Leçon #3: Systèmes S/F - Université de Sherbrooke€¦ · Résumé: Systèmes S/F...
Transcript of Leçon #3: Systèmes S/F - Université de Sherbrooke€¦ · Résumé: Systèmes S/F...
Leçon #3: Systèmes S/F
Norman Birge
Michigan State University
Résumé: Systèmes S/F
• L’histoire ancienne: Meservey & Tedrow • La réflection d’Andréev croisée • La réflection d’Andréev à l’interface S/F (en
présence de l’énergie d’échange) • L’éffet de proximite dans les systèmes S/F
• Tc des multicouches • Densité d’états • Jonctions Josephson: junctions “”
• Corrélations induit du type “spin-triplet” • Jonctions Josephson • Tc des multicouches
Spin-dependent tunneling: S/F Tedrow & Meservey, PRL 26, 192 (1971); Meservey & Tedrow, PRB 7, 318 (1973)
S/I/N tunnel junction Split quasiparticle density of states with B field
S/I/F tunnel junction with B field
Spin-dependent tunneling S/F Tedrow & Meservey, PRL 26, 192 (1971); Meservey & Tedrow, PRB 7, 318 (1973)
Spin imbalance in a superconductor Quay, Chevallier, Bena, Aprili, Nature Phys. 9, 84 (2014).
Crossed Andreev Reflection (CAR) Deutscher & Feinbert, Appl. Phys. Lett. 76, 487 (2000)
The reflected hole goes into a different wire! The two wires must touch S within a distance S
Experiments on Crossed Andreev Reflection (CAR) - 1 Beckmann, Weber & von Löhneysen, PRL 93, 197003 (2004).
Experiments on Crossed Andreev Reflection (CAR) - 2 Russo, Kroug, Klapwijk & Morpurgo, PRL 95, 1027002 (2005).
Experiments on Crossed Andreev Reflection (CAR) - 3 Hermann, Portier, Roche, Levi-Yeyati, Kontos & Strunk, PRL 104, 026801 (2010).
Andreev Reflection at an S/F interface and the superconducting proximity effect in F. Go to whiteboard!
Buzdin, Bulaevskii & Panyukov, JETP Lett. 35, 178 – 180 (1982). Demler, Arnold & Beasley, PRB 55, 15174 (1997)
k
E
-kF
-kF
kF
kF
Proximity effect: “leakage of Cooper pairs”
from S to F
FexFF vEQkk 2
ex
FF
E
D
ex
FF
E
vQ
2
1 ballistic
diffusive
ballistic
diffusive D = diffusion
constant
2Eex
Tk
vv
B
FFN
2
Tk
DD
B
NNN
2
S F
Compare with “normal metal
coherence length:
Pair correlations oscillate in F with
wavevector Q. Length scale of
oscillations is very short due to large Eex.
Proximity effect: S/N vs. S/F
)/exp()( 0 Nxx )/exp()/cos()( 0 FF xxx
nmfewE
D
ex
FF
~
NF
x
mfewTk
D
B
NN
2
How can we detect the oscillating correlation function?
How to detect the oscillating pair correlation function?
Jiang, Davidovic, Reich, Chien, PRL 74, 314 (1995).
1. Measure Tc of S/F bilayers as a function of dF
S F
dF
Problem: interpretation controversial due to magnetic dead layers.
How to detect the oscillating pair correlation function?
Kontos, Aprili, Lesueur, Grison, PRL 86, 304 (2001)
2. Measure tunneling density of states in S/F/I/N structure, as function of dF
S F I N
dF
How to detect the oscillating pair correlation function?
3. Measure critical current of S/F/S Josephson junction, as function of dF
Ryazanov et al., PRL 86, 2427 (2001).
Weak F: Cu48Ni52 alloy, vary T
Kontos, Aprili … 89, 137007 (2002)
Weak F: Pd88Ni12, vary dF
0-state: Is = Ic sin(f2-f1) -state: Is = Ic sin(f2-f1+) S F S
dF
How to detect the oscillating pair correlation function?
3. Measure critical current of S/F/S Josephson junction, as function of dF
Oboznov et al., PRL 96, 197003 (2006).
More Cu48Ni52 alloy
Robinson, Piano, Burnell, Bell, Blamire, PRL 97, 177003 (2005)
Strong F: Co
0.0 1.0 2.0 3.0 4.0 5.0
dCo (nm)
I cR
N (
mV
)
0-state: Is = Ic sin(f2-f1) -state: Is = Ic sin(f2-f1+) S F S
dF
2001 Prediction: spin-triplet pair correlations
i) are long-ranged in F
ex
FS
FE
D
Tk
D
B
FT
F
2
T
F
S
F
Singlet Triplet
Bergeret, Volkov & Efetov, PRL 86, 4096 (2001); PRL 90, 117006 (2003)
Kadrigrobov, Shekhter & Jonson, Europhys. Lett. 54, 394 (2001)
S F
S F2 F1
k
E
-kF
-kF
kFkF
or
ii) can be induced by noncollinear magnetization
S/F/S Josephson junction can carry
spin-triplet supercurrent
Bergeret, Volkov & Efetov, PRL 86, 4096 (2001)
Houzet & Buzdin, PRB 76, 060504(R) (2007):
Non-collinear magnetizations convert pairs
from spin-singlet to spin-triplet dF
Log(Ic)
dF
singlet
triplet
Tk
D
B
FT
F
2
ex
FS
FE
D
Signature of spin-triplet supercurrent:
1. Sputter S/F/S
2. Pattern pillars with photolithography
Nb
Nb bottom contact
F
Au
Image reversal photoresist
Si Substrate
Sample Fabrication
10 – 40 m
Nb
Nb bottom contact
F
Au
Si Substrate
Si Ox
1. Sputter S/F/S
2. Pattern pillars with photolithography
3. Ion mill
4. Deposit SiOx
Sample Fabrication
10 – 40 m
Nb bottom contact
F
Au
Si Substrate
Si Ox
1. Sputter S/F/S
2. Pattern pillars with photolithography
3. Ion mill
4. Deposit SiOx
Nb top contact
1. Sputter S/F/S
2. Pattern pillars with photolithography
3. Ion mill
4. Deposit SiOx
5. Liftoff
6. Deposit top Nb contact
Sample Fabrication
10 – 40 m
Measurement
Low sample resistance ( 100 W)
Measure with SQUID-based
current comparator circuit
Ic critical current
-0.2 -0.1 0.0 0.1 0.2
-5
0
5
V (
nV
)
I (mA)
Ic -Ic
supercurrent
Measure at T = 4.2 K in “quick-dipper”
cryostat in helium storage dewar
I-V characteristic of overdamped
Josephson junction
Problem: Large-area S/F/S junctions with strong
ferromagnets distorted Fraunhofer patterns
-20 -10 0 10 200.00
0.02
0.04
0.06
I c (
mA
)
H (Oe)
dCo = 5 nm, 2R = 40 m
2R
2L + dF Hext
Random Fraunhofer pattern due
to complex domain configuration
Nb
Co
Nb
Solution: Co/Ru/Co synthetic antiferromagnet
cancels flux and restores Fraunhofer pattern
-20 -10 0 10 200.00
0.04
0.08
0.12
0.16
0.20
I c(m
A)
H (Oe)
dCo = 13 nm
w = 20 m
-20 -10 0 10 200.00
0.02
0.04
0.06
I c (
mA
)
H (Oe)
dCo = 5 nm
w = 40 m
0 5 10 15 20 25 30
0.1
1
10
100
1000
DCo
(nm)
I cR
N (
nV
)
How to generate spin-triplet supercurrent
with F, F = PdNi,
d = 4 nm
without F,F
Khaire, Khasawneh, Pratt, & NOB, Phys. Rev. Lett. 104, 137002 (2010)
Nb
F
Co
Ru
Co
F
Nb
Cu
Cu
Cu
Cu
Fix DCo = 20 nm and vary dF’
Control amplitude of triplet with dF’, dF’’
0 2 4 6 8 10
0.1
1
10
100
I C
RN
(n
V)
dF' (nm)
Ni
CuNi
PdNi
Khasawneh, Khaire, Klose, Pratt & NOB, Supercond. Sci. Technol. 24, 024005 (2011).
Nb
F’’
Co
Ru
Co
F’
Nb
Cu
Cu
Cu
Cu
Microscopic mechanism for triplet generation (from discussion with M. Eschrig)
S )
2
10,0
S F1
)
) ) ) )
) )QxQx
QxiQx
ee
zz
iQxiQx
sin0,1cos0,0
sincos2
1
2
1
S F1 F2
FF kkQ
) )
)
1,1
2
sin0,1cos1,1
2
sin0,1
z
long-range triplet
components in F2
short-range triplet
component
k
E
-kF
-kF
kF
kF
rotate basis:
1,1
1,1
M. Houzet and A. I. Buzdin, PRB 76, 060504R 2007
Triplet contribution to the critical current
is observed only for dX (0.5–2.5)ξF
Optimization of triplet generation
0 2 4 6 8 10
0.1
1
10
100
I CR
N (
nV
)dx (nm)
Ni
PdNi
CuNi
CuNi
F
PdNi
F
Ni
F
CuNi
ex
PdNi
ex
Ni
ex EEE
Fxe
/increase ~ sin2(Qx); decrease ~
Earlier observation of triplet:
Keizer, Goennenwein, Klapwijk, Miao, Xiao, Gupta,
Nature 439, 825 (2006)
0.3 – 1 m
Long-range propagation of supercurrent,
but large sample-to-sample variations in Ic.
Reproduced in 2010 by J. Aarts:
M. S. Anwar et al., Phys. Rev. B 82, 100501 (2010)
CrO2 is a “half metal”
k
E
EF
Spin-triplet supercurrents observed by others in 2010
1. Robinson et al., Science 329, 59 (2010)
2. Sprungmann et al., PRB 82, 060505 (2010)
Heusler alloy Cu2MnAl
Spin-triplet supercurrents observed by others in 2010
3. Anwar et al., PRB 82, 100501 (2010)
4. Wang et al., Nature Phys. 6, 389 (2010)
Log(Ic)
dF
singlet:
triplet:
homogeneous M
inhomogeneous M
First step toward control of supercurrent:
magnetize the samples (Expect Ic to drop by reducing non-collinear magnetization?)
Nb
F’’
Co
Ru
Co
F’
Nb
Cu
Cu
Cu
Cu
Ic increases!
0 1000 2000 3000 4000
100
1000
I cR
N (
nV
)
Happlied (Oe)
F = F = Ni
dNi = 1 nm
Why does Ic increase?
Klose et al., Phys.Rev. Lett. 108, 127002 (2012)
Magnetizing field
Co/Ru/Co undergoes “spin-flop transition”
Spin-flop transition optimizes 90 angle between MCo and MNi
and aligns Ni magnetizations
Magnetic configuration confirmed at NIST by SEMPA (McMorran & Unguris) and
PNR (Ginley & Borchers); see Klose et al., Phys.Rev. Lett. 108, 127002 (2012)
Other probes of spin-triplet correlations:
Tc of S/F/F’ trilayers
Singh, Voltan, Lahabi, Aarts,
PRX 5, 021019 (2015).
Next step: Full control of spin-triplet supercurrent
0-junction 0-junction -junction
F
Cu
Cu
Co
Ru
Co
Cu
F Cu
F
Cu
Cu
Co
Ru
Co
Cu
F Cu
F
Cu
Cu
Co
Ru
Co
Cu
F Cu
Ic = 0
• Hard F ferromagnet in bottom layer maintains its magnetization.
• Soft F ferromagnetic top layer drives the state of the junction.
• Use shape anisotropy to help control F’’ magnetization.
• Requires single-domain magnet(s) e-beam lithography
Summary
• Experimental observation of long-range
supercurrent in S/F/S Josephson junctions:
– requires three F layers
– Possibility to control supercurrent with magnetic state
• New type of Fermion pairing occurs in S/F
systems: odd-frequency, spin-triplet, s-wave.
• Further reading: see article by Matthias Eschrig in
Physics Today, January 2011.
Collaborators MSU:
Trupti Khaire, Mazin Khasawneh, Caroline Klose, Reza Loloee, Kurt Boden,
Hamood Arham, Yixing Wang, Eric Gingrich, Simon Diesch, Bethany Niedzielski,
William Martinez, Joseph Glick, Alex Cramer, William P. Pratt, Jr.
NIST: Julie Borchers, John Unguris, Ben McMorran
For memory applications: Northrop Grumman and ASU
spring 2010 summer 2013
Postlude:
What we were taught in quantum mechanics
A convenient basis (for systems with translational and rotational symmetry):
) ) )21212211 ,,,;, ssrrsrsr
Wavefunction for two identical fermions (Spin-Statistics Theorem or Pauli Exclusion)
) )11222211 ,;,,;, srsrsrsr
Two possibilities:
) )2112 ,, rrrr SS
1. even l, and s=0 (singlet) ) )2112 ,, ssss AA
) )2112 ,, rrrr AA
2. odd l, and s=1 (triplet) ) )2112 ,, ssss SS
) ) )f ,, 21,21,
m
llnln YrrRrr
) )
2
11sS ) )
2
10sA
Allowed Cooper pair symmetries
s=0 s=1
l=0
(s-wave)
BCS X
l=1
(p-wave)
X superfluid 3He
Sr2RuO4
l=2
(d-wave)
high-Tc X
) )11222211 ,;,,;, srsrsrsr
Proposal by Berezinskii (1974):
What does this mean?
) )121212212121 ;,;;,; ttssrrFttssrrF
) )122121212121 ;,;;,; ttssrrFttssrrF
Fermions require:
If F is odd in time:
then F is even
under exchange of
space and spin:
) )211212212121 ;,;;,; ttssrrFttssrrF
F(r1,r2,s1,s2,t1,t2 ) “anomalous Green’s function” = pair correlation function
Allowed Cooper pair symmetries
s=0 s=1
l=0 BCS X
l=1 X superfluid 3He
Sr2RuO4
l=2 high-Tc X
= allowed if correlation function is odd
under time-reversal (or odd in frequency)
Berezinski model
for 3He (1974)
Balatsky &
Abrahams (‘92)
Allowed Cooper pair symmetries
s=0 s=1
l=0 BCS S/F
l=1 S/F superfluid 3He
Sr2RuO4
l=2 high-Tc S/F
This talk
Bergeret, Volkov & Efetov, PRL 90, 117006 (2003); RMP 77, 1321 (2005)
Eschrig & Lofwander, Nature Phys. 4, 138 (2008).