confinement-induced vortex phases in superconductors
Post on 14-Jan-2016
40 Views
Preview:
DESCRIPTION
TRANSCRIPT
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.)
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)
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
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
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
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):
ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
B > 0
ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
Φ = nΦ0
vs=0B > 0
ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
Φ = nΦ0
vs=0B > 0
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)
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
ECRYS 2011
Superconductivity: Ginzburg-Landau Approach
Individual Vortex Structure
ECRYS 2011
D ~ ξ, ξ << λ
Our motivation:Phase Diagram of Confined Superconductors
- tiny magnetic response, - variations at nanometer scale
D << λ
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
ECRYS 2011
Phase Diagram of Confined Superconductors
Confined Vortex Configurations: Our Motivations
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
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!
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)
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
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
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
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
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
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
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
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.
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
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
ECRYS 2011
a) b)
c) d)
Model: A SC box with a Single Vortex inside (2/2)
ECRYS 2011
Response of Confined Superconducting Condensate to an External Magnetic Field
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
ECRYS 2011
Response of Confined Superconducting Condensate to an External Magnetic Field:
Giant Vortex States
ECRYS 2011
In bulk superconductors at B=BC2:Nif Naf
Nouf
In our confined case (L=2):
!!
ECRYS 2011
Extras
1 – Vortex Pool: Playing with vortex core size and shape
2 – Quantum Well states and Superconductivity in Pb-Si system
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
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
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
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
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 !
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
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)
ECRYS 2011
STM/STS team at the Institute for Nano-Science of Paris
http://www.insp.jussieu.fr/-Dispositifs-quantiques-controles-.html
top related