2035-21 conference on superconductor-insulator...
TRANSCRIPT
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