Prof. Dale Van Harlingen, Micah Stoutimore University of Illinois at Urbana-Champaign Prof. Valery Ryazanov, Vladimir Oboznov, Vitaly Bolginov ISSP RAS, Chernogolovka, Russia

Superconductor-Ferromagnet-Superconductor Josephson π-junctions

I

φ

In collaboration with:

Sergey Frolov

(this research was performed between 2000 and 2005)

MECHANISM = Cooper pairing Electrons with opposite momentum and spin are coupled!

GROUND STATE = superfluid pair condensate

ψ = ns e iϕ macroscopic phase coherence

All you need to know about superconductivity

superconductor

ψ =√ns eiϕ

Leon Cooper’s autograph!

Josephson junction: two coupled superconductors

superconductor barrier

ψ

superconductor

superconductor barrier

ψ

superconductor

Anti-Symmetric ground state

Conventional “0-junction”:

π-junction:

Symmetric ground state

wavefunction Ψ

Superconducting wavefunction extends across a short barrier allowing the dissiplationless supercurrent to flow through the junction

Josephson Current-Phase Relation of a π-junction

0-junction minimum energy at 0

I

φ

π-junction minimum energy at π

I

φ

IS = Icsin(π+φ) = -Ic sinφ

EJ = E0 [1 - cos(π+φ)]

= E0 [1 + cosφ]

negative critical current

E

φ π −π

E

φ π −π

The well-known “first Josephson relation” connects the supercurrent and the phase difference φ of the superconducting wavefunction across the junction:

Josephson energy is then:

Mechanisms of π−junctions THEORY EXPERIMENT

Klapwijk (1999)

Ryazanov (1999)

? Testa (2003)

+ -

+ - Van Harlingen (1993)

d-wave corner SQUIDs

QP-injection SNS junctions

SFS junctions

d-wave grain boundary junctions

Volkov (1995) non-equilibrium population of Andreev levels Barash (1996) zero-energy bound states

Geshkenbein (1987) - p-wave Leggett (1992) - d-wave directional phase shift

Bulaevskii (1978) tunneling via magnetic impurities

Buzdin (1982) tunneling w/ exchange interaction

S S

! NOT a π-junction

Kouwenhoven (2006) S-quantum dot-S

h

S S

gate

N S S

What happens to the superconducting wavfunction near a Superconductor-Ferromagnet (S-F) interface?

∆−+

∆Ψ x

hpix

hpix expexp

21~)(

F

ex

vE2p =∆

εF

∆p p

E

E↑

E↓

2Eex

Demler, Arnold, Beasley

1) Cooper pairs penetrate into the ferromagnet (proximity effect)

2) there Cooper pairs obtain non-zero net momentum because spin subbands are split by the ferromagnetic exchange interaction:

3) The superconducting wavefunction inside a ferromaget is a sum over Cooper pairs with positive and negative momentum

wavefunction oscillations

Wavefunction oscillations in Superconductor-Ferromagnet are behind the π-junction state

decay

∆−+

∆Ψ x

hpix

hpix expexp

21~)(

−

Ψ

12

expcos~)(FF

xxxξξ

Ψ

x

SC FM

hex

This wavefunction is nothing but a cosine in real space. But one must also add a decay multiplier due to spin-flips inside the ferromagnet (they destroy Cooper pairs)

21 //1/1 FFF i ξξξ +=

It is convenient to describe the wavefunction Inside the ferromagnet using a complex coherence length

Josephson junctions have two S-F ineterfaces, each of them induces an oscillating wavefunction

Ψ

x

φ = 0

Ψ

x

φ = π F S S

0.0 0.5 1.0-1

0

1

dπ2dπ

1

π

0

d / 2π ξF1

G.L

. Fre

e En

ergy

(a.u

.)2EJ

F S S

d

We can calculate the energy stored in the oscillating wavefunction of an S-F-S junction for 0-state and π-state shown on the left. We see that for a certain ferromagnet thickness the π-state is lower in energy. So, the π-junction transition can be induced by changing the junction thickness.

100 µm

50 µm

50 µm

Si SiO

Fabrication of S-F-S junctions (Ryazanov group)

Top Nb layer 240 nm Cu/Ni layer 25 nm

Bottom Nb layer 100 nm

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

Junctions were defined using optical lithography. Metals were deposited by sputtering in a vacuum chamber.

Critical Current Measurements on S-F-S Josephson π-Junctions

SQUID potentiometer measurement RN ~ 10-5 Ω IcRN ~ 10-10 V

The goal is to detect at which current bias the voltage develops across the Josephson junction. Our S-F-S junctions had extremely small resistances in the normal state, hence we needed to detect very small voltages. This was done using a SQUID potentiometer which has sensitivity of 10’s of picovolts! The S-F-S junction in in series with a standard resistor of similar resistance. The current through the inductor L is detected by the SQUID.

Frolov et al PRB 2004

Oscillations of the Josephson critical current

0 5 10 15 20 25 3010-2

10-1

100

101

102

103

104

105

fit using Usadel equations

Nb - Cu0.47Ni0.53 - NbCr

itical

cur

rent

den

sity

(A/c

m2 )

Barrier thickness (nm)

Oboznov et al. PRL 2006

0

π

0

This data from more that 50 S-F-S junctions of different F-layer thickness shows that the critical (maximum) supercurrent that the junction can sustain has sharp nodes at certain thicknesses. These nodes separate 0-junctions from π-junctions. (Note that this measurement cannot reveal the phase shift, so it is indirect)

Transition between 0-state and π-state can also be induced by temperature

2/1

2/1222,1 ))((

±+

=TkETk

D

BexBFF ππ

ξ

0 2 4 6 8 100

2

4

6

1Fξ

2Fξ)nm(ξ

)K(T )K(T

)A(Ic µ

0 1 2 3 4 5 65

4

3

2

1

0

1

2

3

4

d =

24nm 23nm 22nm 21nm

20nm

0-π junction transition can be studied in a single SFS junction with dF near a node, say dF=22 nm. The reason is because the wavefunction oscillation length in a diffusive ferromagnet has a weak temperature dependence

By warming up the junction the π-state can be made energetically favorable!

0-state π-state

Current-Phase Relation Measurement

I

Φ

M L IC SQUID detector

φ

100µ

Φ

Φ+

Φ=

MLCPR

MI

0

2π

0ML2

ΦΦ

π=φ

SFS junction

The phase shift of π at the cusp in IC(T) can be observed in a phase-sensitive measurement. An SFS junction is placed into a superconducting loop. The phase across the junction is varied by tuning the magnetic flux through the loop

0-junction

I

φ

π-junction

I

φ The current-phase relation (CPR) can then be read out by monitoring the current in the loop using a SQUID:

Current-Phase Relation measurements

-200

-100

0

100

200

3.54 K

3.56 K

3.59 K

3.63 K

Phase0 π-π

Curre

nt (n

A)

3.65 K

Our data demonstrated that the current-phase relation flipped going through the 0-π transition temperature T = 3.59 K. Thus we have detected the phase shift of π and the sign change of the critical current of a S-F-S Josephson junction. We found that the current-phase relation is sinusoidal without distortions. Distortions can indicate the presence of higher-order Josephson tunneling processes.

Frolov et al PRB 2004

3.50 3.55 3.60 3.65 3.70-300

-200

-100

0

100

200

300

Ic1

Ic2

I c1 (n

A), I

c2 (n

A)

T (K)

π-junction in a superconducting loop

Clockwise and counterclockwise currents are degenerate in energy, and can be used as two states of a quantum bit Feofanov et al, Nature Physics (2010)

π

S LΙ / Φ0 + π = 2π n

Bulaevskii, Kuzii, Sobyanin, JETP Lett. 1978

Phase change around a superconducting loop must be 2π due to the wavefunction continuity requirement. If a π-junction is part of a loop, the loop becomes frustrated and the wavefunction must acquire an additional phase shift of π.

To comply a loop spontaneously generates a circulating current:

Spontaneous currents can be observed using a scanning SQUID microscope which is sensitive to local magnetic fields. Frolov et al., Nature Physics (2008)

We detected spontaneous currents in SFS junction arrays

Nb CuNi Nb

period = 30 µm, Lcell = 25 pH

Barrier thickness near 0-π transition => 0- and π-state tunable by temperature (here the π-state was lower in temperature)

Variable frustration: Even number of junctions = unfrustrated cell Odd number of junction = frustrated cell

The goal of this word was to encode a ‘frustration pattern’ into an array by choosing how many S-F-S junctions to place in each cell. This would determine whether or not a spontaneous current circulates in a given cell when the S-F-S junctions become π-junctions. If an array show the encoded pattern, we can be sure that spontanous currents are generated due to π-shifts.

Our magnetic probe: Scanning SQUID Microscope

x-y scan

hinge 10µm 50µm

Spatial resolution: 10µm

Flux sensitivity: 10-6 Φ0

A SQUID sensor placed close to the surface of the sample detects local magnetic fields generated by the sample. The sample is scanned underneath the sensor. In our case an array of superconducting loops with S-F-S junctions served as a sample. Note that magnetic field from a current circulating in the loop would have a peak in the center of the cell. The reason for this is a finite distance between the sensor and the array.

6x6 array with 3 SFS junctions per cell:

0-junction state T = 4.2 K

π-junction state T = 1.5 K

optical image

The two grayscale images show scanning SQUID microscope data on a fully-frustrated array. Abobe the 0-p transition temperature a ghostly image of the array is resolved by the microscope due to Meissner effect, i.e. screening of small residual magnetic fields by the superconducting material of the array. Below the 0-π transition temperature, in the π-junction state, a bright pattern of spontaneous currents appeared.

More Array Designs

2 x 2 cells

6 x 6

fully-frustrated checkerboard-frustrated

fully-frustrated unfrustrated checkerboard-frustrated

30µm

Complete loop

Substrate

Base superconductor

Ferromagnetic layer

Top superconductor

Embedded frustration patterns

frustrated non-frustrated

Zero field:

Finite field (2 mG): Spontaneous flux magnitude variations:

Frolov et al Nature Physics 2008

1 2 3 4 5-75

-50

-25

0

25

50

75

I c (µ

A)

T (K)

0-state π-state

0.0

0.1

0.2

0.3

0.4

0.5

1 2 3 4 50.00

0.02

0.04

0.06

0.08

RM

S M

agne

tic fl

ux (Φ

0)

Magnetic flux per cell (Φ

/Φ0 )

T (K)

T = 1.6 K T = 2.8 K T = 4.0 K

Onset of spontaneous currents

Onset broadened due to critical current variations

Frolov et al Nature Physics 2008

9.2 µm 10.4 nm 11 nm

9.2 µm 0.8 µm S F S

“0-π” junctions – junctions in which two phases coexist

effective barrier steps ~ 0.2-1 nm

T (K)

11 nm

10.4 nm Ic

0 1 2 3 4 5

I c1,

I c2,

I c

0

Imagine that the ferromagnetic barrier is non-uniform, such that there is a step in the F-layer thickness. In this case part of the junction can be in the π-state, while the rest of the junction – in the 0-state.

0 5 10 15 20 25 3010-2

10-1

100

101

102

103

104

105

fit using Usadel equations

Nb - Cu0.47Ni0.53 - Nb

Critic

al c

urre

nt d

ensit

y (A

/cm

2 )

Barrier thickness (nm)

We discovered that our junctions with the barrier thickness near 11 nm were slightly not uniform, such that two regions inside the junction had different 0-π transition temperatures. We calculated the evolution of the critical currents of the two sections in temperature.

Φ

500

400

300

200

100

Simulation Experiment

“0-π” junctions – junctions in which two phases coexist

-3 -2 -1 0 1 2 30

100

200

300

400

500

4.2 K 3.0 K 2.2 K 2.0 K 1.9 K 1.4 K

I c, µA

Field, Φ0

In the 0-π junction state the two parts of the junction have opposite critical current signs. When the two critical currents are the same magnitude, the total critical current is zero. But there is a way to know that opposite phase supercurrents circulate in the junction. A magnetic flux of ½ the flux quantum must be applied to the junction. The two supercurrents then add constructively and the supercurrent is recovered. The results of such Josephson interferometry measurements show a zero-field dip in the 0-π junction state. In normal junctions interferometry always shows a peak at zero temperature.

9.2 µm 10.4 nm 11 nm 9.2 µm 0.8 µm

Frolov et al PRB 2006

Summary • Current-Phase Relation of SFS junctions

Sing change of the critical current

• 0-π junctions – intrinsically frustrated system

Josephson interferometry

• Imaging arrays of π-junctions w/ Scanning SQUID Microscope Spontaneous currents

Our experimental publications:

Ryazanov et al. Phys. Rev. Lett. 2001

Frolov et al. Phys. Rev. B 2004

Frolov et al. Phys. Rev. B. 2006

Obozonv et al. Phys. Rev. Lett. 2006

Frolov et al. Nature Physics 2008

Feofanov et al. Nature Physics 2010

Nb CuNi Nb

Slide Number 1All you need to know about superconductivitySlide Number 3Josephson Current-Phase Relation of a -junctionSlide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Our magnetic probe: Scanning SQUID MicroscopeSlide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24