2035-21

Conference on Superconductor-Insulator Transitions

T. Grenet

18 - 23 May 2009

LEPES - CNRGrenobleFrance

Glassiness in insulating granular aluminum thin films

Glassiness in insulating granular Al thin films

Thierry Grenet, Julien Delahaye,Frédéric Gay, Maher Sabra

Institut Néel, CNRS Grenoble (France)

OUTLINE

- how it started

- some aspects of the « glassiness » in granular Al

- is ageing present ? (is it a glass ?)

- is it an electron glass ?

Electron Coulomb glass ?

Ben Chorin et Ovadyahu (1991): anomalous field effect and very slow relaxation of conductance in insulating indium oxide

J. H. Davies, P. A. Lee and T. Rice (1982):

localized electrons + unscreened coulomb repulsion ���� highly correlated ���� new glass (finite T glass transition?)

Manifestation of the electron (Coulomb ?) glass in indium oxide …

Indium oxide … what else ?

QUESTIONS:

- What is special with indium oxide ? Why no other system ?

- Standard doped semi-conductors: Ø

-What about granular metals ?

���� look for these effects in granular Al

actually seen in: granular gold (Adkins et al., 1984)ultrathin lead (Goldman et al. , 1997 and 2001)

OUTLINE

- how it started

- some aspects of the « glassiness » in granular Al

- is ageing present ? (is it a glass?)

- is it an electron glass ?

Granular Aluminium samples

* nanometric Al grains covered by Al2O3

* Al evaporated in P(O2)

Al, Au

Gate Al or Si++

Insulator Al2O3, SiO2 100nm

20 nmGranular Al thin film

Study insulating films:

R/� at 4K: 100 kΩ � 100 GΩ

1000

105

107

109

1011

1013

0 20 40 60 80 100 120 140

T(K)

R (ohms)

-3 .5

-3

-2 .5

-2

-1 .5

-1

-0 .5

0

0 4 0 0 8 0 0 1 2 0 0 1 6 0 0

re la x26

G/G

(%

)t (s )

δ

-3 .5

-3

-2 .5

-2

-1 .5

-1

-0 .5

0

10 100 1000

relax26

G/G

(%

)

t(s)

δ

Out of equilibrium effects

Never ending slow conductance relaxation after a quench

T

tt = 0

4.2K

Vg

tt = 0

Vgeq

- Field effect anomaly (the “cusp” or “dip”)

- Amplitude grows like Ln(t)

Out of equilibrium effects

T

tt = 0

4.2K

Vg

tt = 0

Vgeq 0.992

0.994

0.996

0.998

1

-8 -6 -4 -2 0 2 4 6 8

2mn30mn110mn537mn2670mn

Gno

rm

Vg

80s scans

R�=30MΩ at 4.2K

0.8%

G(t, Vg) after a quench at 4.2K

0.01

0.1

1

10

1 10 100

dG/G

(%)

T(K)

� at low T (most measurements at4K)

When do we see this anomaly ?

� in more insulating samples

- it is most prominent (in %):

- for practical reasons we study samples were the anomaly is not so large (�1%) but it can be a large effect

R�(25 K) = 1 TΩ- the anomaly is always seen in insulating films

R�(4 K) = 200 kΩ 300 MΩ

Cusp dynamics

0.992

0.994

0.996

0.998

1

-8 -6 -4 -2 0 2 4 6 8

2mn30mn110mn537mn2670mn

Gno

rm

Vg

Recall: after a cooling

After a gate voltage change:

Formation of a new dip and erasure of theold one:

� ΔG ~ -ln t ? but see later …

T

t

4.2K

Vg

tt = 0

Vgeq1

Vgeq20.992

0.994

0.996

0.998

1

1.002

-15 -10 -5 0 5 10 15

0mn

40mn

80mnG

norm

Vg (V)

Is the dynamics activated ?

-4 -2 0 2 4Vgate (V)

Eq.t

W= 3 hours

G (A

. U.)

0

0.5

1

1.5

2

10-4 10-3 10-2 10-1 100 101 102

t/tw

G (A

. U.)

Is the dynamics accelerated when T is increased ? (it would explain why thedip becomes very faint)

But how to detect a change of the dynamics if it has no characteristic time ?

� look at the erasure time of a previously formed dip

time (A. U.)

Is the dynamics activated ?

-1 10-9

0

1 10-9

2 10-9

3 10-9

4 10-9

100 1000 104 105

060504_5070504_1

time (s)

time

T8K 8K

5K

time

Vg6V

tw t

time

T8K

5K

time

Vg6V

tw t

� dynamics is not activated

I II G

ξ

Empty site(ni = 0)

Occupied site(ni = 1)

Electron Coulomb glass model

Electron Coulomb glass interpretation

0.992

0.994

0.996

0.998

1

-8 -6 -4 -2 0 2 4 6 8

2mn30mn110mn537mn2670mn

Gno

rmVg

Fixed gate voltage Vg=0:system proceeds slowly to the

equilibrium state (of minimum conductance)

After fast gate voltage change: system in a highly excited state (higher conductance)

OUTLINE

- how it started

- some aspects of the « glassiness » in granular Al

- is ageing present ? (is it a glass?)

- is it an electron glass ?

If it is a glass … does it age ?

T

t

creeptime t

stress σ0strain ε

0

age te

0

Tg

Ex: creep tests on polymersCreep compliance (t) = ε (t) / σ0

PVC quenched from 90°C to 40°C (Tg=80°C)L.C.E Struik, 1978

The dynamics dependson time: the « older » thesystem, the slower theresponse to a stimulus !

AGEING:

« Two dip » versus « ageing protocol

T

t

time t0

age te

0

Tg

Vg

tt = 0

Vgeq1

Vgeq2

tw

T

t4.2K

« Two dips » protocol

teq >> tw

Standard « ageing » protocol

-4 -2 0 2 4Vgate (V)

Eq.t

W= 3 hours

G (A

. U.)

-4 -2 0 2 4Vgate (V)

Eq.t

W= 3 hours

G (A

. U.)

Two dip protocol: full « ageing » ?

t/tw scaling = « full ageing » ?

« Two dips » protocol

0

0.5

1

1.5

2

10-4 10-3 10-2 10-1 100 101 102

t/tw

G (A

. U.)

� −−Δ−=<Δi i

wtGttG ))exp(1()( 0 τ

� −−−−Δ=>Δ

i i

w

i

ww t

tttGttG )exp())exp(1()( 0 τ

… it does not demonstrate ageing

A simple model can reproduce the data:

-collection of independant reversible« degrees of freedom » (e.g. polarisable TLS)- additive effect on G- tunnel � Ln(τi) has a broad (flat) distribution

Then:

But this is NOT ageing ! terasure = tw

Picturial view of the « two dip » protocol

tw = 1 h

t = 0 h 02’ terasure = tw

« full scaling »� tend = tw : trivial effect !

teq very large

Standard ageing protocol (1)

T

t

age teq

Vg

t

G

t

4.2K

New dip growth: NOT like Ln(t) when teq NOT verylarge

(i.e. when system has not already aged !)

-4 -2 0 2 4Vgate (V)

Eq.t

W= 3 hours

G (A

. U.)

Standard ageing protocol (2)

the departure from Ln(t) scales with teq

i.e. «effective» relaxation time distribution depends on the system’s age:

� AGEING !

0

4 10-13

8 10-13

1.2 10-12

1.6 10-12

100 101 102 103 104 105

d ΔΔ ΔΔG

2 ( ΩΩ ΩΩ

-1)

time (sec)

10-5 10-3 10-1 101 103 105

time / tw1

Example of spin glasses

T

t

t

ΗM

0

age te

0

Tg

Zero field cooling relaxation Magnetization (t)

ee

e

time t (s)

E. Vincent, 2006

The age of the system is printed in its relaxation time distribution

Ageing in the two dip protocol ?

teq (1): not Ln(t)

(2) ? Terasure > tw ?

Ageing in the two dip protocol

0 100

5 10-3

1 10-2

1.5 10-2

2 10-2

2.5 10-2

10-3 10-2 10-1 100 101 102 103

ΔΔ ΔΔG2/G

t / tw2

tw1

= 0

tw1

>> tw2

t / tw

teq small

teq largeIndeed when teq is small:

terasure > tw

(here terasure = 3 tw)

Conclusions about ageing

- In very « old » (already aged) samples ageing was hardly visible

- In « young » samples ageing is prominent (and consists in deviations from the « regular » two dip protocol behaviour)

- « old » samples can be rejuvenated e.g. by a moderate higher T excursion or by a large enough Vg change (large perturbations tend to erase any history of the sample) � ageing is restarted

- models involving simple degrees of freedom acting in parallel(independently) are ruled out, we have a glassy behaviour in a strict sense

OUTLINE

- how it started

- some aspects of the « glassiness » in granular Al

- is ageing present ? (is it a glass?)

- is it an electron glass ?

Is this glass purely electronic ?

- 1) a good indication in Indium oxide: effect of carrier concentration

In InOx at 4Kno slow

dynamics for n < 1019cm-3

A. Vaknin et al, 1998

The closer the carriers are fromeach other, the more correlatedthey are (consistent with coulombglass)

- competing « extrinsic » (non electronic) scenarios have been envisaged(slow atomic or ionic processes influencing the conductance)

- what are the indications in favor of the coulomb electron glass ?

0.986

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

-10 -5 0 5 10V

g (V)

G/<

G>

t = 0

2h

6h

14h

38h

98h

Is this glass purely electronic ?

50*40 (mm)2

- 2) slow relaxation in mesoscopic samples :

Size: 30 * 30 μm2

2.2 10-10

2.25 10-10

2.3 10-10

2.35 10-10

-4 -2 0 2 4

G (m

ho)

Vgate(V)

t = 0

t = 4.5 hours

t = 55 min

- mesoscopic fluctuations (fluctuations of percolation path as a functionof Vg) and the cusp coexist

- both seem to have very different time scales (disorder seems totallyfrozen) � may be consistent with electron glass (cusp slow relaxation not due to disorder (atoms) relaxation)

Is this glass purely electronic ?

Conduction path(percolation):« fast » electrons

Islands of coulomb glass« slow » electrons

Apparent paradoxes:

- thermal memory of cusp but not of « back-ground » conductance

- very slow electrons even for weakly insulating samples

Consistent picture (?) :

The conducting channel isinfluenced by the slowly relaxingcoulomb glass islands

Is this glass purely electronic ?

- 3) systematics in other materials:

Up to now:

- studied in: indium oxide, granular aluminium

- seen in: granular gold, ultra thin Pb on a-Ge

- maybe present in icosahedral insulatingquasicrystal i-AlPdRe

0.01

0.1

1

10

100

10 1000 105 107 109

dG/G (%)

R(4K) / R (300K)

S i:B ?i-AlPdRe

… and the materials we’ve heard about in thisconference (MoGe etc…) could also be good

candidates !

All these may be a priori good candidates for the coulomb glass: disordered insulatorswith high electron concentrations