Page 1
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
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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:
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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
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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
Page 5
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
BraggBraggGlassGlass
LiquidLiquid
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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)
BraggBraggGlassGlass
LiquidLiquid
Glass Glass
????
1 st order
Equilibrium
HDCz
HACx
FOT 1:20
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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
Second-order glass transitionSecond-order glass transition
Glass liquid
Bragg Glass
GlassGlass LiquidLiquidEEPinPin EETT
EEPinPin++EEElEl
EETT
BraggBraggGlassGlass
EEPinPin++EEElEl
Lattice Lattice ?!!??!!?
T (K)H. Beidenkopf et al., Phys. Rev. Lett. 95, 257004 (2005)
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AmorphousAmorphous GlassGlass
EPin < ET < EEl
BraggBraggGlassGlass
AbrikosovAbrikosovLatticeLattice
Phase diagram / LindemannPhase diagram / Lindemann
LiquidLiquid((GasGas))
??ET ~ EElET ~ EElEPin ~ EElEPin ~ EEl
EPin ~ ET EPin ~ ET
2nd o
rder
1 st order
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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
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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
Second-order glass transitionSecond-order glass transition
Critical dynamics at the glass transitionCritical dynamics at the glass transition
Outline 0:30
NanoSQUID on a tipNanoSQUID on a tip
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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
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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
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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
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f= 791 Hz
B(2
) (a.u
.)
Edge ResistanceEdge Resistance
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 (
)
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)
Page 15
f= 791 Hz
B(1
) (a.u
.)
0bulk
edge
Bulk Resistance at TBulk Resistance at Tgg
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
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)
Page 16
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))
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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)
Page 18
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
Page 19
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:
Page 20
Superconducting Quantum Interference Device (SQUID)
0
0
πcos2)( II s
SQUID
Superconducting loop
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:
Superconducting current:
Flux quantization:
SQUID critical current:
)sin(0 II s
Josephson critical current:
Φ=BA
Page 21
Superconducting Quantum Interference Device (SQUID)
SQUID
Superconducting loop
Josephson junctions
I
)()()( rrr ie
AJ
ce
me 22
GL order parameter:
Superconducting current:
Koshnick et al., Appl. Phys. Lett. 93, 243101 (2008)
Φ=BA
Page 22
100 400 nm
SQUID-on-a-tip fabrication
1 mm
Page 23
100 400 nm
SQUID-on-a-tip fabrication
Aluminum
Page 24
SQUID-on-a-tip fabrication
Aluminum
Page 25
SQUID-on-a-tip fabrication
Aluminum
Page 26
SQUID-on-a-tip fabrication
Aluminum
SQUID loop
Al leadAl lead
weak links
Page 27
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)
Page 28
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
Al lead Al leadquartz
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)
A. Finkler et al., Nano Letters (2010)
Page 29
SOT high fields 0:50
SQUID on a tipQuantum interference
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
Spin sensitivity = 65 B/Hz1/2
Field sensitivity = 10-7 T/Hz1/2
200 nm
Al lead Al leadquartz
SQUID loop
-50
100
Operational field > 0.5 T
A. Finkler et al., Nano Letters (2010)
Page 30
SOT smallest 0:30
SQUID on a tipQuantum interference
patternsSQUID current
200 nm
Al lead Al leadquartz
SQUID loop
Period = 190 mT Loop diameter = 115 nm
Page 31
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
Spin sensitivity = 65 B/Hz1/2
Field sensitivity = 10-7 T/Hz1/2
200 nm
Al lead Al leadquartz
SQUID loop
Page 32
SQUID on tip I-V characteristics
Rb
Rs
Vin
5 kSQUIDon tip
ISOTSSAA
T = 300 mK
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SQUID on tip noise
Sn = 1.810-6 0/Hz1/2
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SEM tuning fork 0:40
SQUID on tip glued to tuning fork
100 µm
Quartz tuning fork
SQUID on tip
Page 35
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
Page 36
SPM moving VL 0:50
Scanning nano-SQUID microscope
Magnetic field of a vortex lattice
Page 37
Orbital moment of a single electron 25
B
Quantum dot on a carbon nanotube
Scanning nano-SQUID microscope
Spin sensitivity65 B/Hz1/2
F. Kuemmeth, S. Ilani, D. C. Ralph, and P.L. McEuen, Nature 452, 448 (2008).
Page 38
SPM CNT Wigner
Wigner crystal in CNT V.V. Deshpande and M. Bockrath,
Nature Physics 4, 314 (2008).
Scanning nano-SQUID microscope
Page 39
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