confinement-induced vortex phases in superconductors

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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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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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OUTLINE

Conclusion

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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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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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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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B > 0

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Φ = nΦ0

vs=0B > 0

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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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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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Individual Vortex Structure

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D ~ ξ, ξ << λ

Our motivation:Phase Diagram of Confined Superconductors

- tiny magnetic response, - variations at nanometer scale

D << λ

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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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Phase Diagram of Confined Superconductors

Confined Vortex Configurations: Our Motivations

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OUTLINE

Conclusion

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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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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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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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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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OUTLINE

Conclusion

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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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NifNaf

Nouf

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Nif(111)

Naf


(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


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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


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ξEFF ≈ 20-25 nm

λEFF ≈ 170 nm ≈ D

Λ ≈ 12,000 nm >>D

κ ≈ λeff/ξeff ≈ 8Nif

(111)

Naf

(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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0.3K (T/Tc=1/20)0.8T : 10 times Hc(bulk Pb)


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0.3K (T/Tc=1/20)0.8T : 10 times Hc(bulk Pb)STS: G.A. maps

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a) b)

c) d)

Model: A SC box with a Single Vortex inside (2/2)

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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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Response of Confined Superconducting Condensate to an External Magnetic Field:

Giant Vortex States

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In bulk superconductors at B=BC2:Nif Naf

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

T. Cren et al., to be published

160nm

h=8.3nm

h=2.6nm

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Vortex Pool

Pb-Island on Si(111):


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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Vortex Pool

0.1T – 3 Vortex


ZBC STS (T=0.3K):

Lower ZBC – SC stateHigher ZBC – vortex or normal state

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A closer view..


3x2 vortices !

ZBC STS images (T=0.3K):

Vortex Pool

0.2T (6 vortex)0.1T (3 vortex)


Core Deformation !

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0.5T (≈15 Φ0)


3x2 vortices !

ZBC STS images (T=0.3K):

Vortex Pool

0.2T (6 vortex)0.1T (3 vortex)


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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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STM/STS team at the Institute for Nano-Science of Paris

http://www.insp.jussieu.fr/-Dispositifs-quantiques-controles-.html

confinement-induced vortex phases in superconductors

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