HTc Josephson nano-junctions : physics and applications · 2017-12-28 · Dynamics of Josephson...
Transcript of HTc Josephson nano-junctions : physics and applications · 2017-12-28 · Dynamics of Josephson...
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HTc Josephson nano-junctions :physics and applications
Collège de France 2008
Jérôme Lesueur
Phasme team : www.lpem.espci.fr/phasme
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Nicolas Bergeal
Martin Sirena
Thomas Wolf
Giancarlo Faini
Rozenn Bernard, Javier Briatico, Denis Crété
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Nicolas BergealMartin SirenaThomas WolfAlexandre Zimmers
Pascal Febvre
Denis Crété
Sophie Djordjevic
Robin Cantor
RSFQ
Etalon du Volt
THz
SQUID
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Quantum circuits ?
No quantification of the EM field (cf M. Devoret’s lecture)
No quantum states manipulation (cf O. Buisson’s seminar)
1st
2d
!
| 0"+ | 1"
2
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Phase properties and superconducting circuits
Phase rigidity of the condensate
!
" =0"
i#
e
!
V( t)dt0
T
" =0
#
!
d" = 0#
dx2−y2
++-
-kx
ky
Intrinsic phase structure in High Tc SC
Josephson nano-junctions
π-junctions
High speed applications
Analog to Digital converters
Communication systems
PetaFLOPS computer …
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Superconductive electronics
Superconductors Semiconductors
CMOS transistorJosephson Junction
Aluminium
Aluminium
AlOxSiOx
Silicon1-2 nm
1-2 nm
Quantum circuit
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Dream or reality ?
An example : a digital frequency divider
770 GHz ; 1.5 µWTechnology : Nb/Al/AlOx/Nb @4.2 K
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Outline
1. Superconductive electronics
3. Physics of High Tc nanojunctions
Dynamics of Josephson Junctions
Rapid Single Flux Quanta logic
Actual RSFQ devices
Proximity effect
Quasi-classical diffusive approach
D-wave order parameter symmetry
π-junctions and RSFQ devices
4. Conclusions
2. High Tc Josephson nanoJunctionsIon irradiation of High Tc Superconductors
Making Nanojunctions
Major characteristics of the Nanojunctions
A few applications
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Outline
1. Superconductive electronics
3. Physics of High Tc nanojunctions
Dynamics of Josephson Junctions
Rapid Single Flux Quanta logic
Actual RSFQ devices
Proximity effect
Quasi-classical diffusive approach
D-wave order parameter symmetry
π-junctions and RSFQ devices
4. Conclusions
2. High Tc Josephson nanoJunctionsIon irradiation of High Tc Superconductors
Making Nanojunctions
Major characteristics of the Nanojunctions
A few applications
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Josephson Junctions
ψ2=|ψ2 | eiϕ2ψ1=|ψ1 | eiϕ1
SuperconductorSuperconductor Barrier
Josephson Junctions Josephson equations
!
I = Icsin(")
!
" ="1#"
2
Barrier : insulator, normal metal, constriction …
Applications : superconductive electronics
• Photon detection : 1 junction
• SQUID for magnetometry, voltmetry … : 2 junctions
• Rapid Single Flux Quantum (RSFQ) logic : from 10 to millions junctions !
483 597,9 GHz/V
Josephson Energy
!
JE = 0"
cI
2#(1$ cos(% ))
!
"#
"t=2eV
h=2$V
0%
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Modeling a Josephson Junction
RC Shunted Junction Model
Josephson Junction : a non-linear inductance
!
I (t) =JI (t)+ RI (t)+ CI (t)
!
V( t) = 0"2#
$%( t)
$t
!
V( t) =JL"
JI ( t)
"t
!
JL = 0"
2#cI cos$( t)
!
I (t) =cI sin("( t))+
V(t)
JR+
JC#V( t)
#t
!
I( t)
cI= sin("(t))+ J0L
JR
#"(t)
#t+
J0L JC
2
# "(t)
#t
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The mechanical analogy
Normalized equation
!
J0E"
"#(1$ cos(# )$ i# )+
2
h
2e
%
& '
(
) * 1
JR
"#
"t+
2
h
2e
%
& '
(
) * JC
2
" #2
"t= 0
!
i( t) = I(t)
cI
!
"U +#$x
$t+M
2
$ x
2
$t= 0
!
JE =h
cI2e(1" cos(# ))
« Washboard » potential : phase difference motion
« damping » « mass»
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Dynamics of a Josephson Junction
!
I( t)
cI= sin("(t))+ J0L
JR
#"(t)
#t+
J0L JC
2
# "(t)
#t
Characteristic times
!
p" = 02#$ JC
cI
!
LR" = 0#
2$cI JR
!
RC" =JR JC
Mc Cumber parameter
!
C" = RC#
LR#=2$
CI JC2
JR
0%
!
sin"#i+$"
$%+
c&
2$ "
2$%
=0!
" =t
LR"
underdamped
overdamped
!
C" # 1
!
C" >>1
R & C smallNo tunnel
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Voltage and current across a current biased JJ
Ibias Current biased overdamped Josephson Junction
!
LR" = 0#
2$cI JR
!
T =2"
LR#2
i $1τLR
!
V =1
TV(t)dt
0
T
" = 0#T
t/τLR0 5 10 15
0
1
2
3
4
5
V(t)
/IcR
J
Quantized pulses
Timescale τLR≈ps
Vmax≈2IcRJ ≈ mV
Energy≈IcΦ0 ≈ aJ
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Rapid Single Flux Quanta logic
Likarev’s basic idea (1985) : dynamical logic
Transmission line Transmission line
State 0 State 1IcRJΦ0
Current biased overdamped JJ (Ib < Ic)
Josephson transmission line
Inductance (RF SQUID)
!
L" =
2LCI
0#
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Dynamics of an RF SQUID
!
L" =
2LCI
0#
Fluxoid quantification
!
L" <<1
!
L" >>1
!
"
0"
= ext"
0"
# L$2%
sin 2%"
0"
&
'
( (
)
*
+ +
Non-hysteretic
Hysteretic
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Storing a pulse
Storing and manipulating pulses
Φ0 < LIc < 2Φ0
Manipulating pulses
RSFQ circuits : JJ and inductances
Φ0 < LIc Φ0 > LIc
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Advantages of RSFQ logic
Robust pulse along the way
IcRJΦ0
Φ0
Intrisinc speed : THz frequency
!
LR" = 0#
2$cI JR
Ic ≈ 0.1 - 1 mA
RJ ≈ 1 - 10 Ω1/τLR ≈ 1-10 THz
Low power consumption
Energy ≈ IcΦ0 f ≈ 0.1 - 1 THz P ≈ 0.1 - 1 nW
N ≈ 1O6 gates P ≈ 0.1 - 1 mW
Overdamped : no tunnel junctions
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A complete logic library
All logic elements possible
NOT
T-NOR
T-AND
Low Tc Micro processor (ISTEC Japan)
• Technology : Nb/Al/AlOx/Nb @4.2 K
• 8000 to 30000 junctions
• Max speed : 770 GHz, sampler
15.5 GHz 1.6 mW
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Superconductive electronics : the Holy Graal ?
Important parameters
!
LR" = 0#
2$cI JR
!
C" = RC#
LR#=2$
CI JC2
JR
0%
unity
!
LR" # JC
CI
Robust against thermal fluctuations
!
CI > Bk T
0"
Increasing current density jC
Increasing superconducting gap IcRN
Decreasing the JJ characteristic spread
Today Low Tc
• Temperature 4.2 K
• Current density 1-3 kA/cm2
• SC gap 1 mV
• 5 to 10% spread
• 30000 JJ
Tomorrow High Tc
100 K
20-30 mV
>>10 kA/cm2
?????
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High Tc Superconductive electronics … today
HTSc Josephson Junctions technology :
reliability, ageing, integration, cost effective
Complex materials
Multi-component oxides (YBa2Cu3O7)
High temperature processing (700-800°C)
Very sensitive to disorder …
High Tc A/D convertor (ISTEC Japan)
• Technology : YBCO @77.7 K
• 10 to 15 junctions
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Outline
1. Superconductive electronics
3. Physics of High Tc nanojunctions
Dynamics of Josephson Junctions
Rapid Single Flux Quanta logic
Actual RSFQ devices
Proximity effect
Quasi-classical diffusive approach
D-wave order parameter symmetry
π-junctions and RSFQ devices
4. Conclusions
2. High Tc Josephson nanoJunctionsIon irradiation of High Tc Superconductors
Making Nanojunctions
Major characteristics of the Nanojunctions
A few applications
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« Standard » High Tc Josephson junctions
Complex materials …
Grain boundary junctions
Alternative technology Ion irradiation
Ramp junctions
Special substrates
Design constraints
Lack of reproducibility
Kahlmann et al & Katz et al APL’98
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High Tc cuprate superconductors
Y
Cu
Ba
O
O
bc
High Tc superconductors
Hole-doped in the Cu02 plane
YBa2Cu3O6+x
Tc=90K Order parameter symmetry : dx2-y2
++
-
-kx
ky
kX
ky
Anistropic 2D Fermi Surface
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Disorder in High Tc Superconductors
Defect in dx2-y2 superconductor depairing
Abrikosov-Gorkov
YBa2Cu3O7
dx2 −y2
++
-
-
k
k’
kx
ky
Local control of the disorder
Nanoscale engineering (ξN)
30K<T<90K Super/Normal/Super Josephson junction
Substrate
YBCO Tc=90K30K
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Proximity effect based Josephson Junctions
SC Normal SC
Phase coherence through normal metal : Josephson coupling
Diffusive case
!
"N(x) #"
N(0
+)e
$x
%N
De Gennes : Rev Mod Physics 1964
!
Ic
= I0 1"T
Tc
#
$ %
&
' (
2
l /)N
sinh(l /)N)
!
"N
=hD
2#kBT
usiv
A few 10 nm
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Towards the insulator
Defect in dx2-y2 superconductor depairing
Low defect concentration : Tc decreases
Lesueur et al (1995)
Abrikosov-Gorkov
YBa2Cu3O7
dx2−y2
++
-
-
k
k’
kx
ky
High dose : towards the insulator
YCu
BaO
O
bc
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Fabrication of High Tc nano-Junctions
Control the defect density through ion irradiation two-steps strategy :
Abrikosov-Gorkov
YBa2Cu3O7
J. Lesueur et al (1995)
# 1
# 1 : drawing channels : (1015 at/cm2)
# 2
# 2 : creating nanoJunctions : (1013 at/cm2)
Substrate
Film SCInsulator SC channel
Junction
Resist
Au
Oxygen 100 keV
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Tailoring at a nanoscale
First step : channel in a YBa2Cu3O7 film (thickness = 1500Å)
Channel
Embedded
Oxygen 100 keV
Second step : nanojunction through a 20 nm slit
30K<T<90K jonction Super/Normal/Super
Oxygen 100 keV
Substrate
Superconductor
Resist
Substrate
SubstrateSubstrateSubstrate
Superconductor
Au
Ins.
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Fabrication of nanojunctions
20nm slit
Hall cross
Width 1 to 5µm
Irradiationthrough Au mask
Au IBE removed Irradiationthrough Resist mask
N. Bergeal et al, APL 2005
JAP 2007
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R(T) measurements
25
20
15
10
5
0
R (!
)
10090807060504030
Température (K)
Tc
Tc’ Tj
Josephson
regime
L=5µm, E=100keV Φ=6.1013at/cm2
L=5µm, E=100keV
Φ=1.5, 3, 4.5, 6.1013at/cm2
ψ2=|ψ2 | eiϕ2ψ1=|ψ1 | eiϕ1
SupraSupra
3.0
2.5
2.0
1.5
1.0
0.5
0.0
R(!
)
908070605040
Température (K)
Tc’<T<Tj Josephson regime
T<Tc’ <Tj Flux flow regime
Extension of the Josephson regime
ΔT=7K → ΔT=20K
High operating T
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I(V) characteristics
Φ=3.1013at/cm2
RSJ behavior
Resistance Rn ranging from 200mΩ to a few Ω
Flux flow behavior
T < Tc’TJ > T > Tc’
70 K72.5 K
Overdamped JJ
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Fraunhofer pattern Ic(B)
Phase control by the vector potential
30
25
20
15
10
5
0
Ic (µA
)
-15 -10 -5 0 5 10 15B (Gauss)
73,35 K
Sinc fit
!
Ic
= I0sin("# #0)
"# #0
Φ0
Josephson length λJ
w = 5 µm
λJ = 2 µmλJ = 3 µmλJ = 4 µm
!
I = Icsin(")
!
" ="1#"
2
∇ϕ = Cste JS + 2πφ0-1 A
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Shapiro Steps
Phase controlled by microwaves
Almost ideal Bessel functions
N. Bergeal, JAP 2007
!
"#
"t=2eV
h
483 597,9 GHz/V
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2000
1500
1000
500
0
Ic (µA
)
7876747270
T (K)
3 1013
at/cm2
500
400
300
200
100
0
Ic (µA
)
85.084.584.083.583.082.5
T (K)
1.5 1013
at/cm2
2000
1500
1000
500
0
Ic (µA
)
72686460
T (K)
4.5 1013
at/cm2
1400
1200
1000
800
600
400
200
0
Ic (µA
)
5550454035
T (K)
6 1013
at/cm2
Ic(T) measurements
!
Ic = I0 1"T
Tj
#
$ % %
&
' ( (
2
l /)Nsinh(l /)N )
De Gennes-Werthamermodel of proximity effect
1.5 1013 at/cm23 1013 at/cm2
6 1013 at/cm24.5 1013 at/cm2
IcRn ~ a few 100 µV
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Major characteristics and reproducibility
N. Bergeal, APL 2005,JAP 2007
High Jc
Reproducible JJ
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Clues for reproducibility and reliability
Embedded junctions
No annealing of the junctions
In-situ Gold protected YBCO films
All dry process
Low dispersion in IcRn (<10%)
Self-shunted junctions
High values of Jc ( a few 104 A/cm2)
Excellent thermal cycling and aging
N. Bergeal et al, APL 2005
THz detectors
Voltage standard
SQUIDs
RSFQ : T flip-flop
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DC SQUIDs with nanojunctions
10µm* 10µm
W ~ 5µm
L = 32 pH
ϕ0 forB~0.08 G
Geometry #1
40
35
30
25
20
15
I c(µA
)
0.20.10.0-0.1-0.2
B (Gaus)
expérience
I=IcIcos(2!"/"
0)I +C
Ic(B) modulation
Cosinus fit with a period 0.08 G
Geometry #2
6µm* 6µm
W ~ 2µm
L = 17 pH
ϕ0 forB~0.3 G
N. Bergeal et al, APL 2006
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SQUID modulations
20
15
10
5
0
V(µV)
-0.2 0.0 0.2
B(Gauss)
I=25µA
I=20µA
I=30µA
I=35µA
50
40
30
20
10
V(µ
V)
-1.0 -0.5 0.0 0.5 1.0
B (Gauss)
I=18µA
I=25µA
I=30µA
Modulation of I -> modulation of V
Sensitivity : dV/dΦ = 60 µV/Φ0
Temperature = 77.7 K
Geometry #1 Geometry #2
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SQUID characteristics
3 1013 at/cm2
T= 77 K
6 1013 at/cm2
T= 51 K
Fraunhofer + SQUID modulation
Noise < 100pV/√Hz (at 100 Hz)
Sensitivity ≈ qq 10-4 Φ0
Excellent cycling and aging
Networks
N. Bergeal, APL 2006 ; APL 2007
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SQUID for « Mr SQUID »
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RSFQ T Flip-Flop
Design D. Crété (Thales)
Kim et al (2002) 100 GHz @ 12K
f
f/2
IN
0.24m
A
1.2pH
0.9pH
0.15mA
IC = 150u
0.9pH
Ic=
150u
2.1pH
IC = 300u4.3pH
7.1pH
IC=350uA
IC = 300u
0.27mA
Ic=250u
A
1.0pH
OUT
JTL BIAS
Ib1 = 0.25 mA
JTL
TFF BIAS
Ic3 =Ic4 0.38 mA
=
Ib3= 0.28 mA
Ic7 = Ic6 = 0.32 mA
Ic1=Ic20.18 mA
=
Ib4 = 0.12 mA
Ib2 = 0.22 mA
L = 7.1pH
GND
OUT
IN
A
IC=350uA
GND
A
A
f/2
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Outline
1. Superconductive electronics
3. Physics of High Tc nanojunctions
Dynamics of Josephson Junctions
Rapid Single Flux Quanta logic
Actual RSFQ devices
Proximity effect
Quasi-classical diffusive approach
D-wave order parameter symmetry
π-junctions and RSFQ devices
4. Conclusions
2. High Tc Josephson nanoJunctionsIon irradiation of High Tc Superconductors
Making Nanojunctions
Major characteristics of the Nanojunctions
A few applications
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A bit of physics …
Tc , resistivity r(T) vs defects
Damage profile (SRIM)
?
Reduced size ?
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« No-interface » Josephson Junctions
SC Normal SC
!
"N
=hD
2#kBT
Strength of the coupling
Low interface resistance
Fermi Velocities match
Beyond De Gennes’s approximation
No true interface
Self-consistent calculation of the local gap
Calculating the Josephson critical temperature
Calculating Ic(T) for all temperatures
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Quasi-classical approach of the proximity effect
ωn=πkBT(2n+1) Matsubara frequencies
!
"(x) = #S2$K
BT sin%
n
&n
'!
tan"N
=#
$N
Usadel equations parametrized in θ
!
hD(x)
2
" 2#n
"x 2$%
nsin#
n+ &(x)cos#
n$'
AB(x)sin#
ncos#
n= 0
Self-consistant gap equation
Homogeneous SC
G=cosθ
F=sinθ
Limits conditions
Pairs
Quasiparticles
Depairing ΓAB
Δ(x) profil along the junctionIn the limit of vanishing current
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Computing the Josephson coupling temperature
80
60
40
20
0
T (
K)
86420
dose* 1013
at/cm2
Régime normal
Tj
T'c
Régime Josephson
Régime flux-flow
Flux-flowregime
Normalregime
JosephsonregimeTc’
TJ
1.0
0.8
0.6
0.4
0.2
0.0
!/!
0
-400 -200 0 200 400
x (nm)
89K
88K
87K
86K
84K
82K
80K
74K
60K
40K
N. Bergeal et al, submitted to PRL
TJ
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Computing the critical current density
Usadel equations parametrized in θ
Homogeneous SC
G=cosθ
F=sinθ Pairs
Quasiparticles
Depairing ΓAB
!
hD(x)
2
" 2#n
"x 2$%
nsin#
n+ &(x)cos#
n$'
AB(x)sin#
ncos#
n
$hD(x)
2
"(
"x
)
* +
,
- .
2
sin(#)cos(#) = 0
!
hD(x)
2
" 2#n
"x 2$%
nsin#
n+ &(x)cos#
n$'
AB(x)sin#
ncos#
n= 0
Depairing by supercurrent χ
ωn=πkBT(2n+1) Matsubara frequencies
Supercurrent inside the junction
!
j(x) = "#eNDT$%
$xsin
2&'
(
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Comparison with eperiments
Quantitative results for the critical current of our Josephson junctions
Depairing coefficient
Defects profile
With NO adjustable parameters
Irradiations on full films
SRIM simulations
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Changing the junctions parameters
Importance of the slit size and irradiation doses
4 different doses
Simulate various
slit size
film thickness
irradiation dose, …
optimize Josephson junctions
Specific temperaturescritical currents
Reduce spread (identifyimportant parameters)
Ic(T)
Temperature (K)
Ic(A
)
3 different slit size
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Deeper look in the low temperature regime
Want to reach high critical current lower temperature
Strong anharmonicity develops …
Lower temperatures
2.5
2.0
1.5
1.0
0.5
V(t
)/IcR
n
300025002000150010005000
Time (a.u.)
RSFQ pulses robust against anharmonicity
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A d-wave order parameter
1D Quasi-classical equations with an isotropic order parameter
2D symmetry of the d-wave order parameter
!
hD(x)
2
" 2#n
"x 2$%
nsin#
n+ &(x)cos#
n$'
AB(x)sin#
ncos#
n= 0
kx
ky
dx2−y2
++-
-kx
ky
• Anisotropy of the order parameter
• Sign change : Andreev Bound States
• π-junctions and RSFQ circuits
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Order parameter anisotropy ?
dx2−y2
++-
-
kk’
kx
ky
Orientations θ = 0 °,10 °,20 °,30 °,40 °,45°
(a,b)
(a,b)
θ D-wave order parameter
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Order parameter anisotropy ?
θ = 0°θ = 45°
No effect !!
Diffusion ?
2d order parameter ?
Anisotropic pairing !
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Back to Eilenberger equations …
No diffusion approximation
Usadel : l < ξ
Eilenberger : l >< ξ
No wave vector dependence
Confined geometry : full d-wave calculation in a channel
a fe
w ξ
Den
sity
of
stat
es
DOS (E=0)
Andreev Bound State
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Andreev Bound State
D-wave SCInsulator|!|
e-
x0 dn
h+e-
h+
k=kf
k=-kf
!1ei"1 !2e
i"2
SC1 SC2Metal
Surface Bound State
ϕ1-ϕ2=π Bound State E=0
Making a π junctionw = a few ξ
Gumann et al APL 2007
Ic>0
Ic<0
Ic=I0sin(Δϕ)
Ic=I0sin(Δϕ+π)
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Spontaneous super-current
π SQUID
π junction
0 junctionGround state j=0Flux = 0
Ground state j≠0Flux = φ0/2
LIc > φ0
Free energy
Spontaneous current
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π-SQUID in RSFQ circuits
Spontaneous half flux quanta in YBCO/Nb SQUIDs
φ0/2
Numerous bias leads in RSFQ circuits
Ortlepp et al Science 2006
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Toggle flip-flop
Comparison with and without π-junctions
Actual device
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Outline
1. Superconductive electronics
3. Physics of High Tc nanojunctions
Dynamics of Josephson Junctions
Rapid Single Flux Quanta logic
Actual RSFQ devices
Proximity effect
Quasi-classical diffusive approach
D-wave order parameter symmetry
π-junctions and RSFQ devices
4. Conclusions
2. High Tc Josephson nanoJunctionsIon irradiation of High Tc Superconductors
Making Nanojunctions
Major characteristics of the Nanojunctions
A few applications
![Page 61: HTc Josephson nano-junctions : physics and applications · 2017-12-28 · Dynamics of Josephson Junctions Rapid Single Flux Quanta logic Actual RSFQ devices Proximity effect Quasi-classical](https://reader030.fdocuments.net/reader030/viewer/2022041014/5ec559bc13b08355f20aa5e4/html5/thumbnails/61.jpg)
Conclusions
RSFQ logic : a promissing technology
High Tc Josephson nano-Junctions : a promissing path
Applications are on their way
Proximity effect based Josephson Junctions
D-wave order parameter :it matters !
Thank you !JnJ : Bergeal & al, APL 87, 102502 (2005),
JAP 102, 083903 (2007)Squids : Bergeal & al, APL 89, 112515 (2006)
APL 90, 136102 (2007)Optimization : J. Lesueur & al,
IEEE Trans Appl Sup 17, 963 (2007)M. Sirena & al, JAP 101, 123925 (2007)M. Sirena & al, APL 91, 142506 (2007)M. Sirena & al, APL 91, 262508 (2007)