Transcript SQUID on tip - Weizmann Institute of Science

Vortex matter dynamics and thermodynamics
and nanoSQUID on a tip
H. Beidenkopf, N. Avraham,
Y. Myasoedov, A. Finkler, Y. Segev,
M. Rappaport, E. Zeldov
T. Tamegai
Weizmann Institute
Tokyo University
T. Sasagawa
Tokyo Institute of Technology
E. H. Brandt
Max Planck Stuttgart
G. P. Mikitik
Verkin Institute Kharkov
B. Rosenstein
M. Konczykowski, C. J. van der Beek
M. E. Huber
J. Martin, A. Yacoby
Chiao Tung University
Ecole Polytechnique
University of Colorado
Harvard University
Intro / Vortex Matter
Energy scales:
Finite
Temperature
Quenched
Disorder
Elasticity
J & EM coupling
Elastic energy
Pinning potential
Bi2Sr2CaCu2O8+d
CuO2
CuO2
Drive
Thermal energy
Driving potential
CuO2
Length scales:
Interlayer separation
Lattice constant
Disorder-induced
fluctuations
Thermal fluctuations
Skin depth
H
T H
Outline
Introduction
The vortex system
Vortex thermodynamics
Equilibrium at low temperatures with vortex shaking
First-order melting transition
Second-order glass transition
Vortex dynamics
R(T) – Transport vs. self-induced-field
Critical dynamics at the glass transition
NanoSQUID on tip
Method / Local magnetization in BSCCO
Micro-Hall sensor array
V
?
Liquid
Bragg
Glass
Non
Equilibrium
EPin+EEl
150mm
H
ET
-10
10x10
mm2
I
32 K
B – H (G)
EPin
Equilibrium
80 K
0
DB
-20
-5
350
H (Oe)
410
0
100
H (Oe)
Method / ‘Shaking’
A.E. Koshelev, Phys. Rev. Lett. 83, 187 (1999)
G.P. Mikitik and E.H. Brandt, Phys. Rev. B 69, 134521 (2004)
z
HDC
Equilibrium
?
x
HAC
Liquid
Bragg
Glass
Non
Equilibrium
J
z
y
x
H
X
Z
First-order melting
?
z
HDC
Glass
Equilibrium
Non
Equilibrium
dB / dH
Bragg
Glass
Liquid
-10
32 K
B – H (G)
?
x
HAC
shake
-20
N. Avraham et al., Nature 411, 451 (2001)
H. Beidenkopf et al., Phys. Rev. Lett. 95, 257004 (2005)
80 K
0
DB
350
DB
no shake -5
H (Oe)
410
0
100
H (Oe)
Tg
40
dB/dT (mG/K)
Second-order glass transition
30
600
Liquid
EPin
ET
40
ET
Glass
Bragg Lattice
Glass ?!!?
200
35
40
T (K)
45
50
Tg
40
30
liquid
350 Oe
dB/dT (mG/K)
EPin+EEl
300
Bragg Glass
35
H. Beidenkopf et al., Phys. Rev. Lett. 95, 257004 (2005)
36
37
T (K)
38
T (K)
B –aT (G)
380 Oe
400
100
T (K)
420 Oe
B (G)
500
Glass
35
Phase diagram / Lindemann
EPin ~ ET
Amorphous Liquid
Glass (Gas)
EPin ~ EEl
ET ~ EEl
Bragg
Glass
Abrikosov
Lattice EPin < ET < EEl
Phase diagram / Theory vs. Experiment
1000
900
Pinned
RSB
Liquid
700 Liquid
RS
Liquid
Liquid
800
H (Oe)
H
600
500
400
Tc , Hc2 , Gi,
a(r)a(r’)~a02 Rd(r-r’)
2D LLL model
GL
Elastic
D. Giamarchi,
Li, B. Rosenstein,
T.
P.L. Doussal,
Lett.. 72,
90, 1530
167004
(2003)
Phys. Rev. Lett
(1994)
T. Nattermann,
Phys. Rev. Lett. 64, 2454 (1990)
300
200
100
0
0.2
RSB Bragg GlassRS
Solid
Solid
0.3
0.4
0.5
0.6
t=T/T
T c
0.7
0.8
0.9
1
Outline
Introduction
The vortex system
Vortex thermodynamics
Equilibrium at low temperatures
First-order melting transition
Second-order glass transition
Vortex dynamics
R(T) – Transport vs Self-induced-field
Critical dynamics at the glass transition
NanoSQUID on a tip
Dynamics / Theory & Experiment
Liquid
Pinned
Liquid
Thermally activated, Ohmic: r~e-U/T
Critical scaling: r~(T-Tg)a, a~6
H
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)
Bragg Glass
T
Glassy (nonOhmic): r~e-U(j)/T, U(j)~j-0.5
T. Giamarchi, P. Le Doussal, Phys. Rev. B 55, 6577 (1997)
T
Liquid
H
Glass
Bragg
Solid
Glass
Lattice
T
H. Safar et al., Phys. Rev. Lett. 68, 2672 (1992)
D.T. Fuchs et al., Phys. Rev. Lett. 81, 3944 (1998)
or
Non Glassy (Ohmic): r~e-U/T
M. Luo, X. Hu, V. Vinokur, arXiv:0902:0858v1
Transport
B (abu)
Transport noise level
Poor c-axis current penetration
100
350 Oe
R (W)
10-3
10-4
10-5
V
Glass transition
10-1
10-2
R. Busch et al., Phys. Rev. Lett. 69, 522 (1992)
B. Khaykovich et al., Phys. Rev. B 61, R9261 (2000)
10-6
c-axis
Transport noise
10-7
10-8
10-9
10-10
30
40
50
60
70
T (K)
80
90
100
Self Induced Field
Transport noise level
Poor c-axis current penetration
Edges shunt bulk
100
350 Oe
R (W)
bulk
x
10-6
V
B(1)
10-5
edge
B(1)
10-4
j(1)
10-3
edge bulk
j(1)
10-2
Glass transition
10-1
x
c-axis
Transport noise
10-7
10-8
10-9
10-10
30
40
50
60
70
T (K)
80
90
100
D.T. Fuchs et al., Nature 391, 373 (1998)
)
B(2) (a.u.)
( Edge Resistance
-1
f= 10
791
Hz
217
1737
Hz
-10
Hz
Hz3 Hz
100
350 Oe
10-2
10-3
10-4
10-5
Glass transition
10-1
R (W)
Transport noise level
Poor c-axis current penetration
Edges shunt bulk
Inductive edges
V
Thermally
Activated
Re(T)
Le=490 pH
Le=Re
10-6
c-axis
Transport noise
10-7
10-8
10-9
10-10
30
40
50
60
70
T (K)
80
90
100
E.H. Brandt et al.,
PRB 74, 094506 (2006)
H. Beidenkopf et al., PRB 80, 224526 (2009)
)
(Bulk Resistance at Tg
0
-1
f= 791
10
217
1737
Hz
-10
Hz
Hz3 Hz
100
10-3
10-4
10-5
27K
Critical: R~(T-Tg)a
x
V
Glass transition
10-2
bulk
350 Oe
10-1
R (W)
screened
edge
B(1)
B(1) (a.u.)
j(1)
Transport noise level
Poor c-axis current penetration
Edges shunt bulk
Inductive edges and bulk
Thermally
Activated
Rb(T)
Le=490 pH
Lb=140 pH
Thermally
Activated
Re(T)
10-6
Lb=Rb
c-axis
Transport noise
10-7
10-8
10-9
10-10
30
40
50
60
70
T (K)
80
90
100
E.H. Brandt et al.,
PRB 74, 094506 (2006)
H. Beidenkopf et al., PRB 80, 224526 (2009)
)
300 Oe
T (K)
Glass
30
40
50
H (Oe)
350 Oe
(Bulk Resistance at Tg
Liquid
100
350
Glass transition Tg
10-1
R, 2pf Lb (W)
10-2
10-3
10-4
10-5
300
BrG
Thermally
Activated
Rb(T)
Lattice
Thermally
Activated
Re(T)
10-6
10-7
Transport noise
10-8
10-9
10-10
30
40
50
60
70
T (K)
80
90
100
Ohmic
Non-Ohmic!
Critical: R~(T-Tg)a
V
The 1st-order melting and 2nd-order glass
transition divide the vortex phase diagram
into four thermodynamic phases.
Glass
Vortex Matter Summary
New method for measurement of bulk and
edge resistance.
BrG
Liquid
Lattice
The inductance of the edge and the bulk
dominate the flow at low temperatures.
On approaching the glass transition the bulk
resistance plunges critically below the
thermally activated behavior.
The bulk resistance is Ohmic in the liquid
phase but non-Ohmic in the lattice phase.
H. Beidenkopf et al., PRL 95, 257004 (2005); PRL 98, 167004 (2007); PRB 80, 224526 (2009)
SQUID on a tip
Imaging currents and moments on nanoscale
A. Finkler, Y. Segev,
Y. Myasoedov, M.L. Rappaport
and E. Zeldov
Weizmann Institute of
Science
Rehovot, Israel
M.E. Huber
University of Colorado
Denver, CO
J. Martin and A. Yacoby
Harvard University
Cambridge, MA
Superconducting Quantum Interference Device (SQUID)
SQUID
Josephson
junctions
I
Φ=BA
Superconducting
loop
Flux quantization:
GL order parameter:
 (r )   (r ) ei ( r )
Superconducting current:
2
e
J      2e A 
m
c 

 0  hc  20.7 G / μm 2
2e
Josephson critical current:
I s  I 0 sin( D )
SQUID critical current:
 π 

I s ( )  2 I 0 cos
 0 
Superconducting Quantum Interference Device (SQUID)
2
Josephson
junctions
I
Φ=BA
Superconducting
loop
I / I0
SQUID
1
0
-4
-2
0
2
/ 0
Flux quantization:
GL order parameter:
 (r )   (r ) ei ( r )
Superconducting current:
2
e
J      2e A 
m
c 

 0  hc  20.7 G / μm 2
2e
Josephson critical current:
I s  I 0 sin( D )
SQUID critical current:
 π 

I s ( )  2 I 0 cos
 0 
4
Superconducting Quantum Interference Device (SQUID)
SQUID
Josephson
junctions
I
Φ=BA
Superconducting
loop
GL order parameter:
 (r )   (r ) ei ( r )
Superconducting current:
2
e
J      2e A 
m
c 

Koshnick et al., Appl. Phys. Lett. 93, 243101 (2008)
SQUID-on-a-tip fabrication
 100  400 nm
 1 mm
SQUID-on-a-tip fabrication
 100  400 nm
Aluminum
SQUID-on-a-tip fabrication
Aluminum
SQUID-on-a-tip fabrication
Aluminum
SQUID-on-a-tip fabrication
Al lead
Al lead
SQUID loop
weak links
Aluminum
SQUID on a tip
Pulled quartz tube
Al lead
Al lead
quartz
Al lead
bare quartz
Al lead
SQUID
loop
200 nm
200 µm
A. Finkler et al., Nano Letters (2010)
SQUID on a tip
Quantum interference patterns
SQUID current
120
Al lead
quartz
Al lead
V [ mV ]
100
80
60
-0.1
-0.05
0
0.05
0.1
SQUID
loop
200 nm
B[T]
Period = 60.8 mT
I0 = 1.6 mA
Lk = 550 pH
Loop diameter = 208 nm
Flux sensitivity = 2×10-6 0/Hz1/2
 = 2LI0/0 = 0.85
Field sensitivity = 10 T/Hz
(Lg = 0.3 pH)
Spin sensitivity = 65 mB/Hz1/2
-7
1/2
A. Finkler et al., Nano Letters (2010)
SQUID on a tip
Quantum interference patterns
SQUID current
Al lead
100
quartz
Al lead
V [ mV ]
50
0
-50
SQUID
loop
-100
-0.4
-0.2
0
0.2
B[T]
Operational field > 0.5 T
0.4
200 nm
Flux sensitivity = 2×10-6 0/Hz1/2
-7
Field sensitivity = 10 T/Hz
1/2
Spin sensitivity = 65 mB/Hz1/2
A. Finkler et al., Nano Letters (2010)
SQUID on a tip
Quantum interference patterns
SQUID current
Al lead
SQUID
loop
Period = 190 mT
Loop diameter = 115 nm
quartz
Al lead
200 nm
SQUID on a tip
Calculated vortex lattice field B(x,y)
[G]
Al lead
quartz
Al lead
Y [nm]
Z=15 nm above surface
NbSe2, =132 nm, B = 750 G
SQUID
loop
200 nm
X [nm]
Field modulation decays as exp(-2pZ/a0)
Factor of 10 every 65 nm in height
Flux sensitivity = 2×10-6 0/Hz1/2
-7
Field sensitivity = 10 T/Hz
1/2
Spin sensitivity = 65 mB/Hz1/2
SQUID on tip I-V characteristics
5 kW
Vin
Rs
Rb
SSAA
SQUID
on tip
ISOT
T = 300 mK
SQUID on tip noise
Sn = 1.810-6 0/Hz1/2
SQUID on tip glued to tuning fork
Quartz
tuning fork
100 µm
SQUID
on tip
Topographic and magnetic imaging with SQUID on tip
Magnetic field at various heights
Measured
SQUID on tip
×100
Applied current in meander 2 mA
Measurement of topography
Calculated
Scanning nano-SQUID microscope
Magnetic field of a
vortex lattice
Scanning nano-SQUID microscope
Spin sensitivity
65 mB/Hz1/2
Quantum dot
on a carbon nanotube
Orbital moment
of a single electron 25 mB
F. Kuemmeth, S. Ilani, D. C. Ralph, and P.L. McEuen, Nature 452, 448 (2008).
Scanning nano-SQUID microscope
Wigner crystal in CNT
V.V. Deshpande and M. Bockrath,
Nature Physics 4, 314 (2008).
Magnetic field and spin sensitivity
Sensor-sample separation
Field sensitivity / Hz1/2
Scanning
m-SQUIDs
SQUID
on tip
Diamond NV
sensor
C. Degen, Nature Nanotech. 3, 643 (2008)