Presentation given at University of Salamanca in fulfilment for the degree of Doctor of Philosophy

1. FABRICATION
AND
CHARACTERIZATION
OF
GRAPHENE
NANODEVICES
Cayetano
Sánchez-­‐Fabrés
Cobaleda

2. Outline
• IntroducFon
• FabricaFon
of
graphene
devices
• QHE
in
graphene
• WL-­‐WAL
in
graphene
• PPT
in
h-­‐BN/graphene/h-­‐BN
• SuperconducFvity
in
3D
porous
graphene
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
2

3. QHE
in
graphene:
number
of
layer
maXers
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
3

4. Integer
Quantum
Hall
effect
• QuanFzaFon
in
Landau
levels:
Rxy=h/νe2
• Standard
2DEGs:
ν = ng
• Graphene:
ν = g(n+1/2)
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
4

5. Quantum
phase
transiFons
• LocalizaFon-­‐delocalizaFon
transiFons
• CriFcality
of
the
transiFon
• Ec:
criFcal
energy
and
ξ
localizaFon
length
• γ:
criFcal
exponent
of
the
transiFon
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
5
ξ ∝ E − Ec
−γ

6. Experiment<-­‐>Theory
• p:
coherence
length
dependence
on
T
• γ
yields
informaFon
on
the
kind
of
disorder
• Need
of
extremely
high
quality
samples
– Low
n,
high
µ
and
high
homogeneity
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
6
∂ρxy
∂B
"
#
$
%
&
'
max
∝T−κ
κ = p / 2γ
lφ ∝T− p/2

7. FABRICATION
OF
GRAPHENE
NANODEVICES
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
7

8. 18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
8
Graphene
producFon
• Mechanical
exfolia-on:
scotch-­‐tape
technique
• CVD
grown
graphene
• Epitaxial
graphene
• Reduced
graphene
oxide

9. Mechanical
cleavage
• Ingredientes:
Natural
graphite
and
scotch
tape
• Layer
by
layer
exfoliaFon
• DeposiFon
onto
the
wafer
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
9

10. Mechanical
cleavage
• IdenFficaFon
using
the
opFcal
microscope
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
10
50
um
25
um

11. Processing:
e-­‐beam
lithography
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
11
15
um

12. Processing:
e-­‐beam
lithography
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
12
50
um
15
um

13. EvaporaFon
of
contacts
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
13
50
um
15
um

14. Processing:
ReacFve
ion
etching
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
14
25
um
15
um

15. 18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
15
Sample
monFng
and
bonding

16. Our
LAB
3He
Heliox
cryostat
(2008)
0.285
K
<
T
<
300
K
3He/4He
dilu-on
cryostat
(2011)
0.01
K
<
T
<
30
K
RuO2
therm.
closer
to
the
sample
CalibraFon:
nuclear
thermometer
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
16
SC
magnet
(2008)
B
=
12
T
Bore
diameter
55
mm

17. Sample
rod
• Thermally
linked
to
the
cryostat
• Sample
cooled
down
via
the
wires
• Home
made
and
designed
holders
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
17

18. Quantum
Hall
effect
in
graphene
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
18

19. QHE
in
bilayer
graphene
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
19
1 2 3 4 5
2800
3000
3200
3400
3600
3800
µ(cm
2
/Vs)
n (10
12
cm
-2
)

20. QHE
in
trilayer
graphene
• ObservaFon
of
the
ν=6
plateau
• Study
of
the
QHE
as
a
funcFon
of
T
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
20
C.
Cobaleda
et
al.
Physica
E
44
530-­‐533
(2011)
C.
Cobaleda
et
al.
Phys.
Status
Solidi
C
9
1411-­‐1414
(2012)

21. Weak
localizaFon
weak
anFlocalizaFon
• Electrons
counter
propagaFng
in
closed
paths
– Phase
conserved
– Time
reversal
symmetry
conserved
• Broken
if
B
is
applied
• Back
scaXering
enhanced
– WL:
Maximum
of
ρ
at
B=0
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
21

22. Weak
localizaFon
weak
anFlocalizaFon
• Electrons
counter
propagaFng
in
closed
paths
– Phase
conserved
– Time
reversal
symmetry
conserved
• Broken
if
B
is
applied
• Back
scaXering
enhanced
– WL:
Maximum
of
ρ
at
B=0
• Carriers
in
graphene
are
chiral
– Back
scaXering
forbidden!
• WAL:
Minimum
of
ρ
at
B=0
– Chirality
at
low
energies
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
22

23. WAL-­‐WL
transiFon
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
23
-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
0.0
0.2
0.4
0.6
0.8
T=0.3K T=1.6K
T=3K T=6K
T=10K T=15K
σ(B)-σ(0)(e
2
/h)
B(T)
0.3 K
15 K
-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
σ(B)-σ(0)(e
2
/h)
B (T)
T=0.3 K T=1.6 K
T=2.6 K T=6 K
T=10 K T=15 K0.3 K
15 K
Vg
=
0
V
Vg
=
-­‐10
V
S.
Pezzini,
C.
Cobaleda
et
al.
Physical
Review
B
85
165451
(2012)

24. h-­‐BN/bilayer
graphene/h-­‐BN
heterostructure
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
24

25. Dirac
peak
vs
Temperature
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
25

26. Dirac
peak
vs
Temperature
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
26
nc
nc

27. Transport
regimes
• n
<
nc
– T
<
10
K
• ∂ ρxx/ ∂ T<0
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
27

28. Transport
regimes
• n
<
nc
– T
<
10
K
• ∂ ρxx/ ∂ T<0
– 10
K
<
T
<
50
K
• ∂ ρxx/ ∂ T<0
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
28

29. Transport
regimes
• n
<
nc
– T
<
10
K
• ∂ ρxx/ ∂ T<0
– 10
K
<
T
<
50
K
• ∂ ρxx/ ∂ T<0
• n
>
nc
– T
<
10
K
• ∂ ρxx/ ∂ T<0
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
29

30. Transport
regimes
• n
<
nc
– T
<
10
K
• ∂ ρxx/ ∂ T<0
– 10
K
<
T
<
50
K
• ∂ ρxx/ ∂ T<0
• n
>
nc
– T
<
10
K
• ∂ ρxx/ ∂ T<0
– 10
K
<
T
<
50
K
• ∂ ρxx/ ∂ T>0
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
30

31. All
together...
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
31
C.
Cobaleda
et
al.
Phys.
Rev
B
89
121404R
(2014)

32. Magnetotransport
characterizaFon
• Vd~0.5
V
• n~1011
cm-­‐2
• µ~40000
cm2/Vs
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
32

33. Quantum
phase
transiFons
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
33

34. Measurements
• n=10.2·∙1011cm-­‐2
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
34
ν=12
ν=16
ν=8

35. Measurements
• n=10.2·∙1011cm-­‐2
• 12-­‐>8
• 16-­‐>12
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
35
ν=12
ν=16
ν=8

36. Measurements
• n=10.2·∙1011cm-­‐2
• 12-­‐>8
• 16-­‐>12
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
36
ν=12
ν=16
ν=8
∂ρxy
∂B
"
#
$
%
&
'
max
∝T−κ

37. Measurements
• n=10.2·∙1011cm-­‐2
• 12-­‐>8
• 16-­‐>12
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
37
ν=12
ν=16
ν=8
∂ρxy
∂B
"
#
$
%
&
'
max
∝T−κ
κ ≈ 0.3

38. Measurements
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
38
κ ≈ 0.3

39. Universality
of
the
transiFon
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
39
n
=
14.6×1011
cm-­‐2
n
=
10.2×1011
cm-­‐2
n
=
6.07×1011
cm-­‐2

40. Universality
of
the
transiFon
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
40
n
=
14.6×1011
cm-­‐2
n
=
10.2×1011
cm-­‐2
n
=
6.07×1011
cm-­‐2
n
=
(-­‐)4.74×1011
cm-­‐2
n
=
(-­‐)6.84×1011
cm-­‐2
n
=
(-­‐)9.03×1011
cm-­‐2

41. n-­‐independent
κ
• SaturaFon
for
T<5
K
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
41
κ = 0.30 ± 0.02

42. Effect
of
disorder
• γ = p/2κ
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
42
Short
range
disorder
(Anderson
model)
Long
range
disorder
(Classic
percolaFon)
Our
data
κ=0.42
κ=0.75
κ=0.3
If
p=2;
γ=2.38
If
p=2;
γ=4/3
If
p=2;
γ=3.3

43. Effect
of
disorder
• γ = p/2κ
• What
if
p≠2?
• Next
goal:
measure
p
and
γ independently
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
43
Short
range
disorder
(Anderson
model)
Long
range
disorder
(Classic
percolaFon)
Our
data
κ=0.42
κ=0.75
κ=0.3
If
p=2;
γ=2.38
If
p=2;
γ=4/3
If
p=2;
γ=3.3

44. LocalizaFon
length:
γ
• Tails
of
the
LL:
VRH
• CriFcal
transiFon:
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
44
σxx ∝exp − T0 /T( )
T0 ∝ξ−1
γ
νν
ξ
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ −
∝
4
c

45. Coherence
length:
p
• Phase
coherence
preservaFon
depends
on
T
• WL
as
funcFon
of
T
• Measurement
of
lϕ
as
funcFon
of
T
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
45
lϕ ∝T− p/2

46. WL
in
bilayer
graphene
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
46
-10 0 10
0.0
0.1
0.2
0.3
15 K
∆σxx
(e
2
/h)
B (mT)
0.3 K
0.1 1 10
0.1
1
10
Lφ
bestFIT
Lφ
(µm)
T (K)
p
=
0.9

47. Classical
percolaFon
• Measurements
of
κ,
γ and
p
are
compaFble
• Both
methods
are
compaFble
with
a
PPT
driven
by
classical
percolaFon*
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
47
*
C.
Cobaleda
et
al.
SubmiXed
to
Phys.
Rev.
LeX
Short
range
disorder
(Anderson
model)
Long
range
disorder
(Classic
percolaFon)
Our
data
κ=0.42
κ=0.75
κ=0.3
If
p=2;
γ=2.38
If
p=2;
γ=4/3
p
=0.9;
γ=1.4±0.1
γ=1.3±0.3

48. Classical
percolaFon
• Measurements
of
κ,
γ and
p
are
compaFble
• Both
methods
are
compaFble
with
a
PPT
driven
by
classical
percolaFon*
• CompaFble
with
STM
observaFons
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
48
*
C.
Cobaleda
et
al.
SubmiXed
to
Phys.
Rev.
LeX
Short
range
disorder
(Anderson
model)
Long
range
disorder
(Classic
percolaFon)
Our
data
κ=0.42
κ=0.75
κ=0.3
If
p=2;
γ=2.38
If
p=2;
γ=4/3
p
=0.9;
γ=1.4±0.1
γ=1.3±0.3

49. SuperconducFvity
in
3D
porous
graphene
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
49

50. The
samples
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
50
3D
porous
carbon
3D
porous
carbon+Ta
3D
porous
graphene+Ta
3D
porous
graphene

51. 3D
graphene
vs
3D
carbon
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
51
H2c =
φ0
2πξ(0)2
1−
T
T0
"
#
$
%
&
'

52. SuperconducFng
properFes
of
Ta
3D
graphene
• Bc
=
2
T
• Tc
=
1.2
K
• ξ(0)
=
14
nm
• vF
=
1.2·∙104
m/s
3D
carbon
• Bc
=
2.3
T
• Tc
=
0.96
K
• ξ(0)
=
11
nm
• vF
=
0.8·∙104
m/s
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
52
C.
Cobaleda
et
al.
SubmiXed
to
App.
Phys.
LeX

53. SuperconducFng
properFes
of
Ta
3D
graphene
(sp2
bonds)
• Bc
=
2
T
• Tc
=
1.2
K
• ξ(0)
=
14
nm
• vF
=
1.2·∙104
m/s
3D
carbon
(sp3
bonds)
• Bc
=
2.3
T
• Tc
=
0.96
K
• ξ(0)
=
11
nm
• vF
=
0.8·∙104
m/s
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
53
Stronger
hybridizaFon
between
e-­‐
in
Ta
and
3DG
than
between
Ta
and
3DC
C.
Cobaleda
et
al.
SubmiXed
to
App.
Phys.
LeX

54. Conclusions
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
54

55. Conclusions
• FabricaFon
of
graphene
devices
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
55

56. Conclusions
• FabricaFon
of
graphene
devices
• QHE
in
inhomogeneous
graphene
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
56

57. Conclusions
• FabricaFon
of
graphene
devices
• QHE
in
inhomogeneous
graphene
• WL-­‐WAL
transiFon
in
monolayer
graphene
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
57

58. Conclusions
• FabricaFon
of
graphene
devices
• QHE
in
inhomogeneous
graphene
• WL-­‐WAL
transiFon
in
monolayer
graphene
• Transport
regimes
in
hBN/graphene/hBN
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
58

59. Conclusions
• FabricaFon
of
graphene
devices
• QHE
in
inhomogeneous
graphene
• WL-­‐WAL
transiFon
in
monolayer
graphene
• Transport
regimes
in
hBN/graphene/hBN
• First
observaFon
of
a
QPT
fully
driven
by
a
classical
percolaFon
regime in
graphene
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
59

60. Conclusions
• FabricaFon
of
graphene
devices
• QHE
in
inhomogeneous
graphene
• WL-­‐WAL
transiFon
in
monolayer
graphene
• Transport
regimes
in
hBN/graphene/hBN
• First
observaFon
of
a
QPT
fully
driven
by
a
classical
percolaFon
regime in
graphene
• Study
of
charge
transfer
effects
between
tantalum
and
3D
graphene
and
carbon
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
60

61. Agradecimientos
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
61
Dr.
Enrique
Diez
Dr.
Yahya
Meziani
Dr.
ViXorio
Bellani
Dr.
Francesco
Rossella
Sergio
Pezzini
David
López-­‐Romero
Maika
Sabido
Alicia
Fraile
Dr.
Wei
Pan
Dr.
Duncan
Maude
Dr.
Walter
Escoffier
Dr.
Benjamin
Piot
Fabrice
Iacovella

62. Electronic
instrumentaFon
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
62
V~1V
f~15
Hz
100
MΩ
~10
nA
SR
Lock-­‐in
amplifier
830
and
Keithley
Sourcemeter
2601
A
Vg

63. Future
perspecFves
• Novel
routes
towards
effecFve
ambipolar
FETs
– Non
perpendicular
top
gates
– MoS2,
InSb,
etc
– van
der
Waals
structures
• QHE
in
4
layered
graphene
• Study
the
QPT
in
suspended
graphene
• CharacterisaFon
of
QPT
in
TLG
and
4LG
18/06/14
FabricaFon
and
characterizaFon
of
graphene
nanodevices
Cayetano
Sánchez-­‐Fabrés
Cobaleda
63