Dale Van Harlingen

Sergey Frolov, Micah Stoutimore, Martin Stehno

University of Illinois at Urbana-Champaign

Valery Ryazanov

Vladimir Oboznov, Vitaly Bolginov, Alexey Feofanov

Institute of Solid State Physics, Chernogolovka, Russia

10th International Vortex Workshop --- January 14, 2005 --- Mumbai, India

Current-Phase Relations and Spontaneous Vortices

in SFS -Josephson junctions and arrays

Supported by the National Science Foundation and the U. S. Civilian Research Development Fund

                   

I

-Josephson junction

0-junctionminimum energy at 0

I

-junctionminimum energy at

I

J

Spontaneously-broken symmetry

Spontaneous circulating current for L>1 in zero applied magnetic flux

I = Icsin(+) = -Ic

sin

E = EJ [1 - cos(+)]

= EJ [1 + cos]

E

E

negative critical current

-2-2 0

THEORY EXPERIMENT

Klapwijk, 1999

Ryazanov, 2000

Testa, 2003

+-

+- Van Harlingen, 1993

YBCO d-wave corner SQUIDs

Non-equilibrium SNS junctions

SFS junctions

d-wave grain boundary junctions

Not (yet) observed

A.F. Volkov (1995)

non-equilibrium Andreev states

Yurii Barash (1996)

zero-energy bound states

Vadim Geshkenbein (1987) --- p-wave

Tony Leggett (1992) --- d-wave

directional phase shift

Lev Bulaevskii (1978)

tunneling via magnetic impurities

Alex Buzdin (1982)

tunneling w/ exchange interaction

FS

x

S

_+

_

+ _+

_ +

NOT a -junction

The History of junctions

F

p p

E

2Eex

Order parameter oscillations

SF interface: Exchange energy-induced oscillations of the proximity-induced order

parameter

Proximity decay

xSC FM

Ff

ex

f

ex xexpx

v

E2iexpx

v

E2iexp

2

1~)x(

F

ex

v

E2p

RI

xxx

expcos~)(

Exchange energy

Fermi velocity

FS

x

S

FS

x

S

0-state -state

SFS Josephson junctions: dependence of free energy on ferromagnetic barrier thickness

0 0

~ nd ~ (n+½) d

R

2

I

2

R

2

I

2

RIRI0cc

dsinh

dsin

dcosh

dcos

dsinh

dsin

dcosh

dcos

II

Variation of critical current with barrier thickness

2/1

exBI,R )iETk(2

Dlengthcoherence

thicknessbarrierd

energyexchangeEex

tcoefficiendiffusionD

Quasiclassical Usadel equations:Buzdin et al., Kontos et al.

Variation of critical current with temperature

2/1

B2/12

ex2

BI,R Tk)E)Tk((

D

IR

1i

11

2/1

exBI,R )iETk(2

D

Control transition by temperature via coherence length:

I

R)nm(

)K(T )K(T

)A(Ic d =

24nm23nm22nm

21nm

20nm

Si

Si

Si

Si

Step 1: Deposit Base Nb layer

Step 2: Deposit CuNi + protective Cu

Step 3: Define SiO window

Step 4: Deposit Top wiring Nb layer

Si

Si

Si

Window Junctions (Chernogolovka) Trilayer Junctions (Urbana)

Step 1: Deposit Nb-CuNi-Nb trilayer

Step 2: Etch top Nb, backfill with SiO2

Step 3: Deposit Top wiring Nb layer

5m x 5m to 50m x

50m

2m x 2m to 20m x 20m

SFS junction fabrication

Critical current measurements: SFS Junctions

0 5 10 15 20 25 3010-2

10-1

100

101

102

103

104

105

fit to Ic vs. d model

Cu0.47Ni0.53

Crit

ical

cur

rent

den

sity

(A

/cm

2)

Barrier thickness (nm)

Critical current measurements: SFS Junctions

SQUID potentiometer measurement

RN ~ 10-5 IcRN ~ 10-10 V

-40 -20 0 20 400

2

4

6

8

T = 5K

I c (

A)

Magnet current (mA)

Current-Phase Relation Measurement

dc SQUID technique: J.R. Waldram et al., Rev. Phys. Appl. 10, 7 (1975)

SQUID

I

Null SQUID current --- measure I and ~

- junction in an rf-SQUID

0

2

LICL

M

L2sinI

MI

0C

Simulation:

I

Measurement:

• Hysteretic when L > 1

• L varied by changing Ic(T) or L

• CPR is accessible for L < 1

I

MLIC

SQUID detector

6

5

4

3

2

1

0

L=

0M

L2

Near the 0- crossover temperature

0 1 2 3 4 5-10

-5

0

5

10

- junction

Crit

ical

cur

rent

(A

)

Temperature (K)

0 - junction

Study region near crossover

for which -1 < < 1

I

Simulation

0

Temperature:rf SQUID curves

Slight shift die to a background magnetic field ~ 1-10 mG

Current-Phase Relation measurements

Extracted from rf SQUID characteristics:

• 0- crossover is sharp

• Ic = 0 at the crossover temperature T

• CPR is sinusoidal

• No distortions due to sin(2)

Why do we expect a sin(2) component ?

What is the right experiment to probe sin(2

Theoretical predictions:

Radovic et al. Chtchelkatchev et al.

Hekkila et al. Golubov et al.

Suggestive experiments:

Ryazanov et al. (arrays)

Baselmans et al. (SNS SQUIDs)

Current-phase relation measurements

Critical current diffraction patterns:

extra structure in junctions

higher harmonics in SQUIDs/arrays

Shapiro steps (microwave irradiated) --- subharmonic steps

High frequency rf SQUID structure

• Absence of first-order term makes it possible to observe second-order Josephson tunneling

• Interaction of 0 and states at crossover – competing energies

Secondary Josephson Harmonics ?

Results of data fitting: < 5 %

Ic goes to 0 at T, contrary to

predictions of large sin 2

)2sin()sin()( 2 ccc III

Ic resolution ~ 10 nA

-10 -5 0 5 10-80

-60

-40

-20

0

20

40

60

80

Critical curr

ent (m

A)

SQUID Voltage (mV)

Shapiro steps: only integer steps

Diffraction patterns: Fraunhofer

1.70 1.75 1.80 1.85 1.900

10

20

30

40

I c (A

)

T (K)

Critical current vs. temperature

Critical current does not vanish --- this suggests sin(2) term in CPR

Shapiro steps

Half-integer Shapiro steps --- consistent with sin(2) term in CPR

Half-integer steps only occur near T where critical current vanishes

Suggests coexisting “0” and “” states that entangle near degeneracy

Critical current diffraction patterns

Junction barrier is not uniform near T

Average film thickness 24nm

Linear thickness variation of 0.4nm

Effect of sloped barrier thickness variation

2.4 2.6 2.8 3 3.2400

200

0

200

4002.9847 10

2

2.5380 102

Ic d r T( ) i T( )( )

nA

0

3.20002.4 T

T = 2.6K

T = 2.8K

T = 3.0K

T (K)

I c (n

A)

I c (n

A)

I c (n

A)

y (m)

Arrays of -Josephson junctions

Motivation:

1. Observe spontaneous currents and vortices

2. Opportunity to explore non-uniform frustration

3. Opportunity to tune through -transition to measure uniformity of junctions and variation of vortex size

0

cLI2where~

a

a

Cluster Mask

2 x 2

6 x 63 x 3

1 x N

Cluster Designs

2 x 2

6 x 6

fully-frustrated checkerboard-frustrated

fully-frustrated unfrustrated checkerboard-frustrated

30m

Scanning SQUID Microscopy (SSM)

x-y scan

hinge

Square arrays Triangle arrays YBCO films

10m 100mSpatial resolution:

10mFlux sensitivity:

10-6 0

MoGe films

Array images: magnetic field-induced vortices

Single vortex f 0 f = 0.03

f = 0.33 f = 0.50 f = 0.66

-junction array images: spontaneous currents

zero magnetic field

3 x 3

1 x 20

6 x 6

What determines the current pattern?

1. Distribution of frustrated cells --- to maintain phase coherence, each much generate (approximately) 0/2 flux quantum

2. Disorder in cell areas (small) and critical currents (substantial)

3. Thermal fluctuations during cooling --- closely-spaced metastable states

6 x 6

T

T = 1.7K T = 4.2KT = 2.75K

Scanning SQUID Microscope images

T

Ic

Checkerboardfrustrated

Fullyfrustrated

2 x 2 arrays: spontaneous vortices

-1.0 -0.5 0.0 0.5 1.00

1

2

3

4

5

6

-1.0 -0.5 0.0 0.5 1.00

1

2

3

4

5

6

-1.0 -0.5 0.0 0.5 1.00

1

2

3

4

5

6

-1.0 -0.5 0.0 0.5 1.00

1

2

3

4

5

6

-1.0 -0.5 0.0 0.5 1.00

1

2

3

4

5

6

-1.0 -0.5 0.0 0.5 1.00

1

2

3

4

5

6

Ene

rgy

(EJ)

Magnetic flux (0)

Ene

rgy

(EJ)

Magnetic flux (0)

Ene

rgy

(EJ)

Magnetic flux (0)

Ene

rgy

(EJ)

Magnetic flux (0)

Ene

rgy

(EJ)

Magnetic flux (0)

Ene

rgy

(EJ)

Magnetic flux (0)

2 x 2 arrays --- simulations of vortex configurations

all 0-JJ all -JJ

1D-chain arrays --- simulations of vortex configurations

T, K

IC

1 2 3 4

6x6 checkerboard frustrated cluster:

Magnetic field applied (to enhance contrast of SC lines)

T, K

IC

1 2 3 4

6x6 checkerboard frustrated cluster:

Zero magnetic field

6x6 checkerboard frustrated cluster:

Zero Field

Vortices appear at T. (difficult to determine T precisely since diverges)

Resolution improves as Ic increases --- limits for ~ a

T, K

IC

1 2 3 4

6x6 checkerboard frustrated cluster:

Magnetic field applied (to enhance contrast of SC lines)

Conclusions

• Measuring Current-Phase Relation (CPR) of SFS junctions

Observe transition between 0-junction and -junction states

Mixed evidence for any sin 2 in the CPR in the 0- crossover region

Considering effects of barrier inhomogeneities

• Imaging arrays of -junctions by Scanning SQUID Microscopy

Observe spontaneous vortices

Studying crossover region

• Develop trilayer process --- materials and fabrication issues

• Engineer superconducting flux qubit incorporating a -junction

• Measure 1/f noise from magnetic domain dynamics on SFS junctions

• Measure CPR in non-equilibrium -SNS junctions

Work in Progress

1. Provides natural and precisely-degenerate two-level

system

Advantages of -junction flux qubits

J

E

Precisely-degenerate two-level system with no flux

bias

Spontaneous circulating current in rf SQUID

2. Decouple qubit from environment since no external field

needed

(always need some field bias to counteract stray fields and to

control qubit state, but does reduce size of fields needed)

1. Controllability/reproducibility of 0- transition point and

critical currents in multiple-qubit circuits determines

tunneling rate

2. Enhancing normal state resistance of -junction determines decoherence due to quasiparticle dissipation

3. Low frequency magnetic noise in SFS junction barriers source of decoherence

Challenges for -junction flux qubits

Approach: trilayer junction technology

Approach: SIFIS and SFIFS structures

Approach: barrier material engineering

Decoherence from 1/f magnetic domain switching noise

1/f critical current noise modulates tunneling barrier height

Fluctuation of the tunneling frequency causes phase noise decoherence since is different for each successive point of a distribution measurement

t

IC

~ Ic

Magnetic domain switching causes critical current noise

MODEL

S

S

F

SIMULATION

Secondary Josephson Harmonics

Results of data fitting: < 5 %

Ic goes to 0 at T, contrary to

predictions of large sin 2

)2sin()sin()( 2 ccc III

Current

Simulation = 0.5

Ic resolution ~ 10 nA

1. Existence of Josephson sin(2) component

2. Effect of barrier inhomogeneities and fluctuations

• Clustering of magnetic atoms junction aging effects

• Interface conduction reduction of current density

Barrier thickness variations non-uniform current densities

• Ferromagnetic domain noise decoherence in qubits

3. SFS arrays --- magnetic imaging of spontaneous vortices

4. Implementation of -junctions in superconducting flux qubits

Key Issues

BSCCO grain boundary junctions

Possible origin: second-order Josephson coupling

non-sinusoidal current-phase relation … I() = Ic1 sin() + Ic2 sin(2)

(cancellation of tunneling into + and – lobes)

Zero-field peak in critical current has ½ width of finite field peaks

_+

_

+ _+

_ +

Evidence for sin(2) in SNS ballistic -junctionsBaselmans et al., PRL 2002

N SS

E

Andreev levels

V

Suggests sin(2) component

I

I

= =

vortex

Observe half-integer Shapiro steps in a dc

SQUID near 0/2

Another SFS junction – 4x4 m

1.75 1.76 1.77 1.78 1.790

5

10

15

20

I cn (A

)

T (K)

Ic0

Ic1

Ic1/2

Shapiro step maximum amplitude

Half-integer steps only occur near T where critical current vanishes

Suggests coexisting “0” and “” states that entangle near degeneracy