Proximity and Josephson vortices studied by scanning tunneling...

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


Andreev reflection S/N interface + long-range phase coherence in N

diffusive



e-

h+

kF

ξ = ε - μk k

E, E

kF+q kF-q

ξk k

-ξ


Andreev reflection S/N interface + long-range phase coherence in N

The decay length of pair correlations is energy dependent



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)


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)


Belzig et al. (1996)

Belzig et al. 1996

S N S N


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


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


S-N with 2D correlated N, lateral proximity effect

PRL 110,157003 2013



S-N vertical proximity vortices studied by STM/STS


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


S-N lateral proximity effect studied by STM/STS

PRL 110,157003 2013





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


200 nm

STM topography

D. Roditchev et al. Nature Phys. 11, 332 (2015)

200 nm200 nm

dI/dV (V=0) maptopography


Creating phase gradients in Pb islands


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, 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


S-N lateral proximity effect studied by STM/STS

PRL 110,157003 2013





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)


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


B = 5 mT


B = 55 mT

B = 120 mT

Temperature dependance

B = 5 mT


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

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Proximity and Josephson vortices studied by scanning tunneling...

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