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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)