1

CURRENT CROWDING EFFECTS IN

NANOSTRUCTURED SUPERCONDUCTORS

Alejandro V. Silhanek Département de Physique, Université de Liège

BELGIUM

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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)

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CURRENT CROWDING

DEFINITION

http://www.imec.be/ScientificReport/SR2008/HTML/1225045.html

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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

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• 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)

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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

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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)

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SURFACE INDENTATIONS Cerbu et al. New J. Phys. 15, 063022 (2013)

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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

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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

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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

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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

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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

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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

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FLUX AVALANCHES

FLmax

Total screening current

current

crowding

edge

H

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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

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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