vortices in classical systems - harvard...

Vortices in Classical Systems

Vortices in Quantum Systems4He-II vortices:

STM of NbSe2 vortices:

G. A. Williams, R. E. Packard, Hess PRL (1989)., ,Phys. Rev. Lett. 33, 280 (1974)

Hall probe image ofYBCO film at T = 40 K:

Pan, Hudson, Davis, RSI (1999)

3.8

s

Checkerboardsin Bi2Sr2CaCu2O8+xvortices:

0G

auss

Bapplied = 1 Gauss20 um

0

Hoffman et al, Science (2002)

Single Vortex Manipulationin Superconducting Nbin Superconducting Nb

Vortices in Nb Film Cooled to 5 3K in 100GVortices in Nb Film Cooled to 5.3K in 100G

Eric StraverJ H ff

Δf=

2.01

Hz

Jenny HoffmanDan Rugar

Kathryn Moler Δ

1μm

Kathryn Moler

Stanford UniversityStanford UniversityFunded by Packard and AFOSR

P t I li i t t ll d t ti

GoalsPart I: eliminate uncontrolled vortex motion

• bigger magnetsgg g• efficient power lines• quieter sensors & circuits

Part II: controlled single vortex manipulationFermiLab

Part II: controlled single-vortex manipulation

• model for soft condensed mattert t l t• vortex entanglement

• vortex ratchet automaton• Luttinger liquidg q

Part I: eliminate uncontrolled vortex motionPart I: eliminate uncontrolled vortex motion

40Motivation: eliminate uncontrolled vortex motion

30 Hc2H* (where vortices move)

Fiel

d (T

)

20YBCO

10

Temperature (K)0 30 60 90 120

0

Larbalestier Nature 414 368 (2001)Larbalestier, Nature 414, 368 (2001)



Fiel

d (T

)

20YBCO

10


0

Larbalestier Nature 414 368 (2001)e-e- e-e-

Larbalestier, Nature 414, 368 (2001)



Fiel

d (T

)

20YBCO

10


0


Apply current I:Cooper pairs flow


without dissipation



Fiel

d (T

)

20YBCO

10

Normal electrons in vortexcore cause dissipation


0core cause dissipationwhen moved


Apply current I:Cooper pairs flow

e- e-e-

e-e-


without dissipation

Vortex Pinning Measurements:Bulk Transport

10° GB, B = 0 Tesla

p

4° GB B = 1 Tesla4 GB, B 1 Tesla

intra-grain (upper scale)grain boundary

Redwing et al, APL 75, 3171 (1999).Hogg et al, APL 78, 1433 (2001).

Vortex Pinning Measurements:Bulk Transport

10° GB, B = 0 Tesla

p

4° GB B = 1 Tesla4 GB, B 1 Tesla

intra-grain (upper scale)grain boundary

Redwing et al, APL 75, 3171 (1999).Hogg et al, APL 78, 1433 (2001).

What’s really going on here?First detectable Voltage = many, many vortices

Examples of Previous Single Vortex DepinningForce Measurements with Transport Current

Cabrera and coworkers 1992

pFinnemore and coworkers

ongoing work (1988-present)

+ several other groups

Examples of Previous Single Vortex DepinningForce Measurements with Transport Current

Cabrera and coworkers 1992

pFinnemore and coworkers

ongoing work (1988-present)

But we’d like a more reliable way to know the force at the vortex location;and to detect vortex motion with finer spatial resolution on order ξ ~ 10-20 nm

+ several other groups

Vortex Pinning Measurements:STM Imaging

reduce field from3 Tesla to 1 5 Tesla

g g

3 Tesla to 1.5 Tesla

estimate pinning f f flforce from flux

density gradient across twin

boundary

( )

bou da y

Maggio-Aprile et al, Nature 390, 487 (1997)

Vortex Pinning Measurements:STM Imaging

reduce field from3 Tesla to 1 5 Tesla

g g

3 Tesla to 1.5 Tesla

estimate pinning f f flforce from flux

density gradient across twin

boundary

( )

bou da y

Maggio-Aprile et al, Nature 390, 487 (1997)

But we’d like a more versatile way yto directly measure pinning forces at arbitrary defects.

Magnetic Force Microscopy

Pros and Cons of MFM

Tip GeometryTip GeometryCon: Imperfectly knownPro: Up to 20 nm spatial resolution

( )

Signal to NoiseCon: Not as good as SQUIDs, Hall probesPro: Good enough to see vorticesForce between tip and sample:

( )BmF ⋅∇= Other signalsCon: See atomic forces tooPro: Simultaneous topographyImage cantilever resonant frequency

f /InvasivenessCon: Tip exerts force on vortexPro: Tip exerts force on vortex

Δf0 ~ dFz/dzbetter signal-to-noise

Pro: Tip exerts force on vortexVertical force gradient imagingHorizontal force manipulation

T: Decreasing Pinning

Vortex Depinning in NbT: Decreasing Pinning

5.2K 5.5K 6.0K 6.5K 7.0K 7.5K

Colormap adjusted separately for each image.

4 μm

Vortex Pinning vs. Height at T = 5.5 Kz=576nm

Az=518nm

Bz=461nm

Cz=403nm

Dz=346nm

Ez=288nm

Fz=230nm

Gz=173nm

H

Δ f=0.63Hz

I x

Δ f=0.73Hz

J

Δ f=0.85Hz

K

Δ f=0.97Hz

0.4L

Δ f=1.22Hz

1.0M

Δ f=1.50Hz

N

Δ f=2.02Hz

3 0O

2μm

Δ f=2.79Hz

P

-1.2

-1.0

-0.8

Δf

(Hz)

Iy

-1.0

-0.8

-0.6J

-0.8

-0.5

-0.2K

-0.4

0.0

L

0.0

0.5

1.0M

0.5

1.0

1.5N

1.0

2.0

3.0O

500nm

P

-1 0 1x (μm)

-1 0 1x (μm)

-1 0 1x (μm)

-1 0 1x (μm)

-1 0 1x (μm)

-1 0 1x (μm)

-1 0 1x (μm)

Important parameters:

vortex motion eventImportant parameters:

kspring = 2.1±0.7 N/mf0 = 71128.28 HzλNb = 90 nm

Model: Monopole Tip – Monopole Vortex

+M

-Mdoffset

zB

superconductor

zλ

vortex

model vortex as monopolemodel vortex as monopoledistance λ beneath surface

--J. Pearl, J. Appl. Phys. 37, 4139 (1966).

( ) 2/5220

20

220

200

0 )()()(

))(2)()(2

2offset

offsetzspr

z

dzyyxx

dzyyxxMfdfk

dzdF

+++−+−

+++−−−−Φ=−=

λ

λπ

Quantifying the Depinning Force at T = 5.5 K

B-1 00

z (nm)100 200 300 400 600 900

-1.63-1.47

-1.251.00

m)

10-4

-1.97-1.93

-1.85-1.72

dF

/dz

(N/m

17G vs. z 4G vs. z

z+λ+dmin

(nm)

10-5

100 200 300 400 600 900

min( )


B-2 77

z (nm)100 200 300 400 600 900

-3.03-3.00

-2.95-2.77

m)

10-4

-2.95-3.00

-3.00-2.97

dF

/dz

(N/m

17G vs. z 4G vs. z17G vs. z+λ+d

i

z+λ+dmin

(nm)

10-5

100 200 300 400 600 900

G s λ dmin

4G vs. z+λ+dmin

min( )

dFz/dz ~ (z+λ+d)-3


B-2 77

z (nm)100 200 300 400 600 900

-3.03-3.00

-2.95-2.77

m)

10-4

z (nm)100 200 300 400 500 600

-2.95-3.00

-3.00-2.97

dF

/dz

(N/m


i 20

30

40100 200 300 400 500 600

z+λ+dmin

(nm)

10-5

100 200 300 400 600 900

G s λ dmin

4G vs. z+λ+dmin

10

20

F z (p

N)

4 Gaussmin( )

dFz/dz ~ (z+λ+d)-3 5

17 Gauss 4 Gauss

z+λ+dmin

(nm)400 500 600 700 800 900


B-2 77

z (nm)100 200 300 400 600 900

-3.03-3.00

-2.95-2.77

m)

10-4

z (nm)100 200 300 400 500 600

-2.95-3.00

-3.00-2.97

dF

/dz

(N/m


i 20

30

40100 200 300 400 500 600

z+λ+dmin

(nm)

10-5

100 200 300 400 600 900

G s λ dmin

4G vs. z+λ+dmin

10

20

F z (p

N)

4 Gaussmin( )

5 f it bound17 Gauss 4 Gauss

dFz/dz ~ (z+λ+d)-4

z+λ+dmin

(nm)400 500 600 700 800 900


B-2 77

z (nm)100 200 300 400 600 900

z (nm)100 200 300 400 500 600-3.03

-3.00

-2.95-2.77

m)

10-4

20

30

40100 200 300 400 500 600

-2.95-3.00

-3.00-2.97

dF

/dz

(N/m


i

10

20

F z (p

N)

4 Gaussz+λ+dmin

(nm)

10-5

100 200 300 400 600 900

G s λ dmin

4G vs. z+λ+dmin

5 kspring

bound f it bound17 Gauss 4 Gaussmin

( )

dFz/dz ~ (z+λ+d)-4

z+λ+dmin

(nm)400 500 600 700 800 900

Depinning Forces in Two Datasets at 5.5 Kz=576nm z=518nm z=461nm z=403nm z=346nm z=288nm z=230nm z=173nm

A B C D E F G H

12

Δ f=0.63Hz Δ f=0.73Hz Δ f=0.85Hz Δ f=0.97Hz Δ f=1.22Hz Δ f=1.50Hz Δ f=2.02Hz

2μm

Δ f=2.79Hz

Flateral,max = 0.38*Fz,max8

10

17 Gauss 4 Gausstic

es

Fdepin ranges from 4 to 12 pN v

ort

ices

2

4

6 4 Gauss

# vo

rt

pat 5.5 K→

Fz (pN)

#

0 10 20 30 40 500

Fz (pN)

Nb Depinning Forces: Quantitative Comparison Breitwisch (PRB 2000): Tc = 8.55 K; t = 400 nm

1000 Breitwisch (PRB 2000): Tc = 8.55 K; t = 400 nm Park (PRL 1992): Tc = 7.35 K; t = 20 nm Allen (PRB 1989): Tc = 8.91 K; t = 20 nm Allen (PRB 1989): Tc = 5.86 K; t = 50 nm

Limits on motion detectionfrom bootstrapping vortex fits:limited by S/N, can be improved

( ) c ; Park (PRL 1992): Tc = 7.35 K; t = 20 nm Allen (PRB 1989): Tc = 8.91 K; t = 20 nm Allen (PRB 1989): Tc = 5.86 K; t = 50 nm Stoddart (SST 1995): Tc = 9.20 K; t = 700 nm

10

100

μm)

Stoddart (SST 1995): Tc = 9.20 K; t = 700 nm

40

60

80

(n

m) 80

60

40

1f p (pN

/μ

120

20

40

( )

r(95

%)

100200300400500600

40

20

0100 200 300 400 500 600

0 01

0.1

tice

s6

8

10z (nm)

17 Gauss 4 Gaussrti

ces

Fdepin ranges from 15

0.01 0.10.01

1 - T/Tc # vo

rt

2

4

6 4 Gauss#

vor

depin gpN/μm to 40 pN/μm →

Fz (pN)

0 10 20 30 40 500

Fz (pN)

Motivation: soft condensed matter physics

surface

Do vortices split or tilt… …and do vortices entangle?

pancake vortex

vortex core

interlayer Josephson vortex

Reichhardt & Hastings, PRL 92, 157002 (2004) Clem, PRB 43, 7837 (1991)

STM: twin boundary in CuO

Motivation: Luttinger liquid physicsSTM: twin boundary in CuOchain plane of YBa2Cu3O7-x

i ti i t i

0.21nm

pin vortices in twinboundary plane

x

y

Lτ100 Å 0 00

x

Lx

Eric Hudson, et al0.00nm

P lk ik PRB 71 014511 (2005)

z

vortex wandering in z-direction 1D particles moving in time Polkovnikov, PRB 71, 014511 (2005) x

yVortices are like

x

y1D bosons inLuttinger liquid!!

Motivation: vortex ratchet computing

• Maximum speed: simulations show 315 MHzReal material parameters for MgB2:

Maximum speed: simulations show 315 MHz, pair-breaking is in the THz range.

• Minimum size: λ ~ 100nm• Power dissipation: 10-17 Joules / single cell flip

Fabricated defects in a superconductor,used to pin vortices

NAND gate:

Hastings, Reichhardt, Reichhardt, PRL 90, 247004 (2003)

Our Procedure for Single Vortex Manipulationusing Magnetic Force Microscopy

surveillance height

using Magnetic Force Microscopy

manipulation height

Vortex Manipulation Results

A B C D E

2μm

Δ f=79mHz Δ f=87mHz Δ f=96mHz Δ f=74mHz Δ f=70mHz

T = 7 7.2 Kh = 288 nm

T = 5.53 Kh = 86.4 nm1μm

Δf=3.21HzΔf = 3.21 Hz

P t I li i t t ll d t ti

GoalsPart I: eliminate uncontrolled vortex motion

• bigger magnetsgg g• efficient power lines• quieter sensors & circuits

Part II: controlled single vortex manipulationFermiLab


• model for soft condensed mattert t l t• vortex entanglement

• vortex ratchet automaton• Luttinger liquidg q

• Vortex studies in YBCO

Future directions• Vortex studies in YBCO

• Better MFM tips: 200nm20μm Deng, APL (2004)

- model as monopolenanotube oncantilever tip

- better AFM spatial resolution,correlate with topography

p

correlate with topography

• STM studies: image with ξ ~ 15 Å resolution,

100 nm

Hawley, Science, 1991

STM studies: image with ξ 15 Å resolution,100× better than λ ~ 150 nm

Spatial Resolution

0.5μm Hall Probe8μm SQUID MFM STM1.1 Gauss0.5 Gauss 100 Gauss 5 Tesla

10μm

550Å

10μm

Future: How to Pin Vortices in YBCO?STM: spiral growth patterns

(2) Chemical inclusions Ni Vacancy(?)ZnSTM: impurities in Bi2Sr2CaCu2O8+x

(3) Oxygen dopants

(1) Screw dislocationsSTM: spiral growth patterns

10Å

Hudson et al, Nature 411, 920 (2001).Pan et al, Nature 403, 746 (2000).Hudson et al, Physica B 329, 1365 (2003).

(3) Oxygen dopants(4) Twin boundaries

100 nm

STM: superconducting gapinhomogeneity in Bi2Sr2CaCu2O8+x

STM: twin boundary in CuOchain plane of YBa2Cu3O7-x

Hawley, Science, 1991

Vortex imagingin Bi2Sr2CaCu2O8+x

0.21nm

100 Å7020 Δ (meV)

Lang et al, Nature 415, 412 (2002). Eric Hudson, unpublished.

100 Å 0.00nm100Å

Hoffman, Science (2002).

ummary

• Manipulate single vortices with nanoscale control

M d di tl th d i i f i Nb• Measured directly the depinning forces in Nb

already applying same technique to YBCO

1μm

Δf=3.21HzΔf = 3.21 Hz

P

12500nm

vortex motion event

8

10

17 Gauss 4 Gausstic

es

2

4

6 4 Gauss#

vort

Eric Straver Nick KoshnickOphir Ausleander

→0 10 20 30 40 50

0

Fz (pN)

Next:• correlate depinning forces with topography (Moler)• STM studies to explore higher fields (Hoffman)

vortices in classical systems - harvard...

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