proximity and josephson vortices studied by scanning tunneling...
TRANSCRIPT
Brun Christophe
Paris Institute of Nanosciences
CNRS
&
Sorbonne University
Paris, FRANCE
Proximity and Josephson vortices
studied by scanning tunneling spectroscopy
Rencontres de Moriond 2019
60 nm
S SN
Milorad Milosevic – Antwerpen University, Belgium
Collaborations (Theory)
Paris Institute of Nanosciences - CNRS - SU Lise Serrier-Garcia (PhD student)
Vladimir Cerchez (post-doc)
Vassily Stoliarov (post-doc)
François Debontridder (Engineer)
Brun Christophe (CNRS)
Tristan Cren (CNRS)
Technical Engineering School - ESPCI
Dimitri Roditchev (Prof)
Juan-Carlos Cuevas – Madrid University, Spain
Sebastian Bergeret – San Sebastian, Spain
Mikhail Y. Kuprianov – Moscow MIPT, Russia
Alexander A. Golubov – Moscow MIPT, Russia
OUTLINE
Introduction: Proximity effect in superconductors
S-N with 2D correlated N, lateral proximity effect
PRL 110,157003 2013
S-N-S lateral network, Josephson vortices studied by STM/STS
Nature Physics 11, 332 (2015)
S-N vertical, proximity vortices studied by STM/STS
Nature Commun. 9, 2277 (2018)
Superconducting proximity effect
Superconductor Normal metal
Interface
NS
Old experiments
Holm and Meissner (1932)
Bedard and Meissner (1956)
Meissner (1958), (1960)
First theories
De Gennes (1964)
McMillan (1968)
Clarke (1969)
Deutscher and De Gennes (1969)
Interface
NS
Early understanding of proximity effect
First theories
De Gennes (1964)
McMillan (1968)
Clarke (1969)
Deutscher and De Gennes (1969)
Density of Cooper pairs
Order parameter
LT
diffusive metal
Modern description of proximity effect
Andreev (1964), Eilenberger (1968), Usadel (1970), Eliashberg (1971)
Andreev reflection at S/N interface + long-range phase coherence in N
Larkin et al. (1968,75,77), Schmid & Schön (1975), Blonder et al. (1982), Zaitsev (1984)
diffusive
Modern description of proximity effect
Andreev reflection S/N interface + long-range phase coherence in N
diffusive
Andreev (1964), Eilenberger (1968), Usadel (1970), Eliashberg (1971)
Larkin et al. (1968,75,77), Schmid & Schön (1975), Blonder et al. (1982), Zaitsev (1984)
e-
h+
kF
ξ = ε - μk k
E, E
kF+q kF-q
ξk k
-ξ
Modern description of proximity effect
Andreev reflection S/N interface + long-range phase coherence in N
The decay length of pair correlations is energy dependent
Andreev (1964), Eilenberger (1968), Usadel (1970), Eliashberg (1971)
Larkin et al. (1968,75,77), Schmid & Schön (1975), Blonder et al. (1982), Zaitsev (1984)
diffusive
e-
h+
kF
ξ = ε - μk k
E, E
kF+q kF-q
ξk k
-ξ
Energy-dependent and spatially-dependent quantity :The Local Density of States (LDOS)
Energy-dependent and spatially-dependent quantity :The Local Density of States (LDOS)
N of finite length L
mini-gap ∆g linked to
McMillan (1968)
Golubov & Kupriyanov (1988)
Belzig et al. (1996)
S N
N of finite length L N of infinite length
mini-gap ∆g linked to No mini-gap
McMillan (1968)
Golubov & Kupriyanov (1988)
Belzig et al. (1996)
Belzig et al. 1996
S N S N
Energy-dependent and spatially-dependent quantity :The Local Density of States (LDOS)
Various length scales in proximity effect
Proximity effect for an S-N-S junction
Interface
S N
L
S
Interface
Superconducting correlations propagate for E < ETh
mini-gap ∆g linked to ETh
LE > L
Golubov & Kupriyanov (1988)
Zhou et al. (1998)
Tunneling as a probe of proximity effect
InterfaceSuperconductor
N metal
Counter electrode
Thin tunnel barrier
I(V)
Interface
Superconductor
STM tip
Advantage: Direct information about spatial evolution of the DOS
N metal
Lithography techniques
Fixed tunneling probe Scanning tunneling probe
Proximity effect in superconductors
First study of the spatial dependence: nano-lithography
S. Guéron et al. PRL 77, 14 3025 (1996)
Ex situ STS: Vinet et al. PRB 63, 165420 (2001); Moussy et al. EPL 55, 861(2001)
OUTLINE
Introduction: Proximity effect in superconductors
S-N with 2D correlated N, lateral proximity effect
PRL 110,157003 2013
S-N-S lateral network, Josephson vortices studied by STM/STS
Nature Physics 11, 332 (2015)
S-N vertical proximity vortices studied by STM/STS
Nature Commun. 9, 2277 (2018)
STM/STS
UHV : p < 5x10-11 mbar
In situ growth @ p < 3x10-10 mbar
Base T°: 0.285 mK
Telectrons~380 mK
Magnetic Field: 0 –10 T
e-beam evaporatorsSTM head
Home-made apparatus
Silicon substrate
Si(111)-7x7
100nm
Egap~1 eV
Insulating at
low
temperature
STM topography
Mono-atomic
steps separating
atomically flat
terraces
100nm
in situ Pb grown on Si(111)-7x7 in UHV
Pb nanocrystals
(8-16 ML)
Mono-atomic steps
separating atomically
flat terraces
Pb wetting layer 1-2ML thick
STM topography
Amorphous versus Crystalline
atomic monolayers
Amorphous wetting layer
Pb island
Si(111) substrate
Crystalline monolayer
Pb island
Si(111) substrate
S S
N S
Single crystal Single crystal
PRL 110,157003 (2013) PRX 4, 011033 (2014)
Tunneling spectroscopy of superconductors
dEeV
eVEfENdVdI s
)(
)(),()(/ rr
N
S
22NS
E
E)E(N)E(N
-
∆ = 1.20 meV Teff = 0.38K
14 ML
Pb/Si(111)
BCS DOS
Proximity effect: Pb island – 2D disordered metal
5nm
30nm
L. Serrier-Garcia et al.
Phys. Rev. Lett. 110, 157003 (2013)
dI/dV(V=0) map
ℓN ~ few nm
in-situ transport R ~ 2-4 kΩ
L. Serrier-Garcia et al.
Phys. Rev. Lett. 110, 157003 (2013)
Vbias (mV)
dI/
dV
dI/
dV
Proximity effect: Pb island – 2D disordered metal
LDOS spatial dependence
5 nm
WL
island
50 nm
0 nm
Very high interface transparency
Reference spectrum on the 2D disordered metal
- Altshuler-Aronov like ??
- Dynamical Coulomb blockade ?? Zero-bias anomaly
B. L. Altshuler and A. G. Aronov, in Electron-Electron Interactions in Disordered Systems (1985)
M. H. Devoret, D. Esteve et al., Phys. Rev. Lett. 64, 1824 (1990)
Rollbühler and Grabert
Tunneling into a
disordered 2D conductor
Dynamical Coulomb Blockade
in an ultrasmall junction
with an Ohmic environment
J. Rollbühler and H. Grabert, Phys. Rev. Lett. 87, 126804 (2001)
Modeling the tunneling DOS of the 2D metal
Modeling dynamical Coulomb blockade
CWL = 80 aF RWL=3.22 kΩ
RWL consistent with in-situ transport
Ec = e2/2CWL = 1 meV
R ~ 2-4 kΩ
Modeling dynamical Coulomb blockade
Combining 1D Usadel equations
and dynamical Coulomb blockade
ξ = (ћD/ΔPb )1/2 ≈ 15nm
L. Serrier-Garcia et al. Phys. Rev. Lett 110, 157003 (2013)
D = 4.1 cm2.s-1
perfect transparency
negligible inverse proxim effect
lE = (ћD/E)1/2
experiment
theory
OUTLINE
Introduction: Proximity effect in superconductors
S-N lateral proximity effect studied by STM/STS
PRL 110,157003 2013
S-N-S lateral network, Josephson vortices studied by STM/STS
Nature Physics 11, 332 (2015)
S-N vertical proximity vortices studied by STM/STS
Nature Commun. 9, 2277 (2018)
Network of short diffusive SNS junctions
200 nm
STM topography
Position (nm)0 50
4 nm
0
Proximity SNS junctions : growing islands closer to each other !
Elaborating short lateral diffusive SNS proximity junctions
STM topography
S N S
40 nS
0
Proximity link between two Pb islands
dI/dV (V=0) map
Position (nm)0 50
Elaborating short lateral diffusive SNS proximity junctions
S N S
No ajustable parameter here (D,L fixed) good fit from 1D Usadel + DCB
SNS proximity junction
dI/dV spectrum in the middle of N
Δmini-gap ~ 0.21 meVETh = 0.063 meVξ ≈ 12nm
D ≈ 2.5 cm2.s-1
We do have proximity effect, but…
…do we really have Josephson junctions ??
S N S
S2 N S1
Real proof : the Josephson effect
Should strongly affect the LDOS: Zhou et al JLTP (1998) Lesueur et al. PRL (2008)
r1r2
Network of short diffusive SNS junctions
200 nm
STM topography
D. Roditchev et al. Nature Phys. 11, 332 (2015)
200 nm200 nm
dI/dV (V=0) maptopography
Network of short diffusive SNS junctions
Creating phase gradients in Pb islands
D. Roditchev et al. Nature Phys. 11, 332 (2015)
dI/dV (V=0) mapdI/dV (V=0) map
200 nm
Mini-gap
everywhere
Mini-gap
destroyed
200 nm200 nm
Direct observation of Josephson proximity vortices
B= 180 mTB= 120 mT
D. Roditchev et al. Nature Phys. 11, 332 (2015)
D. Roditchev, C. Brun, L. Serrier-Garcia, J.C. Cuevas, V.
Bessa, M. Milošević, F. Debontridder, V. Stolyarov & T. Cren
Nat. Phys. 11, 332 (2015)
Modelling (I) Ginzburg-Landau
Order parameter Phase
Supercurrents
B= 60 mT
Modelling (II) Ginzburg-Landau + SC Interference
STS experiment Model
Explanation: shear phase gradients from neighboring islands
jlOC=jC sin(φ*)
Josephson
current0 +π/2
-π0 -π/2
+π
200 nm Mini-gap destroyed
for φ*= π+-
Where is the flux quantum?
D. Roditchev et al. Nat. Phys. 11, 332 (2015)
2D Usadel calculations for rectangular SNS junctions
LDOS (2D Usadel+DCB)
J.C. Cuevas et al. PRL 99, 217002 (2007); D. Roditchev et al., Nat. Phys. 11, 332 (2015)
Applied currents in the SC leads
induce Josephson vortices
No magnetic field needed!
Magnetic field or current induced Josephson vortices
OUTLINE
Introduction: Proximity effect in superconductors
S-N lateral proximity effect studied by STM/STS
PRL 110,157003 2013
S-N-S lateral network, Josephson vortices studied by STM/STS
Nature Physics 11, 332 (2015)
S-N vertical proximity vortices studied by STM/STS
Nature Commun. 9, 2277 (2018)
Behavior of proximity vortices in vertical S-N
3D proximity effect
mini-gap ∆g linked to
LVortex size ?
Behavior of proximity vortices in vertical S-N
100 nm Nb
diffusive
50 nm Cu
diffusive
L
S-N bilayer R(T) characteristics
S-N bilayer sample preparation
Stoliarov et al. APL 104, 172604 (2014)
dSi02 = 270 nm
dSi = 0.3 mm
dCu = 50 nm
dNb = 100 nm
Cu, Nb:
magnetron
sputtering
Grain size ~ ℓN ~ 20 nmDN= ℓNvF/3 ≈ 100 cm2.s-1
ξN = (ћDN/Δ )1/2 ≈ 37 nm
Topography
Corrugation<1nm
S-N bilayer in finite perpendicular B
B = 5 mT
dI/dV(V=0) maps
B = 55 mT
T=300 mK
200 nm 200 nm
Stoliarov et al. Nature Commun. 9, 2277 (2018)
B = 5 mT
dI/dV(V=0) spatial dependence through the vortex core
Comparison of Abrikosov and proximity vortex
S-N bilayer in finite perpendicular B
B = 5 mT
dI/dV(V=0) maps T=300 mK
200 nm
Stoliarov et al. Nature Commun. 9, 2277 (2018)
bare
∆g ~ 0.5 meV
bare
dI/dV(V) spectra across vortex cores
B = 5 mT
B = 5 mT
B = 55 mT
Usadel modeling of S-N bilayer in perpendicular B
• Circular geometry of the vortex unit cell (radial symmetry around vortex
core centers) → θ(r,z) Wigner-Seitz approximation for low B
• Self-consistently solved in N and S
• External field assumed constant inside a unit cell (OK since λS >> ξS)
• Boundary conditions at N, S surfaces and at Z=0 interface
• Numerical method: Newton Finite Element Method Hecht et al. J. Numer. Math. 20, 251 (2012)
Nature Commun. 9, 2277 (2018)
Other 2D Usadel : Cuevas & Bergeret PRL (2007)
Amundsen & Linder Sci Rep (2016)
Igor A. Golovchanskiy, Daniil I. Kasatonov, Mikhail M. Khapaev,
Mikhail Yu. Kupriyanov, Alexander A. Golubov
Usadel modeling of S-N bilayer in perpendicular B
B = 5 mT
Usadel modeling of S-N bilayer in perpendicular B
B = 55 mT
B = 120 mT
Temperature dependance
B = 5 mT
Usadel modeling of S-N bilayer in perpendicular B
L = (ћD/Δg)1/2 ≈ 110 nm at 5mT
Size of the vortex core at V=0
Josephson proximity vortices(Ginzburg-Landau, Usadel 2D)
SUMMARY
Proximity effect to a 2D correlated metal(Usadel 1D + dynamical Coulomb blockade)
Proximity vortices in S-N vertical bilayer(Usadel 3D->2D)
USADEL EQUATIONS
BOUNDARY CONDITIONS (Z=0)
Conclusion
Remarkable superconducting properties of single atomic layers
Nature Phys. 10, 444 (2014)- New short-scale peak height variations – non BCS e-e terms in 2D
- Rashba spin-orbit coupling effect on superconductivity sing-triplet
- Josephson barriers at step edges - Josephson-Abrikosov vortices
Proximity to a 2D monolayer superconductorPRX 4, 011033 (2014)
Proximity to a 2D diffusive metallic layer
Josephson proximity vortices Nature Phys. (2015)
lfluct~ 2-10 nm < < ξ0 ~ 50nm
Subgap filling lfluct~ 10 nm < ξ0 ~ 50nm
PRL 110, 157003 (2013)
Suggested SNS nano-device
Gauge-Independent Phase Difference
Self-Consistent JV positioning
Since the islands are independent, their gauge-independent phase portraits also
are. There is an arbitrary global phase difference between each pair of islands. It
decides where Josephson Vortices are located inside junctions.
Self-Consistent JV positioning
For each pair of islands the total current crossing each junction and corresponding
kinetic energy are calculated as a function of global phase difference ∆φ0. The
exact position of JV is obtained when jTOT=0 and EC=MinEc(∆φ0).
J4
J4
Induced proximity minigap
5 nm
Very high interface transparency
WL
island
50 nm
0 nm
5 nm
5 nm
5 nm
1
0
VB
ias
(mV
)
Position (nm)
0
1,0
-1,0
0 43The mini-gap exists in the proximity region
Elaborating lateral SNS proximity junctions
Line mode dI/dV spectroscopy
Δmini-gap ~ 0.2 meV