Download 国際会議報告 （VORTEX V ギリシャ、ロドス島）

091127 「グラフェン・グラファイトとそ
の周辺の物理」研究会（筑波大）
グラフェンにおけるスピン伝導・
超伝導近接効果
Akinobu Kanda
University of Tsukuba, Japan
Collaborators
U. Tsukuba
H. Goto, S. Tanaka,
H. Tomori, Y. Ootuka
MANA, NIMS
K. Tsukagoshi, H. Miyazaki
Akita U.
M. Hayashi
Nara Women’s U. H. Yoshioka
Supported by CREST project.
Outline
• Brief introduction to graphene
• Spin transport in multilayer graphene
• Cooper-pair transport in single and
multilayer graphene
Specialty of multilayer graphene
Allotropes of graphite
3D
diamond, graphite
amorphous carbon
(no crystalline structure)
1D
carbon nanotubes
0D
fullerenes (C60, C70 ...)
2D
(graphene)
Graphene is a material that should NOT exist!
Thermodynamically unstable (Landau, Peierls,
1935, 1937)
Atom displacements due to thermal fluctuation
is comparable to interatomic distance at any
temperature.
In 2004, graphene was discovered by Geim’s group.
Obtained by mechanical cleavage from bulk graphite.
High crystal quality, as a metastable state
From Wikipedia
Electronic structure of graphene
Linear dispersion at K and
K’ points.
E  kvF
Charge carriers behave as
massless Dirac fermions,
described by Dirac eq.
Conventional metals and
semiconductors have
シュレディンガー方程式
parabolic
dispersion relation,
ruled
by Schoedinger eq.
parabolicな分散関係
Electrons and holes correspond to electrons and positrons, having
charge conjugation symmetry in quantum electrodynamics (QED).
Relativistic effects in graphene
Klein paradox
(propagation of relativistic particles
through a barrier)
O. Klein, Z. Phys 53,157 (1929); 41, 407 (1927)
Geim & Kim, Scientific American, April, 2008
Relativistic Josephson effect
Superconducting proximity effect
Graphene as a nanoelectronics material
K. S. Novoselov et al., Science 306 (2004) 666.
– Electric field effect
– High mobility
– Band gap possible
– Stable under ambient conditions
– Easy to microfabricate (O2 plasma
etching)
– Abundance of resource
Also good for spintronics
Small spin-orbit interaction
Small hyperfine interaction
Long spin relaxation length
Multilayer graphene (MLG)
Thickness
bilayer
bulk graphite
semimetal
band overlap
~ 40meV
single layer
graphene
Multilayer graphene
thickness：1-10 nm
(interlayer distance = 0.34 nm)
Electric field effect
Screening of gate electric field
interlayer screening length lSC ~ 1.2 nm (3.5 layers)
(Miyazaki et al., APEX 2008)
Spin transport in multi-layer graphene
FM/MLG/FM sample
optical microscope image
Cr/Au
Co1
Co2
Cr/Au
4 m
Scotch tape method
Graphene was found in 2004
by Novoselov, Geim et al. (Manchester).
Micromechanical cleavage (Scotch tape method)
(Geim, Kim, Scientific American (April, 2008)）
Scotch tape method
Graphene was found in 2004
by Novoselov, Geim et al. (Manchester).
Micromechanical cleavage (Scotch tape method)
(Geim, Kim, Scientific American (April, 2008), 日経サイエンス（2008年7月））
Scotch tape method
Graphene was found in 2004
by Novoselov, Geim et al. (Manchester).
Micromechanical cleavage (Scotch tape method)
(Geim & Kim, Scientific American (April, 2008), 日経サイエンス（2008年7月））
Repeat cleavage
Scotch tape method
Graphene was found in 2004
by Novoselov, Geim et al. (Manchester).
Micromechanical cleavage (Scotch tape method)
(Geim, Kim, Scientific American (April, 2008), 日経サイエンス（2008年7月））
Si Substrate with 300 nm of SiO2
Scotch tape method
Graphene was found in 2004
by Novoselov, Geim et al. (Manchester).
Micromechanical cleavage (Scotch tape method)
(Geim, Kim, Scientific American (April, 2008), 日経サイエンス（2008年7月））
Under optical microscope
Scotch tape method
Graphene was found in 2004
by Novoselov, Geim et al. (Manchester).
Micromechanical cleavage (Scotch tape method)
(Geim, Kim, Scientific American (April, 2008), 日経サイエンス（2008年7月））
Optical microscope image
No need for MOCVD...
FM/MLG/FM sample
AFM image
optical microscope image
Cr/Au
substrate UGF
SEM image
I
H
I
Co1: 200 nm
L = 290 nm
Co2: 330 nm
Co1
Cr/Au
Co2 V
4 m
1 m
–+
V
thickness ~ 2.5 nm (AFM)
Highly doped Si substrate is used as a back gate.
(4 - 5 layers)
Nonlocal measurement
F. J. Jedema et al. Nature 416, 713 (2002)
FM/MLG/FM sample
AFM image
optical microscope image
Cr/Au
substrate UGF
SEM image
I
H
I
Co1: 200 nm
L = 290 nm
Co2: 330 nm
Co1
Cr/Au
Co2 V
4 m
1 m
–+
V
thickness ~ 2.5 nm (AFM)
Highly doped Si substrate is used as a back gate.
(4 - 5 layers)
Nonlocal measurement
Ferro1
F. J. Jedema et al. Nature 416, 713 (2002)
Ferro2
Parallel alignment of magnetization
 positive voltage
FM/MLG/FM sample
AFM image
optical microscope image
Cr/Au
substrate UGF
SEM image
I
H
I
Co1: 200 nm
L = 290 nm
Co2: 330 nm
Co1
Cr/Au
Co2 V
4 m
1 m
–+
V
thickness ~ 2.5 nm (AFM)
Highly doped Si substrate is used as a back gate.
(4 - 5 layers)
Nonlocal measurement
Ferro1
F. J. Jedema et al. Nature 416, 713 (2002)
Ferro2
Parallel alignment of magnetization
 positive voltage
Antiparallel alignment of magnetization
 negative voltage
Nonlocal measurement
0.55
0.4
g
R
P
0.1
0.40
Rs
0
R: 4-terminal resistance of MLG
-0.1
200
R
-0.2
-0.3
0.45
0.35
AP
-2000 -1000
0
1000 2000
H (Oe)
RP ~ -RAP > 0
R ()
V/I ()
0.2
Rs ()
0.3
Rs: spin signal
0.50
V =0V
4K
150
100
50
-100
-50
0
V (V)
g
Rs: spin accumulation signal
(spin signal)
50
100
Nonlocal measurement
0.55
0.4
g
R
P
0.1
0.40
Rs
0
R: 4-terminal resistance of MLG
-0.1
200
R
-0.2
-0.3
0.45
0.35
AP
-2000 -1000
0
1000 2000
H (Oe)
RP ~ -RAP > 0
R ()
V/I ()
0.2
Rs ()
0.3
Rs: spin signal
0.50
V =0V
4K
150
100
50
-100
-50
0
V (V)
g
Rs: spin accumulation signal
(spin signal)
50
100
Nonlocal measurement
0.6
0.4
0.3
g
0.5
0.2
V <V
n
n
P
0.4
0.1
-0.1
R
-0.2
AP
-2000 -1000
0
1000 2000
H (Oe)
RP ~ -RAP > 0
Rs: spin accumulation signal
(spin signal)
s
Rs
0
-0.3
g
g
R
R ()
V/I ()
V >V
V =0V
4K
0.3
0.2 Spin signal is a linearly decreasing
function of resistance.
0.1 Quite different from
conventional spin signals
0
0
50
100 150 200
R ()
250
General expression for spin signal
Takahashi and Maekawa, PRB 67, 052409 (2003)
 PJ Rii
pF RRFF 



2 R
R
i 1 1  PJ N
1  pF2 RN 
N
 L / lN
RS  4 RN e
2
2 Ri
2 RRFF  2 L / lN

 1 

e
2 R
2 R

R
i 1
1  PJ NN 1  pF NN 
2
PJ: interfacial current polarization
pF: current polarization of F1 and F2
L: separation of F1 and F2
General expression for spin signals
Takahashi and Maekawa, PRB 67, 052409 (2003)
 PJ Rii
pF RRFF 



2 R
R
i 1 1  PJ N
1  pF2 RN 
N
 L / lN
RS  4 RN e
2
2 Ri
2 RRFF  2 L / lN

 1 

e
2 R
2 R

R
i 1
1  PJ NN 1  pF NN 
2
Two limiting cases are well studied.
Tunnel junctions
R1,R2 >> RN >> RF
Co/Al2O3/Al Jedema et al., Nature 416, 713 (2002).
RS  PJ2 RNN eL / lN
General expression for spin signals
Takahashi and Maekawa, PRB 67, 052409 (2003)
 PJ Rii
pF RRFF 



2 R
R
i 1 1  PJ N
1  pF2 RN 
N
 L / lN
RS  4 RN e
2
2 Ri
2 RRFF  2 L / lN

 1 

e
2 R
2 R

R
i 1
1  PJ NN 1  pF NN 
2
Two limiting cases are well studied.
Tunnel junctions
R1,R2 >> RN >> RF
Co/Al2O3/Al Jedema et al., Nature 416, 713 (2002).
RS  PJ2 RNN eL / lN
Transparent junctions
RN >> RF >> R1,R2
Py/Cu
RS 
Jedema et al., Nature 410, 345 (2001).
4 pF2
(1  pF2 ) 2
 RF  e L / lN
1

RN 

 2 L / lN
RNN
R
 RRNN  1  e
2
General expression for spin signal
Takahashi and Maekawa, PRB 67, 052409 (2003)
 PJ Rii
pF RRFF 



2 R
R
i 1 1  PJ N
1  pF2 RN 
N
 L / lN
RS  4 RN e
2
2 Ri
2 RRFF  2 L / lN

 1 

e
2 R
2 R

R
i 1
1  PJ NN 1  pF NN 
2
Two limiting cases are well studied.
Tunnel junctions
R1,R2 >> RN >> RF
Co/Al2O3/Al Jedema et al., Nature 416, 713 (2002).
Transparent junctions
RN >> RF >> R1,R2
Py/Cu
Jedema et al., Nature 410, 345 (2001).
Intermediate interface
RN >> R1,R2 >> RF
RS  a  bRN
RS  PJ2 RNN eL / lN
RS 
4 pF2
(1  pF2 ) 2
 RF  e L / lN
1

RN 

 2 L / lN
RNN
R
 RRNN  1  e
2
General expression for spin signal
Takahashi and Maekawa, PRB 67, 052409 (2003)
 PJ Rii
pF RRFF 



2 R
R
i 1 1  PJ N
1  pF2 RN 
N
 L / lN
RS  4 RN e
2
2 Ri
2 RRFF  2 L / lN

 1 

e
2 R
2 R

R
i 1
1  PJ NN 1  pF NN 
Linearly decreasing asymptotic form
R1R2
2 P 2 R1R2
2

2
P
R
RsRs 
(1)
2
2 R
1  P R1  R2
( R1  R2 )
2
only under the following condition,
( R1  R2 ) RN
2 R1 R2

R
R

.
N
1  P2
(1  P 2 )2
(2)
From the fitting and condition (2),
Interface resistance: R1+R2 = 540  (c.f. 490  from independent estimation)
Current polarization: PJ = 0.047 (c.f. PJ ~ 0.1 in Co/graphene[*])
Fitting parameters take reasonable values, justifying
the fit to eq. (1).
[*] Tombros et al. Nature 448, 571 (2007).
General expression for spin signal
Takahashi and Maekawa, PRB 67, 052409 (2003)
 PJ Rii
pF RRFF 



2 R
R
i 1 1  PJ N
1  pF2 RN 
N
 L / lN
RS  4 RN e
2
2 Ri
2 RRFF  2 L / lN

 1 

e
2 R
2 R

R
i 1
1  PJ NN 1  pF NN 
Linearly decreasing asymptotic form
R1R2
2 P 2 R1R2
2

2
P
R
RsRs 
(1)
2
2 R
1  P R1  R2
( R1  R2 )
2
only under the following condition,
( R1  R2 ) RN
2 R1 R2

R
R

.
N
1  P2
(1  P 2 )2
(2)
From the fitting and condition (2),
Interface resistance: R1+R2 = 540  (c.f. 490  from independent estimation)
Current polarization: PJ = 0.047 (c.f. PJ ~ 0.1 in Co/graphene[*])
Spin relaxation length: lN >> 8 m
Longer than lN of SLG, Al, and Cu.
RN >> R1,R2 >> RF
Intermediate interface
Long spin relaxation length in MLG
graphite
1. Nearly perfect crystal free of structural
defects
2. Origins of scattering
MLG
SLG on SiO2
charged impurities
J. H. Chen et al. Nature Nanotech. (2008)
Long spin relaxation length in MLG
graphite
1. Nearly perfect crystal free of structural
defects
2. Origins of scattering
contaminant
MLG
(multilayer) graphene
lSC
SLG on SiO2
charged impurities
adsorbed molecules
modulation of carrier density
charge impurities, phonon
SiO2 layer
J. H. Chen et al. Nature Nanotech. (2008)
Smaller scattering
 Longer spin relaxation length
lSC: interlayer screening length
lSC ~ 1.2 nm (3.5 layers)
(Miyazaki et al., APEX 2008)
Distance from contaminant and
c.f. lN = 1.5 - 2 m in SLG
adsorbed molecules becomes larger.
Tombros et al. Nature 448, 571 (2007). Ripple becomes smaller.
Contact resistance in thick MLG devices
c1
c2
c3
c4
Ni
c1 （L = 180 nm）
c2 （L = 290 nm）
c3 （L = 380 nm）
c4 （L = 490 nm）
thickness: 5 nm
lSC
C4
C1
contact
resistance
Contact resistance in thick MLG devices
c1
c2
c3
c4
Ni
c1 （L = 180 nm）
c2 （L = 290 nm）
c3 （L = 380 nm）
c4 （L = 490 nm）
thickness: 5 nm
lSC
C4
C1
contact
resistance
Contact resistance in thick MLG devices
c1
c2
c3
c4
Ni
c1 （L = 180 nm）
c2 （L = 290 nm）
c3 （L = 380 nm）
c4 （L = 490 nm）
thickness: 5 nm
lSC
C4
C1
contact
resistance
Contact resistance in thick MLG devices
c1
c2
c3
c4
Ni
c1 （L = 180 nm）
c2 （L = 290 nm）
c3 （L = 380 nm）
c4 （L = 490 nm）
thickness: 5 nm
lSC
Gate-controllable intrinsic contact
C4
resistance in thick
C1 MLG
Layered structure
Screening of gate
electric field
contact
resistance
Contact resistance in thick MLG devices
c1
c2
c3
c4
Ni
lSC
Gate-controllable intrinsic contact
resistance in thick MLG
Layered structure
Screening of gate electric field
Contact resistance in thick MLG devices
c1
c2
c3
c4
lSC
Gate-controllable intrinsic contact
resistance in thick MLG
Layered structure
Screening of gate electric field
Ni
R1,2 
contact
Rc
intrinsic
 Rc
(Vg )
Rccontact can be reduced.
Contact resistance in thick MLG devices
c1
c2
c3
c4
Ni
c1 （L = 180 nm）
c2 （L = 290 nm）
c3 （L = 380 nm）
c4 （L = 490 nm）
Rccontact
thickness: 5 nm
C4
Rcintrinsic (Vg )  Rgraphene(Vg )
C1
contact
resistance
slope:
graphene
resistance
If one can sufficiently reduce Rccontact,
Ri
 const.
RN
Contact resistance and spin signal
Takahashi and Maekawa, PRB 67, 052409 (2003)
 PJ Rii
pF RRFF 



2 R
R
i 1 1  PJ N
1  pF2 RN 
N
 L / lN
RS  4 RN e
2
2 Ri
2 RRFF  2 L / lN

 1 

e
2 R
2 R

R
i 1
1  PJ NN 1  pF NN 
2
Tunnel junctions R1,R2 >> RN >> RF
 L / lN
RS  PJ2 RN
 RN
Ne
Transparent junctions (Rccontact) with MLG,
Transparent junctions
RN >> RF >> R1,R2
 RF  e L / lN
1


RS 
R

N
N

 2 L / lN
RNN
R
(1  pF2 ) 2
 RRNN  1  e
4 pF2
2
(RF ~ 1m)
Ri
 const.
RN
RS  RN
Sample for local measurement
I
+
_V
Thickness: 9 nm
Spin valve effect
parallel – small R
R
MLG
antiparallel – large R
H
46.50
V =0V
g
46.49
46.48
-1500-1000 -500 0 500 1000 1500
Magnetic field (Oe)
Gate voltage dependence
4K
46.50
V =0V
g
46.48
V = 80 V
g
37.72
37.71
V = -80 V
29.86


1200 Oe
0 Oe
46.49
37.73
spin induced magnetoresistance (SIMR)
g
29.85
29.84
-1500-1000 -500 0 500 1000 1500
Magnetic Field (Oe)
R

( H )  R ( H )dH
Gate voltage dependence
4K
46.50
V =0V
g
spin induced magnetoresistance (SIMR)


1200 Oe
0 Oe
46.49
R

( H )  R ( H )dH
46.48
37.73
V = 80 V
g
37.72
37.71
V = -80 V
29.86
g
29.85
29.84
-1500-1000 -500 0 500 1000 1500
Magnetic Field (Oe)
Might indicate Rs proportional to RN?
Contact resistance and spin signal
Takahashi and Maekawa, PRB 67, 052409 (2003)
 PJ Rii
pF RRFF 



2 R
R
i 1 1  PJ N
1  pF2 RN 
N
 L / lN
RS  4 RN e
2
2 Ri
2 RRFF  2 L / lN

 1 

e
2 R
2 R

R
i 1
1  PJ NN 1  pF NN 
2
Tunnel junctions R1,R2 >> RN >> RF
 L / lN
RS  PJ2 RN
 RN
Ne
Transparent junctions (Rccontact) with MLG,
Transparent junctions
RN >> RF >> R1,R2
 RF  e L / lN
1


RS 
R

N
N

 2 L / lN
RNN
R
(1  pF2 ) 2
 RRNN  1  e
4 pF2
2
(RF ~ 1m)
Ri
 const.
RN
RS  RN
Gate controllable
Cooper pair transport in single and multi-layer graphene
Why Cooper-pairs in graphene?
Single layer graphene (SLG)
relativity
superconductivity
Injection of Cooper-pairs by proximity effect
Andreev reflection
Intraband A. R.
Interband A. R.
Beenakker, Rev. Mod. Phys. 80, 1337 (2008).
Why Cooper-pairs in graphene?
Multilayer graphene (MLG)
semimetal
Usual proximity effect
Large gate electric field effect (-1012cm-2 < n < 10-12cm-2)
Never obtained in other SNS systems
S/graphene/S junctions
superconductor
superconductor
graphene
 Mechanical exfoliation of kish graphite
followed by e-beam lithography and metal
deposition.
 Electrode: Pd(5 nm)/Al(100 nm) or
Ti(5 nm)/Al(100 nm)/Ti(5 nm)
 Gap of electrodes d ≈ 0.2 - 0.6 m
 Doped Si is used as a back gate.
graphene
Josephson effect in SLG
Gate voltage dependence
gap: d = 0.22 m
IV characteristics
0.2
V (mV)
0.1
T=200mK, B
B=0.00mT
=0
Vg
-75V
-50V
-25V
8V
Magnetic field dependence
0.0
-0.1
-0.2
-3000 -2000 -1000
sweep
0
I (nA)
1000 2000 3000
Temperature dependence of critical supercurrent
Vg =
-75 V
-50V
75V
50V
-25V
25V
0V
8V
gap: d = 0.22 m
Conventional theory for Ic(T)
Long junctions (d >> xN)
Ic  exp(d / x N )

 exp((T / T0 ) )
0.5    1
Clean limit:
l  x N
Dirty limit:
l  x N
Conventional theory for Ic(T)
Long junctions (d >> xN)
Ic  exp(d / x N )

 exp((T / T0 ) )
Clean limit:
l  x N
Dirty limit:
l  x N
0.5    1
(l: mean free path)
Short junctions (d << xN)
Two kinds of Kulik-Omel’yanchuk theory
ballistic, ideal interface
diffusive, ideal interface
Conventional theory for Ic(T)
Long junctions (d >> xN)
Ic  exp(d / x N )
 exp((T / T0 ) )
Clean limit:
l  x N
0.5    1
Dirty limit:
l  x N
Short junctions (d << xN)
Two kinds of Kulik-Omel’yanchuk theory
ballistic, ideal interface
diffusive, ideal interface
Ambegaokar-Baratoff result
Temperature dependence of critical supercurrent
Vg =
-75 V
-50V
75V
50V
-25V
25V
0V
8V
gap: L = 0.22 m
Temperature dependence of critical supercurrent
Vg =
-75 V
-50V
75V
KO1 theory
(short junction
dirty limit:
l << d << xN)
50V
-25V
25V
0V
8V
I. O. Kulick and A. N. Omel'yanchuk, JETP Lett. 21, 96 (1975).
Temperature dependence of critical supercurrent
Injection of Cooper
pairs into graphene
Vg =
-75 V
75V
Ic
KO1 theory
(short junction
dirty limit:
l << d << xN)
Ic(T=0)
1500
Ic(T=0) (nA)
-50V
2000
1000
500
0
-75
-50
-25
0
25
50
75
Vg (V)
50V
-25V
1.0
Tc
0.8
Tc (K)
0.6
0.4
0.2
25V
0V
8V
0.0
-75
Tc
-50
-25
Never seen in other
SNS systems
0
25
50
75
Vg (V)
Ballistic junction is
needed for relativistic
Josephson effect!
I. O. Kulick and A. N. Omel'yanchuk, JETP Lett. 21, 96 (1975).
Making ballistic junctions
mean free path
shorter junctions
Angle deposition of metals
300
Resist mask
250
mfp (nm)
200
graphene
150
Substrate
100
50
0
-60
l
50 nm
-40
-20
0
20
Vgate(V)
40
60
h
2e 2 k F
cleaner graphene
kF   Vg  Vn
  7.2 1014 m 2 V 1
K.I. Bolotin et al., SSC 146, 351 (2008)
Multilayer graphene
Temperature dependence of resistance
(Inset: Vg dependence of normal-state resistance)
Tc of Pd/Al
Current-voltage (I-V) characteristics
hole
supercurrent
0.2 K
electron
supercurrent
Vgp
Ic
supercurrent
dV/dI at 0.06 K
 Critical supercurrent Ic depends on the gate voltage. Ambipolar
behavior was observed.
I-V curves do not show hysteresis due to small Rn, in clear contrast
to the single layer graphene Josephson junctions.
Electron and hole supercurrents
Relation between Ic and Rn
Electron and hole supercurrents
Temperature dependence of resistance
(Inset: Vg dependence of normal-state resistance)
Tc of Pd/Al
Asymmetry in electron and hole supercurrents
Temperature dependence of Ic
Vg=75V
60V
45V
d 2 Ic
dT
2
0
Ic  exp((T / T0 ) 2 )
Conventional theory for Ic(T)
Long junctions (d >> xN)
Clean limit:
l  x N
Ic  exp(d / x N )
Dirty limit:
l  x N

 exp((T / T0 ) )
0.5    1
Short junctions (d << xN)
(l: mean free path)
In our measurement,  = 2.
Two kinds of Kulik-Omel’yanchuk theory
measurement
ballistic, ideal interface
diffusive, ideal interface
Ambegaokar-Baratoff result
d 2 Ic
dT
2
0
d 2 Ic
dT
2
0
Possible origin of exp(T/T0)2 behavior
MLG
lSC ~ 3.5 layers
SiO2 (300 nm)
Si (Back gate)
In thick MLG, when large Vg is applied, the carriers at the bottom of the
MLG increases due to the screening of the gate electric field.
Assumption:
The number of superconducting layers increases with decreasing temperature.
Model for Ic(T) of multilayer graphene
Assumptions
 Regard each layer as independent single-layer graphene with
different carrier density.
Model for Ic(T) of multilayer graphene
Assumptions
 Regard each layer as independent single-layer graphene with
different carrier density.
 Critical supercurrent of each layer follows the KO1 theory.
(Note that the results are almost the same for Ambegaoker-Baratoff or
KO2 theory.)
Model for Ic(T) of multilayer graphene
Assumptions
 Regard each layer as independent single-layer graphene with
different carrier density.
 Critical supercurrent of each layer follows the KO1 theory.
(Note that the results are almost the same for Ambegaoker-Baratoff or
KO2 theory.)
 The onset temperature TC(n), and zero-temperature critical
supercurrent IC0(n) of n-th layer becomes infinitesimally small when
the carrier density of the layer is small enough:
For example
I C 0 (n), TC (n)  N gate (n)
Ngate: gate-induced carrier density
Numerical result
A, B, C... :
Onset of supercurrent in
1st, 2nd, 3rd... layers
Ic  exp((T / T0 ) 2 ) is reproduced in a wide temperature range.
Message
• Multilayer graphene is also an attractive material!
Screening of gate electric field leads to
– Large spin relaxation length
– gate-dependent contact resistance
Good for spintronics
– Large modulation of supercurrent
Good for superconducting transistors