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1 31.12.2014
Experiments with arrays of
Josephson junctions near
superconductor-insulator transition
Alexey Ustinov
Karlsruhe Institute of Technology, Germany
Acknowledgements:
H. Rotzinger, R. Schäfer, A. Shnirman , N. Vogt, J. Zimmer
Alexey Ustinov Arrays of Josephson junctions
2
Outline
Josephson junctions and arrays
Fabrication of Josephson junctions
Measurement techniques
Experimental limitations and typical problems
Brief history of experiments with JJ arrays near S/I transition
2D arrays
1D/2D channels – shooting and localizing quantum vortices
1D arrays – searching for ballistic Cooper pairs
Our recent experiments with 1D arrays
tuning EJ/EC , dual IV-curves
conductance ~ EJ2, incoherent Cooper pair tunneling
thermal activation of charges
depinning of charges => talk of A. Shnirman today
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
3
Josephson junction
)(exp 111 i
)(exp 222 i
sinCS II
teV
d
d
2
superconductor
tunnel barrier
superconductor
21 superconducting phase difference:
Josephson
relations
cos2d
d 0
C
SJ
It
IVL
Josephson inductance
Alexey Ustinov
4
4
J
CC
eE
2
2
2
0 c
J
IECharging energy Josephson energy
flux
limit
JC EE
1 nUncertainty relation for a superconductor:
charge
limit
JC EE
810electrons
Energy scales
VG
insulating state superconducting state
5
Phase-charge duality in
Josephson junction circuits
31.12.2014
Review of the duality ideas for JJ arrays:
W. Guichard and F. W. J. Hekking, Phys. Rev. B 81, 064508 (2010)
J. E. Mooij and Yu. V. Nazarov, Nature Phys. 2, 169 (2006)
Duality between
Josephson junction and
phase slip junction
CJ EE CJ EE
phase inertia charge inertia
Alexey Ustinov Arrays of Josephson junctions
6 Alexey Ustinov Arrays of Josephson junctions 31.12.2014
Junction size and energy scales
J
CC
eE
2
2
2
0 c
J
IE
charging energy
Josephson energy
0
0 exp~2 d
dA
RI
n
c
d
a b
d
ACJ
~
baA junction area
dtunnel barrier thickness
0
2 exp~d
ddA
E
E
C
J
Typically, achieving requires 2μm01.0A1
C
J
E
E
7
Simple estimate of conditions needed
for observing quantum effects in a JJ
A simple estimate for value of the junction
resistance above which clear quantum effects
become visible
The Heisenberg relation
taking and
the junction resistance should satisfy
for quantum effects to be observable
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
E
C
eEE C
2
2
RC
24e
hRR Q
8
Josephson junctions and weak links
Prof. Max Mustermann - Title 31.12.2014
SIS
SNS
tunnel junction
normal metal
point contact
nano-bridge
(constriction)
intrinsic junctions
(crystal)
proximity link
N
S
SISISISISISISISISIS
9
The simplest way of making
a Josephson junction
Alexey Ustinov Arrays of Josephson junctions
10
Josephson junctions and weak links
Prof. Max Mustermann - Title 31.12.2014
SIS
SNS
tunnel junction
normal metal
point contact
nano-bridge
(constriction)
intrinsic junctions
(crystal)
proximity link
N
S
SISISISISISISISISIS
11
Nb-AlOx-Nb
Nb sputtering
Al sputtering and oxidation
Tc = 9.2 K
Jc from 102 to 104 A/cm2
Al-AlOx-Al
Al evaporation
Al oxidation
Tc = 1.2 K
Jc from 1 to 102 A/cm2
Fabrication of Josephson devices
1. circuit layout (CAD)
2. fabrication of photomasks
3. deposition of superconducting and
insulating layers on a wafer
4. photo (or e-beam) lithography
5. dicing the wafer into chips
Alexey Ustinov Arrays of Josephson junctions
12
CAD = computer aided design
15 mm
0.15 mm
Example:
2D array
JJs
Circuit layout
Alexey Ustinov Arrays of Josephson junctions
13
design rules of Hypres Inc. See: http://www.hypres.com
Si substrate resistive layer (Mo or AuPd) Insulator (SiO2)
Nb-AlOx-Nb
insulator
Nb
Stacking thin-film layers: Example
Alexey Ustinov Arrays of Josephson junctions
14
Clean room
mask alignment
Photolithography can be used
for JJ size down to 1 mm
Wafer processing
Alexey Ustinov Arrays of Josephson junctions
15
Evaporation of superconducting thin films
Prof. Max Mustermann - Title 31.12.2014
PLASSYS electron beam evaporation unit with load lock. The unit is dedicated for
fabrication of Josephson junctions and was installed at RQC lab at ISSP
Chernogolovka in June 2014
16
In a first step metal is evaporated from one angle, indicated by the dark arrows
and dark structures on the substrate surface. The evaporation from another angle
leads to an overlap of the features in the middle. (Picture by Mattias Urech)
Electrom beam lithography
Al deposition
wafer
resist
Electron beam lithography can
produce JJ size < 0.1 mm
Shadow evaporation technique
Alexey Ustinov Arrays of Josephson junctions
17
Pattern is written
in the resist using
an electron beam
After the sample
is developed, a
suspended resist
bridge is left
The bottom layer
of aluminum is
deposited under
an angle +a
The sample is
exposed to O2
to form the
oxide layer
The top layer of
aluminum is
deposited under
an angle -a
Lift-off in acetone
removes the
resist and a
tunnel junction is
left
Shadow evaporation of Al-AlOx-Al
junctions
Alexey Ustinov Arrays of Josephson junctions
18
Shadow evaporation of SQUID arrays
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
step 1
step 2
result
19
Sub-micron Al-AlOx-Al JJs produced by
electron beam lithography
3-JJ flux qubit
Alexey Ustinov Arrays of Josephson junctions
20
Experiments with JJs
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
V I
voltage
current
detection of
Josephson
radiation
applying
microwaves
1 GHz – 1 THz
AC techniques DC techniques
cheap and easy expensive and more difficult
21
Experiments with 2D arrays
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
22
Early works on 2D Josephson arrays
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
Ph.D. Thesis of L.J. Geerligs, Delft 1990
Review: R. Fazio and H. van der Zant, Phys. Rep. 355, 235 (2001)
23
Observation of S/I transition in 2D
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
H.S.J. van der Zant, W.J. Elion, L.J. Geerligs, J.E. Mooij, Phys. Rev. B 54, 10081 (1996)
24
Field-induced S/I transition in 2D
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
H.S.J. van der Zant, W.J. Elion, L.J. Geerligs, J.E. Mooij, Phys. Rev. B 54, 10081 (1996)
25
Experiments with 1D/2D channels
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
26 Alexey Ustinov Arrays of Josephson junctions 31.12.2014
Quantum vortices in 1D/2D channels
A. van Oudenaarden and J. E. Mooij, Phys. Rev. Lett. 76, 4947 (1996)
A. van Oudenaarden, S. J. K. Várdy, and J. E. Mooij, Phys. Rev. Lett. 77, 4257 (1996)
27
Quantum vortices in 1D/2D channels
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
A. van Oudenaarden and J. E. Mooij, Phys. Rev. Lett. 76, 4947 (1996)
Mott insulator
28
Experiments with 1D arrays
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
29
Shadow evaporation of SQUID arrays
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
step 1
step 2
result
30 31.12.2014 Alexey Ustinov Arrays of Josephson junctions
31
Observation of S/I transition in 1D
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
E. Chow, P. Delsing, and D. B. Haviland, Phys. Rev. Lett. 81, 204 (1998)
zero-bias resistance,
extrapolated to T = 0,
is independent of
length at a critical
magnetic field
32 31.12.2014 Alexey Ustinov Arrays of Josephson junctions
33 31.12.2014 Alexey Ustinov Arrays of Josephson junctions
34
31.12.2014
assumption taken:
equation of motion for the charge:
Alexey Ustinov Arrays of Josephson junctions
35
Duality between charge and flux solitons
31.12.2014
(x)
x 0
magnetic flux
parallel array EJ >> EC
Q(x)
x 2e
electric charge
series array EJ << EC
Alexey Ustinov Arrays of Josephson junctions
36
Soliton pinning problem
31.12.2014
For flux regime:
Φi – random fluxes
-Φ0/2 < Φi < Φ0/2
pinned random fluxes
0
-e/2 < Qi < e/2
pinned random charges
2e
Alexey Ustinov Arrays of Josephson junctions
37
Depinning of solitons
31.12.2014
voltage
curr
ent
Idepin
0 voltage
curr
ent
Vdepin 0
depinning of flux soliton depinning of charge soliton
Alexey Ustinov Arrays of Josephson junctions
38
Problem of non-uniform voltage bias
31.12.2014
V+
Alexey Ustinov Arrays of Josephson junctions
39
Uniform forcing of solitons
31.12.2014
Vin
bias “comb” yielding uniform voltage bias
x 2e x 0
magnetic flux electric charge
Vin
force
Alexey Ustinov Arrays of Josephson junctions
40
Implementation of the uniform biasing
for charge solitons
31.12.2014
voltage bias gates
SQUID array
non-uniform voltage bias
20 µm
V+ V-
V+ 2e
force
Alexey Ustinov Arrays of Josephson junctions
41
Experiments with JJ arrays in Karlsruhe
31.12.2014 Alexey Ustinov Arrays of Josephson junctions
R. Schäfer, W. Cui, K. Grube, H. Rotzinger, and A. V. Ustinov, arXiv:1310.4295
42
Tunable Josephson energy EJ
31.12.2014 Alexey Ustinov Arrays of Josephson junctions
R. Schäfer, W. Cui, K. Grube, H. Rotzinger, and A. V. Ustinov, arXiv:1310.4295
43
Large-scale I-V characteristics
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
R. Schäfer, W. Cui, K. Grube, H. Rotzinger, and A. V. Ustinov, arXiv:1310.4295
44
Conductance of dissipative branch
31.12.2014 Alexey Ustinov Arrays of Josephson junctions
R. Schäfer, W. Cui, K. Grube, H. Rotzinger, and A. V. Ustinov, arXiv:1310.4295
45
Re-trapping voltage change with flux
31.12.2014
Re-trapping voltage Vretr
Vretr
Vretr
Vretr
-1
Alexey Ustinov Arrays of Josephson junctions
R. Schäfer, W. Cui, K. Grube, H. Rotzinger, and A. V. Ustinov, arXiv:1310.4295
46
Offset voltage change with flux
31.12.2014
Voff
Voff
Voff
-1
Offset voltage Vretr
Alexey Ustinov Arrays of Josephson junctions
R. Schäfer, W. Cui, K. Grube, H. Rotzinger, and A. V. Ustinov, arXiv:1310.4295
47
Switching and retrapping voltages
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
48
Retrapping voltage normalized
to the number of islands
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
255
59
39
number of islands
© A. Fiebig and R. Schäfer
49
Switching voltage normalized
to the number of islands
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
255
59
39
© A. Fiebig and R. Schäfer
50
Switching voltage histograms
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
© R. Schäfer
51 Alexey Ustinov Arrays of Josephson junctions 31.12.2014
Switching voltage histograms
© R. Schäfer
52
Thermally activated conductance
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
Φ/Φ0 = 0.5 Φ/Φ0 = 0
© R. Schäfer
53
Thermally activated conductance in
arrays of small Josephson junctions
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
J. Zimmer, N. Vogt, A. Fiebig, S. V. Syzranov, A. Lukashenko, R. Schäfer, H. Rotzinger,
A. Shnirman, M. Marthaler, and A. V. Ustinov, Phys. Rev. B 88, 144506 (2013)
experimental setup
54
I-V characteristic of the 255-JJ array
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
J. Zimmer, N. Vogt, A. Fiebig, S. V. Syzranov,
A. Lukashenko, R. Schäfer, H. Rotzinger, A.
Shnirman, M. Marthaler, and A. V. Ustinov,
Phys. Rev. B 88, 144506 (2013)
55
Thermally activated conductance in
arrays of small Josephson junctions
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
J. Zimmer, N. Vogt, A. Fiebig, et al.,
Phys. Rev. B 88, 144506 (2013)
inelastic hopping of Cooper pairs
between neighboring islands
! gap of Al
thermally generated quasiparticles?
56
Charge depinning in arrays of small JJs
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
N. Vogt, R. Schäfer, H. Rotzinger, W. Cui, A. Fiebig, A. Shnirman, and A. V. Ustinov,
arXiv (2014)
The switching voltage
normalized to the array
length N as a function of the
magnetic flux for 3 arrays of
length 255
switching voltage
Larkin length
disorder correlation parameter
=> talk of A. Shnirman today
57
Charge depinning in arrays of small JJs
Alexey Ustinov Arrays of Josephson junctions 31.12.2014
N. Vogt, R. Schäfer, H. Rotzinger, W. Cui, A. Fiebig, A. Shnirman, and A. V. Ustinov,
arXiv (2014)
The switching voltage
normalized to array length N
as a function of the
magnetic flux for arrays of
length 39, 59 and 255
switching voltage
Larkin length
disorder correlation parameter
=> talk of A. Shnirman today
58
Summary
Brief review of experiments with JJ arrays near S/I
transition
2D arrays
1D/2D channels – shooting and localizing quantum
vortices
1D arrays – searching for ballistic Cooper pairs
Our recent experiments with 1D arrays
tuning EJ/EC
conductance ~ EJ2, incoherent Cooper pair tunneling
thermal activation of charges
depinning of charges => talk of A. Shnirman today
Alexey Ustinov Arrays of Josephson junctions 31.12.2014