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CURRENT CROWDING EFFECTS IN
NANOSTRUCTURED SUPERCONDUCTORS
Alejandro V. Silhanek Département de Physique, Université de Liège
BELGIUM
2
In collaboration with
O. Adami (ULg, BE) D. Cerbu, M. Timmermans, J. Van de Vondel, V.V. Moshchalkov (KUL, BE) V. Gladilin, J. Tempere, J. Devreese (UA, BE) B. Hackens (UCL, BE) M. Motta, F. Colauto, W. Ortiz (Sao Carlos, BR) J.I. Vestgarden, T.H. Johansen (Oslo, NO) J. Fritzsche (Chalmers, SE) C. Cirillo, C. Attanassio (Salerno, IT)
3
CURRENT CROWDING
DEFINITION
http://www.imec.be/ScientificReport/SR2008/HTML/1225045.html
4
MOTIVATION
WHY IS IT IMPORTANT ?
Superconducting single-photon detectors
(a) Hiroyuki Shibata, NTT Technical Review
Electromigration Design of Kelvin 4 probe bridges
J
Dominant in nanostructured superconductors
5
• CURRENT CROWDING IN NORMAL METALS
• CURRENT CROWDING IN SUPERCONDUCTORS
SHARP BENDS
SURFACE INDENTATIONS
MAGNETIC FLUX AVALANCHES
• CONCLUSION
OUTLINE
6
PREHISTORY
conformal
mapping r
0
3/1
ir
giABC
i0 is the asymptotic current
density in the leg
Optimum curvature The perturbations of the
current crowding
propagate about three
strips widths into the legs
7
PREHISTORY
a as small as possible
and
b and N as large as possible
if b >> a and N >> 1
8
HISTORY
Silhanek et al.,
Appl. Phys. Lett. 92, 176101 (2008)
…we have observed a substantial deformation of the current-voltage characteristic
when the voltage pads are attached close to the cross’ vertices.
9
MORE RECENTLY…
dW /2 2
Definition of Jc…the critical current of a superconducting
strip in the absence of thermal excitations is the current at
which a nucleating vortex surmounts the Gibbs-free-energy
barrier at the wire edge and then is driven entirely across
the strip
Jc = C J0
J0 the critical current of a superconducting strip
C < 1
10
COMPARISON
W
3/1
42
3
WC
Jc = C J0
3/1
W
rC
Hagedorn-Hall
(normal metal)
Clem-Berggren
(superconductor)
does not play a role
The ratio / W defines the behavior
There is an optimum curvature which
permits to avoid current crowding. The
minimum radius being 1,27W
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Clem-BERGGREN PREDICTIONS
Voltage Contact
3/1
2
3
bC
if Wb
b
Current Contact
1C if b
3/1
22
2
)(2
3
aaW
WC
W
a
Clem et al., Phys. Rev. B 84, 174510 (2011)
12
EXPERIMENTAL EVIDENCE
H. L. Hortensius et al. Appl. Phys. Lett. 100, 182602 (2012)
NbTiN
~ 7 nm
~ 20 mm
W ~ 1 mm
D. Henrich et al., Phys. Rev. B 86, 144504 (2012)
NbN
~ 5 nm
>> W
W ~ 0,3 mm
13
London
Compensation effect between the field induced stream-lines and
the externally applied current at the current crowding point
Magnetic field dependence Clem et al., Phys. Rev. B 85, 144511 (2012)
H >0
H >0
H <0
tdGL
14
180°
90°
SiO2
H > 0
V+ V-
I
Al
(0) ~ 120 nm
(1,22 K) ~ 8,3 mm
W ~ 3,3 mm
EXPERIMENTAL CONFIRMATION Adami et al., Appl. Phys. Lett. 102, 052603 (2013)
-0,08 -0,04 0,00 0,04 0,08
650
700
750
800
850
900
S180
I C (
mA
)
H (mT)
1.18K, I+
-0.10 -0.05 0.00 0.05 0.10300
350
400
450
500
550
600
650
700
750
S90 Hmax
1.18K, I+
1.18K, I-
1.20K, I+
1.20K, I-
1.22K, I+
1.22K, I-
I C (
µA
)
H (mT)
15
180°
EXPERIMENTAL CONFIRMATION Adami et al., Appl. Phys. Lett. 102, 052603 (2013)
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
0.1
0.2
0.3
0.4
0.5T = 0.92 T
c
Freq = 1kHz
H[mT]
ac a
mp
litu
de
[m
A]
Vdc
[µV]
S90
-200 -120 -40 40 120 200
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
0.1
0.2
0.3
0.4
0.5T = 0.92 T
c
Freq = 1kHz
H[mT]
ac a
mplit
ude [m
A]
Vdc
[µV]
S180
-200 -120 -40 40 120 200
H >0 H <0
Fixed J > 0
J >0 J <0
Fixed H > 0
16
SURFACE INDENTATIONS
2
1C
3/1
aC
if
90
Current crowding is more important for the triangle
Clem et al., Phys. Rev. B 84, 174510 (2011)
17
SURFACE INDENTATIONS Cerbu et al. New J. Phys. 15, 063022 (2013)
18
SURFACE INDENTATIONS Cerbu et al. New J. Phys. 15, 063022 (2013)
The onset of the resistive regime is
mainly determined by the properties of
the ‘inlet’ boundary of the strip.
The effect due to patterning of the ‘outlet’
boundary facilitates the formation of
PSLs
19
CURRENT CROWDING IN NANOSTRUCTURED
SUPERCONDUCTORS
J
Nakai & Machida Physica C 470 1148 (2010)
superconducting current curves around crossing points of superconducting
lines … such a current makes high flux density around the corner of the square hole.
Tsuchiya et al. Physica C 470 S788 (2010)
20 R. G. Mints, and A. L. Rakhmanov, Reviews of Modern Physics 53, 551 (1981).
FLUX AVALANCHES
THERMAL DIFFUSION >> MAGNETIC DIFFUSION
SMOOTH PENETRATION
THERMAL DIFFUSION << MAGNETIC DIFFUSION
THERMOMAGNETIC INSTABILITIES
21
FLUX AVALANCHES
NbN 4.8 K, 26 Oe Rudnev et al. 2005
MgB2 10 K, 170 Oe Johansen et al. 2004
Nb3Sn 3.5 K, 263 Oe Rudnev et al. 2003
Nb 5.97 K, 135 Oe Remanent state Durán et al. 1995
YBCO 1.8 K, 600 Oe After laser pulse
Leiderer et al. 2004
YNi2B2C 4 K, 198 Oe (decreasing field) Beihler et al. 2005
22
FLUX AVALANCHES
T = 4.5 K and H = 12 Oe
ADs guiding the avalanches Pb with ADs
h = 1.5 mm - b = 0.8 mm Nb with ADs
h = 2 mm - b = 0.2 mm
TMI strongly interact with the underlying AD lattice
T = 6 K and H = 15 Oe
Branching at 90o
23
FLUX AVALANCHES
MoGe-I (Square lattice and Square ADs)
RGB image – T = 3 K and H = 1.4 Oe T = 4.5 K and H = 1 Oe
MoGe-I
a = 1.5 mm
b = 0.4 mm
d = 25 nm
24
FLUX AVALANCHES
T = 5K and H = 2.1 Oe
1st Prize
Photography – Science and Arts
Award CNPq (2011)
Nb-I
a = 4 mm
b = 1.5 mm
d = 50 nm
25
FLUX AVALANCHES
FLmax
Total screening current
current
crowding
edge
H
26
FLUX AVALANCHES
Centered rectangular 2D / Square ADs (MoGe-II)
T = 3 K and H = 1 Oe
Statistics
for several T:
a0 = (61.9 1.5)o
20 branches
= (54.0 1.3)o
14 branches
0
0
27
CONCLUSION
In the same way that magnetic field lines lead to demagnetization
effects, deformation of current stream lines lead to current
crowding.
This effect have important consequences on
- the resistance calculation in normal metals
- V(I) characteristics in superconductors
- unwanted ratchet signal
- hot spots (joule heating)
- reduction of the critical current
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