Title 0:40

Vortex matter dynamics and

thermodynamics

and nanoSQUID on a tip

Vortex matter dynamics and

thermodynamics

and nanoSQUID on a tipH. Beidenkopf, N. Avraham,

Y. Myasoedov, A. Finkler, Y. Segev, M. Rappaport, E. Zeldov

Weizmann Institute

T. Tamegai Tokyo University

T. Sasagawa Tokyo Institute of Technology

E. H. Brandt Max Planck Stuttgart

G. P. Mikitik Verkin Institute Kharkov

B. Rosenstein Chiao Tung University

M. Konczykowski, C. J . van der Beek Ecole Polytechnique

M. E. Huber University of Colorado

J . Martin, A. Yacoby Harvard University

Title 0:40

Disorder-induced fluctuations

Pinning potential

BiBi22SrSr22CaCuCaCu22OO8+8+

Thermal fluctuations

Thermal energy

Lattice constant

Elastic energy

Intro / Vortex MatterIntro / Vortex Matter

Energy scales:Energy scales:

H

T

J & EM coupling

Interlayer separation

Drive

FiniteTemperatur

eElasticity

QuenchedDisorder

H

BiBi22SrSr22CaCaCuCu22OO8+8+

CuO2

CuO2

CuO2

Skin depth

Driving potential

Length scales:Length scales:

Vortex thermodynamicsVortex thermodynamics

Vortex dynamicsVortex dynamics

IntroductionIntroductionThe vortex systemThe vortex system

OutlineOutline

First-order melting transitionFirst-order melting transition

R(T) – Transport vs. self-induced-fieldR(T) – Transport vs. self-induced-field

Equilibrium at low temperatures with vortex Equilibrium at low temperatures with vortex shakingshaking

Second-order glass transitionSecond-order glass transition

Critical dynamics at the glass transitionCritical dynamics at the glass transition

Outline 1:00

NanoSQUID on tipNanoSQUID on tip

1 st order

-5

0

0 100

80 KNonEquilibrium

??Equilibrium

B

Method / Method / Local magnetization in BSCCOLocal magnetization in BSCCO

-20

-10B

– H

(G

)

350 410H (Oe)

32 K

BraggBraggGlassGlass

LiquidLiquid

H (Oe)

H

B = V

/ R H

I

B = V

/ R H

I

150m

Micro-Hall sensor array

I

V

10x10m2

10x10m2

EEPinPin

EETT

EEElElEEPinPin++EEElEl

Local magnetiz. 2:00

Jz

y

x X ZH

H

Method / ‘Shaking’Method / ‘Shaking’A.E. Koshelev, Phys. Rev. Lett. 83, 187 (1999)G.P. Mikitik and E.H. Brandt, Phys. Rev. B 69, 134521

(2004)

HDCz

HACx

1 st orderNonEquilibrium

??Equilibrium


LiquidLiquid

dB

/ d

H

N. Avraham et al., Nature 411, 451 (2001)H. Beidenkopf et al., Phys. Rev. Lett. 95, 257004 (2005)

-5

First-order melting First-order melting

NonEquilibrium

??

Bno shake

shake-20

-10B

– H

(G

)

350 410H (Oe)

32 K0

0 100

80 K

B

H (Oe)


LiquidLiquid

Glass Glass

????

1 st order

Equilibrium

HDCz

HACx

FOT 1:20

T (K)

B (

G)

100

200

300

400

500

600

30 35 40 45 50

350 Oe

B –

T (G

)

420 Oe

380 Oe

30 35 40T (K)

dB/d

T (

mG

/K)

40

Tg

30 35 40T (K)

dB/d

T (

mG

/K)

40

Tg

35 36 37 38T (K)

dB

/dT

(m

G/K

)

40

Tg

35 36 37 38T (K)

dB

/dT

(m

G/K

)

40

Tg


Glass liquid

Bragg Glass

GlassGlass LiquidLiquidEEPinPin EETT

EEPinPin++EEElEl

EETT


EEPinPin++EEElEl

Lattice Lattice ?!!??!!?

T (K)H. Beidenkopf et al., Phys. Rev. Lett. 95, 257004 (2005)

AmorphousAmorphous GlassGlass

EPin < ET < EEl


AbrikosovAbrikosovLatticeLattice

Phase diagram / LindemannPhase diagram / Lindemann

LiquidLiquid((GasGas))

??ET ~ EElET ~ EElEPin ~ EElEPin ~ EEl

EPin ~ ET EPin ~ ET

2nd o

rder

1 st order

Elastic modelElastic modelT. Giamarchi, P.L. Doussal, Phys. Rev. Lett. 72, 1530 (1994)

T. Nattermann, Phys. Rev. Lett. 64, 2454 (1990)

2D LLL GL2D LLL GLD. Li, B. Rosenstein, Phys. Rev. Lett. 90, 167004 (2003) T

H

Bragg Glass

PinnedLiquid Liquid

Phase diagram / Phase diagram / TheoryTheory

2nd o

rder

1 st order

t=T/Tc

H (

Oe)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

100

200

300

400

500

600

700

800

900

1000

1st order m

elting

Solid

Liquid

2nd order R

SB

RSBSolid

RSLiquid

RSSolid

RSBLiquid

TTc c , HHc2 c2 , GiGi,

(r)(r’)~02

RR(r-

r’)

TTc c , HHc2 c2 , GiGi,

(r)(r’)~02

RR(r-

r’)

vs. Experimentvs. Experiment

OutlineOutline

Vortex thermodynamicsVortex thermodynamics

Vortex dynamicsVortex dynamics

IntroductionIntroductionThe vortex systemThe vortex system

First-order melting transitionFirst-order melting transition

R(T) – Transport vs Self-induced-fieldR(T) – Transport vs Self-induced-field

Equilibrium at low temperaturesEquilibrium at low temperatures


Critical dynamics at the glass transitionCritical dynamics at the glass transition

Outline 0:30

NanoSQUID on a tipNanoSQUID on a tip

H

Bragg Glass

PinnedLiquid

Liquid

T

Dynamics / Dynamics / Theory & ExperimentTheory & Experiment

Critical scaling:Critical scaling: ~(T-T~(T-Tgg)), , ~6~6

T

T

H

1st order

Solid

2nd orderBragg

Glass

Liquid

Lattice

Glass

Non Glassy (Ohmic):Non Glassy (Ohmic): ~e~e-U/T-U/T

T. Giamarchi, P. Le Doussal, Phys. Rev. B 55, 6577 (1997)

D.T. Fuchs et al., Phys. Rev. Lett. 81, 3944 (1998)

D.S. Fisher, M.P.A. Fisher, D.A. Huse, Phys. Rev. B 43, 130 (1991)

R.H. Koch et al., Phys. Rev. Lett. 63, 1511 (1989)

H. Safar et al., Phys. Rev. Lett. 68, 2672 (1992)

M. Luo, X. Hu, V. Vinokur, arXiv:0902:0858v1

Thermally activated, Ohmic:Thermally activated, Ohmic: ~e~e-U/T-U/T

Glassy (nonOhmic):Glassy (nonOhmic): ~e~e-U(j)/T-U(j)/T, U(j)~j, U(j)~j-0.5-0.5

oror

c-axis

TransportTransport

Transport noise

100

10-1

10-2

10-3

10-4

10-5

10-6

10-7

10-8

10-9

10-10

T (K)

R (

)B

(ab

u)

30 40 50 60 70 80 90 100

Gla

ss t

ransi

tion

350 Oe

Transport noise levelTransport noise levelPoor c-axis current penetrationPoor c-axis current penetration

R. Busch et al., Phys. Rev. Lett. 69, 522 (1992)B. Khaykovich et al., Phys. Rev. B 61, R9261 (2000)

V

Self Induced FieldSelf Induced Field

c-axis Transport noise

100

10-1

10-2

10-3

10-4

10-5

10-6

10-7

10-8

10-9

10-10

T (K)

R (

)

30 40 50 60 70 80 90 100

Gla

ss t

ransi

tion

350 Oe

D.T. Fuchs et al., Nature 391, 373 (1998)

Transport noise levelTransport noise levelPoor c-axis current penetrationPoor c-axis current penetrationEdges shunt bulkEdges shunt bulk

B(1

)

xj (1

)

bulk

edgebulk

B(1

)

x

j (1)

edge

V

Self induced B 2:00

f= 791 Hz

B(2

) (a.u

.)

Edge ResistanceEdge Resistance


100

10-1

10-2

10-3

10-4

10-5

10-6

10-7

10-8

10-9

10-10

T (K)

R (

)

Le=Re

ThermallyActivated

Re(T)

30 40 50 60 70 80 90 100

Gla

ss t

ransi

tion

350 Oe

H. Beidenkopf et al., PRB 80, 224526 (2009)

Inductive edgesInductive edges

Transport noise levelTransport noise levelPoor c-axis current penetrationPoor c-axis current penetrationEdges shunt bulkEdges shunt bulk

Le=490 pH

217 Hz37 Hz7 Hz1 Hz10-1-103 Hz

V

(( ))

E.H. Brandt et al., PRB 74, 094506 (2006)

f= 791 Hz

B(1

) (a.u

.)

0bulk

edge

Bulk Resistance at TBulk Resistance at Tgg


100

10-1

10-2

10-3

10-4

10-5

10-6

10-7

10-8

10-9

10-10

T (K)

R (

)

30 40 50 60 70 80 90 100

Gla

ss t

ransi

tion

ThermallyActivated

Rb(T)

350 Oe

Transport noise levelTransport noise levelPoor c-axis current penetrationPoor c-axis current penetration

Inductive edgesInductive edgesEdges shunt bulkEdges shunt bulk

Le=490 pH

Lb=140 pH

217 Hz37 Hz7 Hz1 Hz10-1-103 Hz

Lb=Rb

and bulkand bulk

B(1

)

x

j (1)

screened

27K

Critical: R~(T-TCritical: R~(T-Tgg))

V

(( ))

ThermallyActivated

Re(T)

H. Beidenkopf et al., PRB 80, 224526 (2009)

E.H. Brandt et al., PRB 74, 094506 (2006)

V

Transport noise

100

10-1

10-2

10-3

10-4

10-5

10-6

10-7

10-8

10-9

10-10

T (K)

R,

2f

Lb (

)

30 40 50 60 70 80 90 100

350

Oe

300

Oe T (K)

30 40 50

300

350

H (O

e)

LatticeLattice

GlassGlass

Gla

ss t

ransi

tion T

g

LiquidLiquid

BrGBrG

OhmicOhmic

(( ))Bulk Resistance at TBulk Resistance at Tgg

ThermallyActivated

Rb(T)

ThermallyActivated

Re(T)

Non-Ohmic!Non-Ohmic!

Critical: R~(T-TCritical: R~(T-Tgg))

Vortex Matter SummaryVortex Matter Summary

On approaching the glass transition the bulk resistance plunges critically below the thermally activated behavior.

New method for measurement of bulk and edge resistance.

The 1st-order melting and 2nd-order glass transition divide the vortex phase diagram into four thermodynamic phases.

The bulk resistance is Ohmic in the liquid phase but non-Ohmic in the lattice phase.

Liquid

LatticeBrG

Gla

ss

bulk

edge

The inductance of the edge and the bulk dominate the flow at low temperatures.

H. Beidenkopf et al., PRL 95, 257004 (2005); PRL 98, 167004 (2007); PRB 80, 224526 (2009)

SOT title 1:00

SQUID on a tipImaging currents and moments on

nanoscale

SQUID on a tipImaging currents and moments on

nanoscale

Weizmann Institute of ScienceRehovot, Israel

Weizmann Institute of ScienceRehovot, Israel

M.E. HuberM.E. HuberUniversity of Colorado Denver, CO

University of Colorado Denver, CO

J. Martin and A. YacobyJ. Martin and A. YacobyHarvard UniversityCambridge, MA

Harvard UniversityCambridge, MA

A. Finkler, Y. Segev, Y. Myasoedov, M.L. Rappaport and E. Zeldov

A. Finkler, Y. Segev, Y. Myasoedov, M.L. Rappaport and E. Zeldov

Superconducting Quantum Interference Device (SQUID)

0

0

πcos2)( II s

SQUID

Superconducting loop

Josephson junctions

I

Φ=BA

)()()( rrr ie

AJ

ce

me 22

20 μm/G7.20

2

ehcGL order parameter:

Superconducting current:

Flux quantization:

SQUID critical current:

)sin(0 II s

Josephson critical current:


0

0

πcos2)( II s

SQUID


Josephson junctions

-4 -2 0 2 40

1

2

/0

I /

I 0

I

)()()( rrr ie

AJ

ce

me 22

20 μm/G7.20

2

ehcGL order parameter:


Flux quantization:

SQUID critical current:

)sin(0 II s

Josephson critical current:

Φ=BA


SQUID


Josephson junctions

I

)()()( rrr ie

AJ

ce

me 22

GL order parameter:


Koshnick et al., Appl. Phys. Lett. 93, 243101 (2008)

Φ=BA

100 400 nm

SQUID-on-a-tip fabrication

1 mm

100 400 nm


Aluminum


Aluminum


Aluminum

SQUID loop

Al leadAl lead

weak links

SOT SEM 1:30

SQUID on a tip

200 µm

Al lead

Al lead

bare quartz

Pulled quartz tube

200 nm

Al lead Al leadquartz

SQUID loop

A. Finkler et al., Nano Letters (2010)

SOT interference 2:20

SQUID on a tipQuantum interference

patterns

B [ T ]

V [

mV

]

0-0.05 0.1-0.1 0.05

SQUID current

100

120

80

60200 nm


SQUID loop

Period = 60.8 mT Loop diameter = 208 nmFlux sensitivity = 2×10-6 0/Hz1/2

Spin sensitivity = 65 B/Hz1/2

Field sensitivity = 10-7 T/Hz1/2 I0 = 1.6 A = 2LI0/0 = 0.85

Lk = 550 pH (Lg = 0.3 pH)


SOT high fields 0:50


patterns

B [ T ]

V [

mV

]

0-0.2 0.4-0.4 0.2

SQUID current

50

0

-100

Flux sensitivity = 2×10-6 0/Hz1/2


Field sensitivity = 10-7 T/Hz1/2

200 nm


SQUID loop

-50

100

Operational field > 0.5 T


SOT smallest 0:30


patternsSQUID current

200 nm


SQUID loop

Period = 190 mT Loop diameter = 115 nm

SOT VL B calcul 1:20

SQUID on a tip

X [nm]

Y [n

m]

Calculated vortex lattice field B(x,y)

Z=15 nm above surfaceNbSe2, =132 nm, B = 750 G

Field modulation decays as exp(-2Z/a0)

Factor of 10 every 65 nm in height

[G]

Flux sensitivity = 2×10-6 0/Hz1/2


Field sensitivity = 10-7 T/Hz1/2

200 nm


SQUID loop

SQUID on tip I-V characteristics

Rb

Rs

Vin

5 kSQUIDon tip

ISOTSSAA

T = 300 mK

SQUID on tip noise

Sn = 1.810-6 0/Hz1/2

SEM tuning fork 0:40

SQUID on tip glued to tuning fork

100 µm

Quartz tuning fork

SQUID on tip

Topographic and magnetic imaging with SQUID on tip

Applied current in meander 2 mA

Magnetic field at various heights

Measurement of topography

CalculatedMeasured

SQUID on tip×100

SPM moving VL 0:50

Scanning nano-SQUID microscope

Magnetic field of a vortex lattice

Orbital moment of a single electron 25

B

Quantum dot on a carbon nanotube


Spin sensitivity65 B/Hz1/2

F. Kuemmeth, S. Ilani, D. C. Ralph, and P.L. McEuen, Nature 452, 448 (2008).

SPM CNT Wigner

Wigner crystal in CNT V.V. Deshpande and M. Bockrath,

Nature Physics 4, 314 (2008).


Magnetic field and spin sensitivity

C. Degen, Nature Nanotech. 3, 643 (2008)

Field sensitivity / Hz1/2

Mag

netic

mom

ent se

nsiti

vity

/ H

z1/

2

Senso

r-sa

mple

separa

tion

Diamond NVsensor

Scanning-SQUIDs

SQUIDon tip

Title 0:40

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