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ECRYS 2011
Confinement-Induced Vortex Phases in Superconductors
Institut des Nanosciences de Paris INSP, CNRS, Université Pierre et Marie Curie Paris 6, Paris, FRANCE
Dimitri RODITCHEVwith:
Tristan Cren (researcher)Lise Serrier-Garcia (PhD) François Debontridder (Eng.)
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ECRYS 2011
Vortex: An Universal Property of Quantum Condensates
Scanning Tunneling Spectroscopy of Vortices
Confinement-induced vortex configurations- Ultra-dense vortex lattice- Giant Vortex
OUTLINE
ConclusionT. Cren et al. Phys. Rev. Lett. 102, 127005 (2009),T. Cren et al. Phys. Rev. Lett. 107, 097202 (2011)
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ECRYS 2011
Vortex: An Universal Property of Quantum Condensates
Scanning Tunneling Spectroscopy of Vortices
Confinement-induced vortex configurations- Ultra-dense vortex lattice- Giant Vortex
OUTLINE
Conclusion
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ECRYS 2011
First image of Vortex, 1967
Vortex Physics in Rotating Quantum Condensates
Vortex in ultracold condensate of atoms Vortex in superfluid He
Superconductors (BCS) Cold atoms (BEC) Quantum liquids
3 vortices in SC nano-islandSTM/STS, INSP, 2009
100nm
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ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
Boundary condition at the sample edge:
Superconducting phase is described by macroscopic wave function:
Two equations:
(1)
(2)
where
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ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
Fluxoid quantification:
Integrating the 2nd G-L equation over an area S:
where , Φ being the magnetic flux crossing S
where Φ0 is the flux quantum:
Condition on the phase φ (since ψ is a single-valued function):
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ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
B > 0
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ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
Φ = nΦ0
vs=0B > 0
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ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
Φ = nΦ0
vs=0B > 0
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ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
Two characteristic scales: coherence length ξ(T) and penetration depth λ(T)
Influence of electron scattering:
Additionally, in thin films (h<<λ):
Mean free path l : l = τ vF
G-L parameter separates the superconductors of type-I (k<1) from type-II (k>1)
Dirty limit : (l<<ξ)
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ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
Φ = nΦ0
vs=0B > 0
In type II superconductors (k>1) the Abrikosov vortex lattice forms, each vortex containing the flux quantum Φ0
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ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
Individual Vortex Structure
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ECRYS 2011
D ~ ξ, ξ << λ
Our motivation:Phase Diagram of Confined Superconductors
- tiny magnetic response, - variations at nanometer scale
D << λ
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ECRYS 2011
V. Schweigert et al., Phys. Rev. Lett. 81, 2783 (1998)B. Baelus and F. Peeters, Phys. Rev. B 65, 104515 (2002)
Superconducting nano-islands having a size of ~ξ should have peculiar properties due to the lateral confinement.
Phase Diagram of Confined Superconductors
Confined Vortex Configurations: Our Motivations
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ECRYS 2011
Phase Diagram of Confined Superconductors
Confined Vortex Configurations: Our Motivations
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ECRYS 2011
Vortex: An Universal Property of Quantum Condensates
Scanning Tunneling Spectroscopy of Vortices
Confinement-induced vortex configurations- Ultra-dense vortex lattice- Giant Vortex
OUTLINE
Conclusion
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ECRYS 2011
Scanning Tunneling Spectroscopy of Superconductors
S
N
T = 4.2 K
B = 1.0 T
400
nm
2H-NbSe2
T. Cren, H. Brune et al. (2001)EPFL de Lauzanne, Suisse
dVVdI )(
Negative Positive0
Sample Bias
1
T. Cren, H. Brune et al. (2001)EPFL de Lauzanne, Suisse
dVVdI )(
Negative Positive0
Sample Bias
1
dVVdI )(
Negative Positive0
Sample Bias
1
Vortex imaging in bulk superconductors by STS
NB: The relation between the gap in the LDOS and Ψ(r) (GL) is not simple!
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ECRYS 2011
Scanning Tunneling Spectroscopy of Superconductors
S
N
Local Tunneling Spectra contain two important informations:
Scale of ξ: Gap in dI/dV(V) Scale of λ: Effects of currents
A. Anthore et al. PRL 90, 127001 (2003)
A. Kohen et al. PRL 97, 027001 (2006)
H. F. Hess et al. PRL 64, 2711 (1990)
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ECRYS 2011
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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ECRYS 2011
Scanning Tunneling Spectroscopy of Superconductors
S
N
T = 4.2 K
B = 1.0 T
STS: Vortex CORES
(scale of ξ )Field-sensitive methods:
(scale of λ)
400
nm
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ECRYS 2011
Vortex: An Universal Property of Quantum Condensates
Scanning Tunneling Spectroscopy of Vortices
Confinement-induced vortex configurations- Ultra-dense vortex lattice- Giant Vortex
OUTLINE
Conclusion
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ECRYS 2011
100nm
Response of Confined Superconducting Condensate to an External Magnetic Field
Samples: in-situ grown Pb-islands on 7x7 reconstructed Si(111)
Si (111) + Pb-wetting layer (1-2 ML)
Pb-nanocrystals(3-15 ML)
Mono-atomic steps separating atomically
flat terraces
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ECRYS 2011
Samples: in-situ grown Pb-islands on 7x7 reconstructed Si(111)
Response of Confined Superconducting Condensate to an External Magnetic Field
NifNaf
Nouf
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ECRYS 2011
Nif(111)
Naf
Samples: in-situ grown Pb-islands on 7x7 reconstructed Si(111)
(111)
(111)Nif:D ≈ 140 nmh= 2.8nm – 10ML
Naf:D ≈ 80-140 nmh= 2.3nm – 8ML
Nouf:D ≈ 80 nmh= 2.3nm – 8ML
Nouf
Response of Confined Superconducting Condensate to an External Magnetic Field
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ECRYS 2011
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
Result: our Pb-island is the type II dirty limit SC;
Magn. Field fully penetrates (Λ >> D), flux is not quantized.
Additionally, in thin films (h<<λ):
l = τ vF
Dirty limit : (l<<ξ)
h
Response of Confined Superconducting Condensate to an External Magnetic Field
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ECRYS 2011
ξEFF ≈ 20-25 nm
λEFF ≈ 170 nm ≈ D
Λ ≈ 12,000 nm >>D
κ ≈ λeff/ξeff ≈ 8Nif
(111)
Naf
(111)
(111)
Nouf
Response of Confined Superconducting Condensate to an External Magnetic Field
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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ECRYS 2011
0.3K (T/Tc=1/20)0.8T : 10 times Hc(bulk Pb)
Response of Confined Superconducting Condensate to an External Magnetic Field
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ECRYS 2011
Response of Confined Superconducting Condensate to an External Magnetic Field
0.3K (T/Tc=1/20)0.8T : 10 times Hc(bulk Pb)STS: G.A. maps
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ECRYS 2011
a) b)
c) d)
Model: A SC box with a Single Vortex inside (2/2)
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ECRYS 2011
Response of Confined Superconducting Condensate to an External Magnetic Field
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ECRYS 20110 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
M agn etic F ield m TG
apFi
lling
normaliz
ed
Zer
oB
ias
Con
duct
ance
normaliz
ed
Zero Bias Gapped Area
0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
M agn etic F ield m T
Gap
Filli
ngnormal
ized
Zer
oB
ias
Con
duct
ance
normaliz
ed
0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 00 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
M a g n e t i c F i e l d m T
Gap
Filli
ngnormal
ized
Zer
oB
ias
Con
duct
ance
normaliz
ed
At the border
Nif Naf
Nouf
Nif
Naf
Nouf
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ECRYS 2011
Response of Confined Superconducting Condensate to an External Magnetic Field:
Giant Vortex States
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ECRYS 2011
In bulk superconductors at B=BC2:Nif Naf
Nouf
In our confined case (L=2):
!!
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ECRYS 2011
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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ECRYS 2011
Vortex Pool
Pb-Island on Si(111): Topographic STM Iimage
T. Cren et al., to be published
160nm
h=8.3nm
h=2.6nm
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ECRYS 2011
Vortex Pool
Pb-Island on Si(111):
T. Cren et al., to be published
Sample Bias, mVdI
/dV
, a
rb.
units
B=0T=0.3K
BCS Fit:Δ=1.12meVTeff=0.39KГ=0
Topographic STM Iimage Local SIN Tunneling Spectrum
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ECRYS 2011
Vortex Pool
0.1T – 3 Vortex
T. Cren et al., to be published
ZBC STS (T=0.3K):
Lower ZBC – SC stateHigher ZBC – vortex or normal state
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ECRYS 2011
Vortex Pool
0.1T – 3 Vortex
T. Cren et al., to be published
ZBC STS (T=0.3K):
Lower ZBC – SC stateHigher ZBC – vortex or normal state
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ECRYS 2011
A closer view..
Lower ZBC – SC stateHigher ZBC – vortex or normal state
3x2 vortices !
ZBC STS images (T=0.3K):
Vortex Pool
0.2T (6 vortex)0.1T (3 vortex)
T. Cren et al., to be published
Core Deformation !
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ECRYS 2011
0.5T (≈15 Φ0)
Lower ZBC – SC stateHigher ZBC – vortex or normal state
3x2 vortices !
ZBC STS images (T=0.3K):
Vortex Pool
0.2T (6 vortex)0.1T (3 vortex)
T. Cren et al., to be published
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ECRYS 2011
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
Conclusions
T. Cren et al. Phys. Rev. Lett. 102, 127005 (2009),T. Cren et al. Phys. Rev. Lett. 107, 097202 (2011)
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ECRYS 2011
STM/STS team at the Institute for Nano-Science of Paris
http://www.insp.jussieu.fr/-Dispositifs-quantiques-controles-.html