Vortex matterVortex matter in HTSin HTS Grain Boundary Josephson JunctionsGrain Boundary Josephson Junctions::IntrinsicIntrinsic andand ExtrinsicExtrinsic dd--wave Effects wave Effects

Francesco TafuriINFM –Coherentia Seconda Università di Napoli

In collaboration with: J. Kirtley and C. Tsuei, IBM T.J. Watson Research Center

F. Lombardi and T. Bauch, Chalmers University A. Barone, F. Miletto, D. Stornaiuolo and U. Scotti , Napoli Federico II

E.Ilichev, IPHT JenaG. Balestrino, P.G. Medaglia, P. Orgiani, Roma Tor Vergata

d-wave OP symmetrysearch for spontaneous currents

in HTS and HTS JJ (π-ring)

Novel devices exploiting d-wave OP (π-circuitry)and possibly truly quantum effects

Background and motivation

Flux dynamicsPearl vortices

Vortex quantum tunneling

Phase transition “Cosmological experiments”

Topological defects

Quantum effectsd-wave OPsymmetry

π-junctions

Vortex matter

HTS JJ

Half flux quantum effect inYB2C3O7-x

J. Kirtley, C. Tsuei et al. Nature (‘97)C. Tsuei, J. Kirtley et al. PRL (‘94)

B= 0 mGB= 3.7 mG

π

IC = ICo sin (π−ϕ)

IC = ICo sin ϕ

0

Josephson Effectand π-phase shift

L.N. Bulaevskii, V.V. Kuzii and A.A. Sobyanin, JETP Lett. 25, 290 (1977)V.B. Geshkenbein, A.I. Larkin and A. Barone, Phys. Rev. B 36, 235 (1987)M. Sigrist and T.M. Rice, J. Phys. Soc. Jpn. 61, 4283 (1992)

+

ΦΦ

×

Φ

−

Φ

Φ−ΦΦ=ΦΦ ϕπ

π oo

c

o

aoo

ILL

U 2cos2

),(22

D.Van Harlingen. Rev. Mod. Phys. 67, 515(‘95)

Spontaneous nucleation of “topological defects” inphase transition (normal-superconductor)

Amorphous Mo3Si superconducting thin film

Tc = 7.81 K; 50 nm thick;30 µm Outer Diameter, 20 µm Inner Diameter ,60 µm spacing

Optical Microscope Scanning SQUID Microscope

2.1x10-4 K/sec 9.2x10-3 K/sec 21 K/sec

Spontaneous (Φ=0) nucleation of topological defects in Mo3Si ringsDependence on the cooling rate

Probability of Mo3Si rings having a final fluxoid +1 as a function of the cooling rate

Zero field cooling

T. Kibble, J. Phys. A 9, 1387 (1976).W. Zurek, Nature 317, 505 (1985);Physics Reports 276, 177 (1996)

Cosmological experiments in condensed matter systemsKibble-Zurek mechanism

Keywords: Topological defects; Superfluids; Symmetry breaking dynamics; Vortex lines; Cosmological phase transitions

Second order phase transition-equilibrium correlation length diverges;True correlation length ξ cannote be infinite-reaches maximum value ξ

∧

Correlated domains of diameterVortices where these domains meet

ξ∧

Quantum computation

Pre-requisites-tunnel junctions-low dissipation-doubly degenerate states-tunability of π-component-macroscopic quantum effects……

L.B. Ioffe, V.B. Geshkenbein, M.V. Feigel'man,A.L. Fauchere, and G. Blatter. Nature 398, 679 (1999)

A. Zagoskin, Cond. Mat. 9903170 (1999)

“qubit” condenses most of aspects related to unconventional orderparameter symmetry and “quantum” effects

Andreev bound statesTime reversal symmetry breakingImaginary component of OP, ... Gap.......

dd--wave effects in JJ: the extreme case ofwave effects in JJ: the extreme case of45° asymmetric configuration (45° asymmetric configuration (θθLL=0° =0° θθRR =90°):=90°):second harmonic andsecond harmonic and AndreevAndreev bound statesbound states

Relatively easy access to second harmonicRelatively easy access to second harmonic…a price to pay…a price to pay

++--

++--

eh

eh

A1

A2

D N S

for instance: C.R. Hu, Phys. Rev. Lett. 72, 1626 (1994 );T.Lowfander, V.S. Shumeiko and G. Wendin, Supercon. Sci. Technol. 14, R53 (2000); G. Blatter, V. B. Geshkenbein and L. B. IoffePhys. Rev. B 63, 174511 (2001)

MacroscopicGB

GB facets

π

dd--wave effects wave effects in JJin JJ: : forfor instanceinstance ππ--loops loops and and facetingfaceting

J. Mannhart, H.Hilgenkamp, B. Mayer, Ch. Gerber, J.R. Kirtley, K.A. Moler and M. Sigrist,Phys. Rev. Lett. 77, 2782 (1996);

Grain boundary techniques

H.Hilgenkamp and J. Mannhart, Rev. Mod. Phys. (2002)

(110) MgO(103) YBCO

twist

c

a

bc

(001) YBCO

c

tilt

twist - tilt AGB

(103) YBCO

(001) YBCO

ca b

c

c

tilt + tilt BP MgO vs BP CeO2 : “0” vs π

twist + tilt

F. Tafuri, F. Carillo, F. Lombardi,F. Miletto Granozio, F. Ricci, U. Scotti di Uccio,A. Barone, G. Testa, E. Sarnelli and J.R. Kirtley, Phys. Rev. B 62, 14431 (2000).

TEM: “clean” basal plane GB (45° tilt)

-3.0 -1.5 0.0 1.5 3.0

-2

-1

0

1

2

Tilt (Ix10)

Twist

I(m

A)

V(mV)

Anisotropy MgO vs CeO2 in the extreme cases of tilt and twist

-2 -1 0 1 2-300

-200

-100

0

100

200

300 twist α=90° tilt α=0°

I (µA

)V (mV)

θ

(103)

(001)

Tilt-tilt

Twist-tilt

Transport properties in presence of H

-100

-50

0

50

100

-10

1

I (µA

)

V (mV)H (G)

0

4.5

T= 4.2 K

-30 -20 -10 0 10 20 30

-2.0x10-6

-1.5x10-6

-1.0x10-6

-5.0x10-7

0.0

5.0x10-7

1.0x10-6

1.5x10-6

2.0x10-6BP twist 20 µm; T = 800 mK

critical current retrapping current

I C (A

)

B (µT)

Anisotropy in CeO2 :Jc vs θ ... intrinsic d-wave effects in all HTS single junctions

0.0 1.60

2x102

3x102

5x102T = 4.2 K

Bp CeO2

π/4 π/20

J C (A/

cm2 )

Angle (rad)

102

103

104

105

Bp MgO

JC vs θ

(103) YBCO

(001) YBCO

(100)/(010) Y

(103) YBCO film

(001) YBCO film

Tilt-tilt

(010)/(100) YTwist-tilt

θ

c)

0 20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

modified d-wave

I C / I C

MAX

θ (degrees)0 20 40 60 80

0.0

0.2

0.4

0.6

0.8

1.0

I C / I C

MAX

θ (degrees)

d-wave S-R

0 20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

I C / I C

MAX

θ (degrees)

BP 10µm BP 4µm

Intrinsic d-wave effects: angular dependence of JC

AB C D

0

30

60

90

120

150

180

210

240

270

300

330

Spontaneous currentsYES NO

H.Hilgenkamp and J. Mannhart, Rev. Mod. Phys. (2002)

BiepitaxialBiepitaxialvs othervs other GBsGBs

F. Tafuri, , J. Kirtley, F. Lombardi and F. Miletto Phys. Rev. B (2003)

J. Kirtley, K. Moler and D. Scalapino, PRB (1997)

ModellingModelling: long : long junctionjunction

Our data

Families of vortices in a biepitaxial sample including closed geometry

θ

θ

twi st- tilt

a b

c d

Half flux quantum Effect: “manipulation”along BP GBs JJ

T (K) 4030

2010

4.2

CT

Phase angle α between drive current Irfand tank voltage

Leff effective inductanceReff effective resistanceif Reff does not depend on Hdc

Q quality factork coupling tank coil sampleχm ac magnetci susceptibitity

Paramagnetic signal (RF) along a GB line and absence of spontaneous currents (SSM)

600 µm x 400 µm

(103)

H = 0

200 µm x 200 µm

(103)

(001)

Finite H

(103)

(001)

600 µm x 400 µm

Paramagnetic signal (RF) and absence of spontaneous currents (SSM) : possible hint for Andreev bound states in biepitaxial JJ ??!!

Presence of a mechanism able to split themidgap states, to populate themidgaps states unequally

Higashitani, J. Phys. Soc. Jap. 66, 2556 (‘97); C.R. Hu, Phys. Rev. Lett. 72, 1626 (1994 );T.Lowfander, V.S. Shumeiko and G. Wendin,Supercon. Sci. Technol. 14, R53 (2000)

yk±

++--

++--

eh

eh

A1

A2

D N S

MacroscopicGB

GB facets

π

ANDREEV BOUND STATESANDREEV BOUND STATES

0 20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

I C / I CM

AX

θ (degrees)

BP 4µm BP 10µm d-wave S-R modified d-wave

junctions with intrinsic Half flux quantum effect

d-wave induced effects

without necessarily extrinsic Andreev bound states

effects (additional noise)

Flavour of d-wave induced effects

intrinsic Intrinsic and extrinsic extrinsicJc

-150 -100 -50 0 50 100 150-2

-1

0

1

2I (

µA)

V (µV)

T = 4.2 K

Hysteretic behavior-switching currents

T = 4.2 K

0.0 1.60

2x102

3x102

5x102T = 4.2 K

Bp CeO2

π/4 π/20

J C (A

/cm

2 )

Angle (rad)

102

103

104

105

Bp MgO

F. Lombardi , T. Bauch et al. Unpublished (2003)

-30 -20 -10 0 10 20 30

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

Bp twist 900 w=20 µmT = 4.2 K

critical current retrapping current

B (µT)

I C (µA

)

Doubly degenerate states and π loops

A

B

C D

L.B. Ioffe, V.B. Geshkenbein, M.V. Feigel'man,A.L. Fauchere, and G. Blatter. Nature 398, 679 (1999); G. Blatter, V. B. Geshkenbein and L. B. IoffePhys. Rev. B 63, 174511 (2001)

0 20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

I C /

I CMAX

θ (degrees)

BP 4µm BP 10µm d-wave S-R modified d-wave

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0-2

-1

0

1

2

twist, T = 25 mK

I (µ

A)

V (mV)

An example of novel approaches

to HTS junctions

150 nm

GB8 nm

GB

Λ

8.8 Å

6.4 ÅΛ

17.6 Å

6.4 Å

#1151

1 cell 5x2x5

#1179

20 cells4x2

#1106

28 cells2x2

CuO2 PlanesCaBa

F. Tafuri, J. Kirtley, P.G. Medaglia, P.Orgiani and G. Balestrino, submitted (2003)

2 IL2 IL5 CR5 CR

5 CR5 CR2 CR2 CR

2 CR2 CR

dL /2 2λ=Λ

Pearl length

Evidence of vortex broadening for decreasing d

-0.4 -0.2 0.0 0.2 0.4-2.0-1.5-1.0-0.50.00.51.01.52.0

1mm wide 5mm wide 5mm wide with H

I (m

A)

V(mV)

200 µm x 200µm

T = 4.2 K

Hints for Hints for JosephsonJosephson--like behaviorlike behavior

GB

0°-24° asymmetric12°-12° symmetric

HTS JJHTS JJ

Quantum effectsQuantum effectsdd--wave OPSwave OPS

ππ--junctionsjunctionsIntrinsic dIntrinsic d--wave effectswave effects

Novel devices Novel devices exploiting dexploiting d--wave OP (wave OP (ππ--circuitry)circuitry)and possibly truly quantum effectsand possibly truly quantum effects

PrePre--requisitesrequisites--tunnel junctions ...low dissipationtunnel junctions ...low dissipation

--doubly degenerate statesdoubly degenerate states--tunabilitytunability of of ππ--componentcomponent

--macroscopic quantum effectsmacroscopic quantum effects

0 20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

I C / I C

MA

X

θ (degrees)

BP 4µm BP 10µm d-wave S-R modified d-wave

Vortex matterVortex matter

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0-2

-1

0

1

2

twist, T = 25 mK

I (µA

)

V (mV)