Inhomogeneous electronic states in superconductors ( Chapelier , Ioffe )

Inhomogeneous electronic states in superconductors (Chapelier, Ioffe)How to disentangle the unavoidable atomic level inhomogeneity of real materials from the electronic inhomogeneity

discussion-session

Maud VinetWalter EscoffierBenjamin SacépéThomas DubouchetCharlène Tonnoir

Claude ChapelierCEA INAC-SPSMS-LaTEQS, Grenoble

Very Low Temperature STM: a powerful probe for inhomogeneous superconducting states (tutorial)

Very Low Temperature STM: a powerful probe for inhomogeneous superconducting states (tutorial)

I. STM/STS and usual inhomogeneous superconducting states

II. Highly disordered superconductorsIII. Discussion

Coarse approach motor

Coarse positioning X-Y table

Sample holderTipPiezo tube10

cm

Scanning Tunneling Microscopy

Michael Schmid, TU Wien

P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996) Michael Schmid, TU Wien

NbSe2

Scanning Tunneling Microscopy

P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996)

D. Roditchev’s group, http://ln-www.insp.upmc.fr/

Michael Schmid, TU Wien

NbSe2

Scanning Tunneling Microscopy

Scanning Tunneling Spectroscopy

P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996)

I

V

dI/dV

VeVfNd

dVdIVG T

S)()()(

NbSe2

D. Roditchev’s group, http://ln-www.insp.upmc.fr/

Scanning Tunneling Spectroscopy

P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996)

I

V

dI/dV

VeVfNd

dVdIVG T

S)()()(

NbSe2

D. Roditchev’s group, http://ln-www.insp.upmc.fr/H. Hess et al., Physica B 169, 422 (1991)

I

V

dI/dV

Scanning Tunneling Spectroscopy

P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996)

VeVfNd

dVdIVG T

S)()()(

NbSe2

D. Roditchev’s group, http://ln-www.insp.upmc.fr/H. Hess et al., Physica B 169, 422 (1991)

I

V

dI/dV

Scanning Tunneling Spectroscopy

P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996)

VeVfNd

dVdIVG T

S)()()(

NbSe2

D. Roditchev’s group, http://ln-www.insp.upmc.fr/I. Guillamon et al., Phys. Rev.B 77, 134405 (2008)

http://www.oettinger-physics.de/

VortexNbSe2

Sachdev & Zhang, Science

http://www.oettinger-physics.de/

Vortex

H. Hess et al., Phys. Rev. Lett. . 62, 214 (1989)

NbSe2

http://www.oettinger-physics.de/

Vortex

H. Hess et al., Phys. Rev. Lett. . 62, 214 (1989)

NbSe2

http://www.oettinger-physics.de/

VortexNbSe2

H. Hess et al., Physica B 169, 422 (1991)

http://www.oettinger-physics.de/

Vortex

H. Hess et al., Physica B 169, 422 (1991)

Ch. Renner et al., Phys. Rev. Lett. (1991)

Nb1-x TaxSe2

http://www.oettinger-physics.de/

Vortex

J.E. Hoffman., Science 295, 466 (2002)

Bi2Sr2CaCu2O8+

Hybrid nanostructures

N. Moussy et al., Europhys. Lett. 55, 861 (2001)

M. Vinet et al., Phys. Rev. B 63, 165420 (2001)

-4 -2 0 2 4

0,5

1,0

1,5

dI/d

V (n

orm

aliz

ed)

V [mV]

195 nm

75 nm

12 nm

H. Le Sueur et al., Phys. Rev. Lett. 100, 197002 (2008)

Very Low Temperature STM: a powerful probe for inhomogeneous superconducting states (tutorial)

Superconductor-Insulator Transition

Granular systems Homogeneously disordered materials

H.M. Jaeger, et al., Phys. Rev. B 34, 14920 (1986)

D.B. Haviland, et al., Phys. Rev. Lett. 62, 2180 (1989)

GalliumBismuth

Superconductor-Insulator TransitionTiNReactive sputter deposition of TiN films

Homogeneously disordered ?

N. Hadaceket al., Phys. Rev. B 69, 024505 (2004)

100 nm

10 nm

Superconductor-Insulator TransitionTiN

100 nm

10 nm

T (K)

R (O

hms)

Reactive sputter deposition of TiN films

Granular ?Homogeneously disordered ?

N. Hadaceket al., Phys. Rev. B 69, 024505 (2004)

Superconductor-Insulator TransitionTiN

T (K)

R (O

hms)

Reactive sputter deposition of TiN films

Granular ?Homogeneously disordered ?

N. Hadaceket al., Phys. Rev. B 69, 024505 (2004)

≈ 80 × 80 × 2 nm

≈ 400

× 4

00 ×

3

nmW. Escoffier et al.,Phys. Rev. Lett. 93, 217005 (2004)

100 nm

10 nm

Superconductor-Insulator TransitionTiNReactive sputter deposition of TiN films

Homogeneously disordered ?

N. Hadaceket al., Phys. Rev. B 69, 024505 (2004)

≈ 80 × 80 × 2 nm

≈ 400

× 4

00 ×

3

nmW. Escoffier et al.,Phys. Rev. Lett. 93, 217005 (2004)

100 nm

10 nm

M. Baklanov and A. Satta (IMEC)

Superconductor-Insulator TransitionTiNAtomic layer deposition of 5 nm thick TiN films

-1,0 -0,5 0,0 0,5 1,00,0

0,5

1,0

1,5

2,0

G(V

), no

rmal

ized

V [mV]

= 260 µeVTeff = 0,25 K

-1,0 -0,5 0,0 0,5 1,00,0

0,5

1,0

1,5

2,0

= 225 µeVTeff = 0,32 K

G(V

), no

rmal

ized

V [mV]

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,00

1

2

3

4

5

6

7

8

R [k

]

T [K]

TiN 1 TiN 2 TiN 3

-1,0 -0,5 0,0 0,5 1,00,0

0,5

1,0

1,5

2,0

= 154 µeVTeff = 0,35 K

G(V

), no

rmal

ized

V [mV]

Increasing disorder

Superconductor-Insulator transition

Sacépé et al., Phys. Rev. Lett. 101, 157006 (2008)

TiN

Superconductor-Insulator transitionTiN

λ

Sacépé et al., Phys. Rev. Lett. 101, 157006 (2008)

Tc [K] Δ/TcVar.

[%]

4.7 1.8 ---1.3 2.3 121 2.6 20

0.45 4 50

A. Ghosal, M. Randeria, N. Trivedi, Phys. Rev. Lett. 81, 3940, (1998)Phys. Rev. B 65, 014501 (2001)

M. Ma and P.A. Lee, Phys. Rev. B 32, 5658, (1985)A. Kapitulnik, G. Kotliar, Phys. Rev. Lett. 54, 473, (1985)M. Feigel’man et al., Phys. Rev. Lett. 98, 027001, (2007)M. Feigel’man et al., Ann. Phys. 325, 1390 (2010)M. A. Skvortsov et al., Phys. Rev. Lett. 95,057002, (2005)

Pseudogap

B. Sacépé, et al., Nature Communications 1:140 (2010)

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,00

1

2

3

4

5

6

7

8

R [k

]

T [K]

TiN 1 TiN 2 TiN 3

Superconducting fluctuations correction to the DOSShort-lived Cooper pairs above Tc

A. Varlamov and V. Dorin, Sov. Phys. JETP 57, 1089, (1983)

Pseudogap

B. Sacépé, et al., Nature Communications 1:140 (2010)

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,00

1

2

3

4

5

6

7

8

R [k

]

T [K]

TiN 1 TiN 2 TiN 3

Superconducting fluctuations correction to the DOSShort-lived Cooper pairs above Tc

A. Varlamov and V. Dorin, Sov. Phys. JETP 57, 1089, (1983)

Pseudogap

B. Sacépé, et al., Nature Communications 1:140 (2010)

R□

[kΩ]Tc (R□) [K]

Tc (DOS)

[K]

3.5 1.31.3 1.271.27

4.3 1.01.0 0.980.98

7.4 0.450.45 0.450.45

An extreme sensitivity to Tc

Very Low Temperature STM: a powerful probe for inhomogeneous superconducting states (tutorial)

How to disentangle the unavoidable atomic level inhomogeneity of real materials from the electronic inhomogeneity ?

Which inhomogeneities ?

Down to which scale a real material must be considered granular or not ?

What is a homogeneously disordered material ?

How can we relate global macroscopic behavior (transport) and local signatures (STS) ?

Dilution fridge setup

Anomalous proximity effectSuperconducting granular TiN films

-1,5 -1,0 -0,5 0,0 0,5 1,0 1,50,0

0,5

1,0

1,5

2,0

2,5

3,0 xexp

= 0 nm x

cal = 0 nm

xexp

= 12 nm x

cal = 9 nm

xexp

= 20 nm x

cal = 21 nm

xexp

= 32 nm x

cal = 31 nmdI

/dV

E (meV)

dS,N

W. Escoffier et al., Phys. Rev. Lett. (2004)

≈ 80 × 80 × 2 nm

≈ 400

× 4

00 ×

3

nm

Theory : Zhang & Xiong,

Physica C (2006)

Anomalous proximity effectSuperconducting granular TiN films

B. Sacépé (unpublished)

1500 nm x 1500 nm

Superconducting fluctuations quantum corrections

Tc [K]

1.31

0.45

One parameter fit : Tc

Superconducting fluctuations quantum corrections