c-axis
vortex core
pancake
vortex
John Clem
interlayer
Josephson
vortex
Vortex Interactions and Pinning
Images from CUNY web site
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
10
5
Hc2
10
4
liquid / gas
disordered
3
B [G]
10
10
Zeldov & co-workers
Nature 2001
10
2
second
magnetization
peak
1
0
Nelson and Seung 1989
quasi-ordered-lattice
(Bragg glass)
20
40
60
T [K]
80
100
Theoretical Proposals for Single-Vortex Manipulation
Previous Single-Vortex Manipulation with Transport Current
Finnemore and coworkers
ongoing work (1988-present)
Cabrera and coworkers 1992
What a vortex looks like to a surface magnetic probe:
London model of the field from a vortex
above a bulk superconductor:
F
e z
2
ik r
Bz (r, z ) =
d ke
2 
2l
k 2  l2  k k 2  l2
where l = lab, r = (x, y), k = (kx , ky)
For r2+z2 » l2, a vortex looks like a
monopole one penetration depth (lab) below
the surface
z  l ab
F
Bz (r , z ) =
2 r 2  z  l 2
ab

z
B
r

c
SC
32
ab plane
lab
Single-Vortex Manipulation with a micro-SQUID
Create and observe vortex-antivortex pair:
Current applied to field coil pulls/pushes vortex with ~0.5pNshielded
leads
Gardner et al. 2001, 2002
F0=20.7Gm2
Magnetic Sensors for sub-Flux-Quantum Imaging
representative 4 Kelvin data from the literature and from the Moler Lab
10
-1
SQUIDs
Hall Probes
MFM
Flux Sensitivity(F
1/2
/Hz
)
0
10
-2
Hess APL 1992
10
-3
Hasselbach RSI 2001 (0.5 K)
2004
10
10
10
-4
2003
-5
Bending APL 2001
Chen Phys C 2002
2004
2002
Bending APL 1996
Moler RSI 2001
Kirtley APL 1995
2003
2004
-6
-7
10 -2
10
10
-1
10
0
Sensor Size (mm)
10
1
10
2
Previous Single-Vortex Manipulation
with Magnetic Force Microscopy
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
Force between tip and sample:
F = m  B
Image cantilever resonant frequency
Df0 = dFz/dz
better signal-to-noise
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
More slides deleted
Next generation:
Improved spatial resolution and interpretability
with metal-coated carbon nanotube tips
cantilever with carbon nanotube tip
typical metal-coated carbon nanotube tips
100 nm
1 mm
conventional tip image nanotube tip image
Z. Deng et al., APL, Dec. 2004.
More slides deleted
Students and Postdocs
Eric Straver
Nick Koshnick
Ophir Ausleander
Jenny Hoffman
Not shown: summer student Andrew Whitehead
Mesoscopic magnetism toolbox
Magnetic Force
Microscopy
SQUID Magnetometry
& Susceptometry
Hall Probe
Microscopy
I
cantilever
V
magnetic tip
F=
 
B  da
• Measures F or F
• Measures
• Sensitivity: difficult to quote
• Sensitivity: 1 mF0/Hz1/2
(~0.3 mG/Hz1/2)
• Sensitivity: ~1-50 mG/Hz1/2
(flux HF: 10 mF0/Hz1/2)
(flux DC: 1 mF0/Hz1/2)
• Spatial resolution: 4 mm
(goal = 0.5 mm)
• Spatial resolution: 0.5 mm
(goal = 30 nm)
• B<100 G and T<10 K
• Broad field and temp range
• Spatial resolution: <30 nm
goal = 10nm
loop
• Measures Bz
• Broad field and temp range