Confinement-Induced Vortex Phases in
Superconductors
Dimitri RODITCHEV
with:
Tristan Cren (researcher)
Lise Serrier-Garcia (PhD)
François Debontridder (Eng.)
Institut des Nanosciences de Paris INSP,
CNRS, Université Pierre et Marie Curie Paris 6, Paris, FRANCE
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OUTLINE
Vortex: An Universal Property of Quantum Condensates
Scanning Tunneling Spectroscopy of Vortices
Confinement-induced vortex configurations
- Ultra-dense vortex lattice
- Giant Vortex
Conclusion
T. Cren et al. Phys. Rev. Lett. 102, 127005 (2009),
T. Cren et al. Phys. Rev. Lett. 107, 097202 (2011)
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OUTLINE
Vortex: An Universal Property of Quantum Condensates
Scanning Tunneling Spectroscopy of Vortices
Confinement-induced vortex configurations
- Ultra-dense vortex lattice
- Giant Vortex
Conclusion
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Vortex Physics in Rotating Quantum Condensates
Superconductors (BCS)
Cold atoms (BEC)
Quantum liquids
First image of Vortex, 1967
Vortex in ultracold
condensate of atoms
Vortex in superfluid He
3 vortices in SC nano-island
STM/STS, INSP, 2009
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Superconductivity: Ginzburg-Landau Approach
Superconducting phase is described by macroscopic wave function:
Two equations:
(1)
(2)
where
Boundary condition at the sample edge:
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Superconductivity: Ginzburg-Landau Approach
Integrating the 2nd G-L equation over an area S:
where
, Φ being the magnetic flux crossing S
Condition on the phase φ (since ψ is a single-valued function):
Fluxoid quantification:
where Φ0 is the flux quantum:
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Superconductivity: Ginzburg-Landau Approach
B>0
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Superconductivity: Ginzburg-Landau Approach
Φ = nΦ0
B>0
vs=0
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Superconductivity: Ginzburg-Landau Approach
Φ = nΦ0
B>0
vs=0
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Superconductivity: Ginzburg-Landau Approach
Two characteristic scales: coherence length ξ(T) and penetration depth λ(T)
G-L parameter
separates the superconductors of type-I (k<1)
from type-II (k>1)
Influence of electron scattering:
Mean free path l :
l = τ vF
Dirty limit :
(l<<ξ)
Additionally, in thin films (h<<λ):
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Superconductivity: Ginzburg-Landau Approach
Φ = nΦ0
B>0
vs=0
In type II superconductors
(k>1) the Abrikosov vortex
lattice forms, each vortex
containing the flux
quantum Φ0
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Superconductivity: Ginzburg-Landau Approach
Individual Vortex Structure
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Our motivation:
Phase Diagram of Confined Superconductors
D ~ ξ, ξ << λ
D << λ
- tiny magnetic response,
- variations at nanometer scale
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Confined Vortex Configurations: Our Motivations
Phase Diagram of Confined Superconductors
Superconducting nano-islands having a size of ~ξ should have peculiar
properties due to the lateral confinement.
V. Schweigert et al., Phys. Rev. Lett. 81, 2783 (1998)
B. Baelus and F. Peeters, Phys. Rev. B 65, 104515 (2002)
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Confined Vortex Configurations: Our Motivations
Phase Diagram of Confined Superconductors
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OUTLINE
Vortex: An Universal Property of Quantum Condensates
Scanning Tunneling Spectroscopy of Vortices
Confinement-induced vortex configurations
- Ultra-dense vortex lattice
- Giant Vortex
Conclusion
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N
Scanning Tunneling Spectroscopy of Superconductors
S
Vortex imaging in bulk superconductors by STS
2H-NbSe2
400 nm
dI(V )
dV
1
T = 4.2 K
B = 1.0 T
Negative
0
Positive
T. Cren, H. Brune et al. (2001)
Sample
EPFL Bias
de Lauzanne, Suisse
NB: The relation between the gap in the LDOS and Ψ(r) (GL) is not simple!
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N
Scanning Tunneling Spectroscopy of Superconductors
S
Local Tunneling Spectra contain two important informations:
A. Kohen et al. PRL 97, 027001 (2006)
Scale of ξ: Gap in dI/dV(V)
Scale of λ: Effects of currents
H. F. Hess et al. PRL 64, 2711 (1990)
A. Anthore et al. PRL 90, 127001 (2003)
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STM/STS in Paris
(3rd generation)
UHV : p < 5x10-11 mbar
In-situ growth @ p < 3x10-10 mbar
Base T°: 0.285 mK
Magn. Field: 0 –10 T
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N
Scanning Tunneling Spectroscopy of Superconductors
S
Field-sensitive methods:
(scale of λ)
400 nm
STS: Vortex CORES
(scale of ξ )
T = 4.2 K
B = 1.0 T
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OUTLINE
Vortex: An Universal Property of Quantum Condensates
Scanning Tunneling Spectroscopy of Vortices
Confinement-induced vortex configurations
- Ultra-dense vortex lattice
- Giant Vortex
Conclusion
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Response of Confined Superconducting
Condensate to an External Magnetic Field
Samples:
in-situ grown Pb-islands on 7x7 reconstructed Si(111)
Pb-nanocrystals
(3-15 ML)
Mono-atomic steps
separating atomically
flat terraces
100nm
Si (111) + Pb-wetting layer (1-2 ML)
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Response of Confined Superconducting
Condensate to an External Magnetic Field
Samples:
in-situ grown Pb-islands on 7x7 reconstructed Si(111)
Naf
Nif
Nouf
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Response of Confined Superconducting
Condensate to an External Magnetic Field
Samples:
in-situ grown Pb-islands on 7x7 reconstructed Si(111)
(111)
Nif
Naf
Nif:
D ≈ 140 nm
h= 2.8nm – 10ML
Naf:
D ≈ 80-140 nm
h= 2.3nm – 8ML
(111)
(111)
Nouf
Nouf:
D ≈ 80 nm
h= 2.3nm – 8ML
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Response of Confined Superconducting
Condensate to an External Magnetic Field
Bulk Pb (ξ0 = 80nm, λ0 = 50nm) – Type I, no vortices
Our case: disordered Pb/Si interface limits the mean free path l:
l ≈2h=2x5.5nm = 11nm << ξ0
Dirty limit SC
l = τ vF
Dirty limit :
(l<<ξ)
Additionally, in thin films (h<<λ):
h
Result: our Pb-island is the type II dirty limit SC;
Magn. Field fully penetrates (Λ >> D), flux is not quantized.
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Response of Confined Superconducting
Condensate to an External Magnetic Field
ξEFF ≈ 20-25 nm
λEFF ≈ 170 nm ≈ D
(111)
Nif
Naf
Λ ≈ 12,000 nm >>D
κ ≈ λeff/ξeff ≈ 8
(111)
(111)
Nouf
Result: our Pb-islands are the Type II dirty limit SCs;
Magn. Field fully penetrates (Λ >> D), flux is not quantized.
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Response of Confined Superconducting
Condensate to an External Magnetic Field
0.8T : 10 times Hc(bulk Pb)
0.3K (T/Tc=1/20)
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Response of Confined Superconducting
Condensate to an External Magnetic Field
STS: G.A. maps
0.8T : 10 times Hc(bulk Pb)
0.3K (T/Tc=1/20)
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Model: A SC box with a Single Vortex inside (2/2)
a)
c)
b)
d)
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Response of Confined Superconducting
Condensate to an External Magnetic Field
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Gapped Area
At the border
Zero Bias Conductance normalized
Zero Bias
Gap Filling normalized
1.0
Nif
0.8
0.6
0.4
0.2
0.0
0
200
400
600
800
1000 1200
1400
Zero Bias Conductance normalized
Magnetic Field mT
Gap Filling normalized
1.0
Nif Naf
Naf
0.8
0.6
0.4
0.2
0.0
0
500
1000
1500
2000
Nouf
Zero Bias Conductance normalized
Magnetic Field mT
Nouf
Gap Filling normalized
1.0
0.8
0.6
0.4
0.2
0.0
0
500
1000
1500
2000
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Magnetic Field mT
Response of Confined Superconducting
Condensate to an External Magnetic Field:
Giant Vortex States
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Nif Naf
In bulk superconductors at B=BC2:
Nouf
In our confined case (L=2):
!
!
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Extras
1 – Vortex Pool: Playing with vortex core size and shape
2 – Quantum Well states and Superconductivity in Pb-Si system
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Vortex Pool
Pb-Island on Si(111): Topographic STM Iimage
h=2.6nm
h=8.3nm
T. Cren et al., to be published
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Vortex Pool
Pb-Island on Si(111):
Local SIN Tunneling Spectrum
B=0
T=0.3K
dI/dV, arb. units
Topographic STM Iimage
BCS Fit:
Δ=1.12meV
Teff=0.39K
Г=0
Sample Bias, mV
T. Cren et al., to be published
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Vortex Pool
ZBC STS (T=0.3K):
0.1T – 3 Vortex
Lower ZBC – SC state
Higher ZBC – vortex or normal state
T. Cren et al., to be published
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Vortex Pool
ZBC STS (T=0.3K):
0.1T – 3 Vortex
Lower ZBC – SC state
Higher ZBC – vortex or normal state
T. Cren et al., to be published
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Vortex Pool
ZBC STS images (T=0.3K):
0.1T (3 vortex)
0.2T (6 vortex)
3x2 vortices !
Lower ZBC – SC state
Higher ZBC – vortex or normal state
A closer view..
Core Deformation !
T. Cren et al., to be published
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Vortex Pool
ZBC STS images (T=0.3K):
0.1T (3 vortex)
0.2T (6 vortex)
0.5T (≈15 Φ0)
3x2 vortices !
Lower ZBC – SC state
Higher ZBC – vortex or normal state
T. Cren et al., to be published
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Conclusions
Vortex phases in strongly confining geometries: Individual and atomically
perfect samples are now experimentally accessible
Coherence length and penetration depth are strongly affected by geometry
Vortex Box: Vortex looses its “Flux Quantum” meaning: Only “Phase” and
“Currents” remain relevant. Magnetic energy is not relevant anymore:
Superconductors start behaving as other (neutral) quantum condensates
(cold atoms, quantum liquids, polaritons etc.)
Multi-Vortex Configurations: Confinement results in super-dense vortex
configurations: The vortex-vortex distance observed up to 3 times shorter
than at BC2 in the bulk! At higher confinement Giant Vortex phase appears
Confinement effects in “Vortex Pool”: Vortex core deformation, Vortex
molecule formation, unexpected phase near BC
Emerging of a New challenging field: Surface/Interface Superconductivity
T. Cren et al. Phys. Rev. Lett. 102, 127005 (2009),
T. Cren et al. Phys. Rev. Lett. 107, 097202 (2011)
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STM/STS team
at the Institute for Nano-Science of Paris
http://www.insp.jussieu.fr/-Dispositifs-quantiques-controles-.html
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