Nano-superconductors: from fundamentals to applications

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The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 1
1
Nano-superconductors:
fromfundamentals to
applications
Victor V. Moshchalkov
INPAC-Institute for Nanoscale
Physics and Chemistry
Catholic University of Leuven,
Belgium
ħω
e
μ
B
ħω
e
μ
B
2
superconductor
1.R=0
below Tc, no losses in wires!
(now about 15% of energy is lost
in cables/wires)
2.B=0

magnetic levitation
The Miraculous Physics and
Applications of Superconductors
Resistance
Temperature
H. Kamerlingh-
Onnes, 1911
Nobel prize 1913
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 2
3
local field
order
parameter
supercurrents
Vortex (fluxon)
φ
0
Vortices in Atmosphere,
in Superconductors...
Current

Lorentz force

Vortex motion

Dissipation
current
F
L
Pinning
Inhances critical current!
100-1000 km
10-100 nm
Abrikosov vortex lattice, Nobel Prize 2003
4
QuantumDesign of Superconducting
Critical Parameters

To design the optimum
confinement pattern for
vortices and condensate by
using their quantumnature

To use modern
nanostructuring techniques
to fabricate these patterns

To improve dramatically
superconducting critical
parameters
current j
t
e
m
p
e
r
a
t
u
r
e
T
magnetic
field H
T
c0
H
c2
or H
c
j
c
Superconducting
state
Nature 373, 319 (1995)
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 3
5
VORTEX CORE PROBLEM
V~L/R
Divergent V for R=0,
solution: L must be zero, finite L impossible!
Alternative: V~L/R x (|Ψ|
2
=0) !!! Finite L is possible!!
VORTEX CORE
6
VORTEX MATTER IN
SUPERCONDUCTORS
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 4
7
superconductor
1.R=0
below Tc, no losses in wires!
(now about 15% of energy is lost
in cables/wires)
2.B=0

magnetic levitation
The Miraculous Physics and
Applications of Superconductors
Resistance
Temperature
H. Kamerlingh-
Onnes, 1911
Nobel prize 1913
8
1.R=0
below Tc
2.B=0
Magnetic levitation - MAGLEV
The Miraculous Physics and
Applications of Superconductors
MRI imaging
SQUID
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 5
9
The Miraculous Physics and
Applications of Superconductors

International Thermonuclear (Tokamak)
Experimental Reactor
10
The Miraculous Physics and
Applications of Superconductors

a hydrogen plasma torus operating at over
100 million °C, and will produce 500 MW of
fusion power
B = 13 T
De Gennes: "We say that we will put the sun into a box. The idea is pretty.
The problem is, we don't know how to make the box"
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 6
11
VORTEX MATTER IN NANO-
SUPERCONDUCTORS
12
VORTEX CORE PROBLEM
V~L/R
Divergent V for R=0,
solution: L must be zero, finite L impossible!
Alternative: V~L/R x (|Ψ|
2
=0) !!! Finite L is possible!!
VORTEX CORE
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 7
13
14
ABRIKOSOV VORTICES
50 years in 2003:
discovered in 1953,
published in 1957
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 8
15
Abrikosov
Abrikosov vortices
16
Abrikosov parameter β
A
=1.19
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 9
17
18
Abrikosov parameter β
A
=1.16
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 10
19
20
STM
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 11
21
QuantumDesign of Superconducting
Critical Parameters

To design the optimum
confinement pattern for
vortices and condensate by
using their quantumnature

To use modern
nanostructuring techniques
to fabricate these patterns

To improve dramatically
superconducting critical
parameters
current j
t
e
m
p
e
r
a
t
u
r
e
T
magnetic
field H
T
c0
H
c2
or H
c
j
c
Superconducting
state
Nature 373, 319 (1995)
22
0
1
2
3
4
5
1
2
3
4
5 µm
5000 A
0
Pb(500Å) film with a
square antidot lattice
Huge enhancement of critical current + ‘matching’ effects
critical
PRL 74 (1995), PRB 57 (1998), Science 302, 1159 (2003)
Local vortex configuration ??
Nanoengineered Pinning Arrays
to Enhance Critical Current
Criticalcurrent
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 12
23
Φ
0
-Vortex lattice

0
-Vortex lattice

0
-Vortex lattice
Multiquanta
Vortex Lattices

0
-Vortex lattice @H
2
Φ
0
-Vortex lattice @H
1
Direct vortex imaging by
scanning Hall probe microscope:
vortices are white spots
PRL 74 (1995), PRB 54 (1996), PRB 57 (1998)
24
•Novel “vortex crystals” have been discovered
•Fundamental problem of “optimum pinning” has been solved
•Critical currents have been very strongly enhanced
Science 274,1167 (1996)
Lorentz microscopy of fluxons
Novel “Vortex Crystals” in
Nanostructured Superconductors
Pinning centers
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 13
25
WHAT NEXT?

Similar vortex physics with superfluids and
Bose–Einstein condensates

Vortex control and manipulation

Ratchet effects in nanosupercnductors
26
Fromsuperconductors to
Bose-Einstein condensates

Novel vortex crystals and
molecules discovered in
nanostructured superconductors:
roadmap for later discoveries of
similar vortex states in Bose-
Einstein condensates

Single quantumand multiquanta
vortices have been already
discovered

More to come (vortex molecules,
antivortices,...)
Single quantum vortices in
Rotating Bose-Einstein condensates.
Figure courtesy of Todd Gustavson at MIT
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 14
27
WHAT NEXT?

Similar vortex physics with superfluids and
Bose–Einstein condensates

Vortex control and manipulation
(ratchet effects, etc)
28
Ratchet and pawl. The ratchet is connected by an axle with the
paddles and with a spool, which may lift a load.
In the absence of the pawl (leftmost object) and the load, the random
collisions of the surrounding gas molecules (not
shown) with the paddles cause an unbiased rotatory Brownian motion.
The pawl is supposed to rectify this motion so as
to lift the load.
Ratchets
M. von Smoluchowski, 1912; R.P. Feynman, 1966
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 15
29
Ratchets: self-propelled droplets
H. Linke, U of Oregon
30
Ratchets:self-propelled droplets
H. Linke, U of Oregon
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 16
31
Nanostructuring
O. Daldini et al. (1974)
1D
2D
A. F. Hebard et al. (1977)
32
Square antidot lattice
d = 1.5 µm
a = 0.5 µm
ξ(0) = 40 nm
Λ
a
(0)= 48 nm
t = 50 nm
2
4
0
0
2
4
µm
d
a
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 17
33
I
F
L
B
θ = 90°
θ = 180°
34
Square array of rectangular antidots
0
2
4
µm
2
4
0
ξ(0) = 51 nm
Λ
a
(0)= 53 nm
t = 150 nm
d = 1.5 µm
a
x
= 0.6 µm
a
y
= 1.15 µm
a
x
d
a
y
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 18
Experimental realization
Asymmetric pinning
centers
µm
0
2
4
6
0
2
4
6
36
Asymmetric Pinning
Δy
pp
= 0.3 a
yo
y
x
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 19
37
U
p(y)
F
Ly
= 2.00
y
Δ
y
pp
= 0.3 a
y0

I
Asymmetric Pinning
F
L

F
Ly
= -2.00
y
Δ
y
pp
= 0.3 a
y0
U
p(y)
I
F
L
38
Model vs. Experiment
0.9 1.0 1.1 1.2 1.3 1.4 1.5
0.0
0.2
0.4
0.6
0.8
1.0
H = 0.99 H
1
T = 0.97 T
c
f = 1 kHz
Normalized DC Voltage
Normalized AC Amplitude
M 0 (overdamped limit)
γ/M = 1.8 (underdamped regime)
Close to H
1
vortex-
vortex interations mostly
cancel out by symmetry

One particle model
PRL 94, 057003 (2005)
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 20
39
Multiple sign reversal of a ratchet
effect
C. De Souza Silva, J.Van de Vondel, M. Morelle,
V.V. Moshchalkov, Nature, 440, 651 (2006)
40
Multiple reversals of a ratchet effect
C. De Souza Silva, J.Van de Vondel, M. Morelle,
V.V. Moshchalkov, Nature, 440, 651 (2006)
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 21
41
VORTEX-ANTIVORTEX MATTER
IN SUPERCONDUCTORS
42
Von Karman Vortex Street
+1 -1 +1 -1 +1 -1...
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 22
43
44
-1
+1
?
?
!
+3
3 = 1 + 1 + 1
3 = 3 + 0
3 = 1+1+1+1-1
Symmetry-induced
Antivortices
+1
+1
+1
+1
+1
+1
Lowest energy solution:
•Superconductors
•Superfluids
•Bose-Einstein Condensates
•Vortex-antivortex states in
triangle have remarkable
similarities with leptons
and quarks
Nature 408, 833 (2000)
also in News and Views
Zoom !
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 23
45
-2 
0
-1 
0
+1 
0
+2 
0
+3 
0
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9 10

Φ
/
Φ
0
a2/ξ2(T)
Irrep E
-
46
The Microelectronics Training Center, IMEC v.z.w.
www.imec.be/mtc
delfi.imec.be
MTC 2008: Capita Selecta
IMEC© 2008
Victor V. Moshchalkov
Page 24
47
Full GL
48
Vortex Matter in Superconductors:
Reference vs Nanostructured

Triangular single quantum
Abrikosov vortex lattice

Multiquanta vortex lattices
(triangular, square)

Composite vortex lattices

Variety of new vortex crystals

Symmetry-induced antivortices

Vortex molecules

Vortex-antivortex molecules in
superconductor/ferromagnet
hybrids

Domain wall superconductivity
Φ
0
Reference Type II superconductors Nanostructured superconductors