1. グラフェンにおけるスピン伝導・ 超伝導近接効果
「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.

2. Outline Brief introduction to graphene
Spin transport in multilayer graphene
Cooper-pair transport in single and multilayer graphene
Specialty of multilayer graphene

3. 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.
Low-dimensional nanocarbon has new potential for nanoelectronics.
This table shows major nonocarbon materials; fullerene for zero dimension, carbon nanotube for one dimension and thin graphite film for two dimension.
Their transport can be measured by attaching metal electrodes like these pictures.
The gating effect is important for electronics.
It is rich for nanotube and graphite film, but poor for fullerene.
To control electron behavior, artificial process is useful.
It goes well in thin graphite films, is difficult in carbon nanotubes, and is impossible in fullerene.
Thus, thin graphite films have potential for variety of low dimensional transport.
However, disorder of the film is important factor therein.
低次元ナノカーボンはナノエレクトロニクスに対する新しい可能性を持ちます。
ここに代表的な低次元ナノカーボン材料を示します。
0，1，2次元の代表的な材料はそれぞれフラーレン、カーボンナノチューブ、グラファイト超薄膜です。
それぞれ、この写真のように金属電極を取り付けて電気伝導を測定することが可能です。
エレクトロニクスへの応用を考えた場合にはゲート効果が重要ですが、０次元の場合は効果が乏しく、１，２次元では効果があります。
また、デバイス設計の自由度を考えると、電子線リソグラフィーによる追加加工ができると都合がよいですが、０次元では不可能、1次元では困難ですが、2次元では容易です。
このようなことから、 thin graphite films have potential for variety of low dimensional transport.
Disorder of the film is important factor therein.
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

4. Electronic structure of graphene
Linear dispersion at K and K’ points.
Charge carriers behave as massless Dirac fermions, described by Dirac eq.
Conventional metals and semiconductors have parabolic dispersion relation, ruled by Schoedinger eq.
シュレディンガー方程式
parabolicな分散関係
Electrons and holes correspond to electrons and positrons, having charge conjugation symmetry in quantum electrodynamics (QED).

5. Relativistic effects in graphene
Klein paradox　
Relativistic Josephson effect　
(propagation of relativistic particles through a barrier)
Superconducting proximity effect
O. Klein, Z. Phys 53,157 (1929); 41, 407 (1927)
Geim & Kim, Scientific American, April, 2008

6. 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

7. Multilayer graphene (MLG)
Thickness
single layer graphene
bilayer
bulk graphite
Multilayer graphene
thickness：1-10 nm (interlayer distance = 0.34 nm)
Electric field effect Screening of gate electric field
semimetal
band overlap ~ 40meV
interlayer screening length lSC ~ 1.2 nm (3.5 layers) (Miyazaki et al., APEX 2008)

8. Spin transport in multi-layer graphene

9. optical microscope image
FM/MLG/FM sample
optical microscope image
Cr/Au
Co1
Co2
4 m
Cr/Au

10. Scotch tape method
Graphene was found in by Novoselov, Geim et al. (Manchester).
Micromechanical cleavage (Scotch tape method) (Geim, Kim, Scientific American (April, 2008)）

11. Scotch tape method
Graphene was found in 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））

12. Scotch tape method
Graphene was found in 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

13. Scotch tape method
Graphene was found in 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

14. Scotch tape method
Graphene was found in 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

15. Scotch tape method
Graphene was found in 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...

16. optical microscope image
FM/MLG/FM sample
thickness ~ 2.5 nm (AFM)
(4 - 5 layers)
AFM image
substrate
UGF
optical microscope image
1 m
Co1: 200 nm
Co2: 330 nm
L = 290 nm
SEM image I V – + H V I
Cr/Au
Co1
Co2
4 m
Cr/Au
Highly doped Si substrate is used as a back gate.
F. J. Jedema et al. Nature 416, 713 (2002)
Nonlocal measurement

17. optical microscope image
FM/MLG/FM sample
thickness ~ 2.5 nm (AFM)
(4 - 5 layers)
AFM image
substrate
UGF
optical microscope image
1 m
Co1: 200 nm
Co2: 330 nm
L = 290 nm
SEM image I V – + H V I
Cr/Au
Co1
Co2
4 m
Cr/Au
Highly doped Si substrate is used as a back gate.
F. J. Jedema et al. Nature 416, 713 (2002)
Nonlocal measurement
Ferro1
Ferro2
Parallel alignment of magnetization  positive voltage

18. optical microscope image
FM/MLG/FM sample
thickness ~ 2.5 nm (AFM)
(4 - 5 layers)
AFM image
substrate
UGF
optical microscope image
1 m
Co1: 200 nm
Co2: 330 nm
L = 290 nm
SEM image I V – + H V I
Cr/Au
Co1
Co2
4 m
Cr/Au
Highly doped Si substrate is used as a back gate.
F. J. Jedema et al. Nature 416, 713 (2002)
Nonlocal measurement
Ferro1
Ferro2
Parallel alignment of magnetization  positive voltage
Antiparallel alignment of magnetization  negative voltage

19. Nonlocal measurement Rs 4K Rs: spin accumulation signal (spin signal)
R: 4-terminal resistance of MLG
Rs: spin signal 4K Rs
RP ~ -RAP > 0
Rs: spin accumulation signal (spin signal)

20. Nonlocal measurement Rs 4K Rs: spin accumulation signal (spin signal)
R: 4-terminal resistance of MLG
Rs: spin signal 4K Rs
RP ~ -RAP > 0
Rs: spin accumulation signal (spin signal)

21. Nonlocal measurement Rs 4K
Spin signal is a linearly decreasing function of resistance.
Quite different from conventional spin signals
RP ~ -RAP > 0
Rs: spin accumulation signal (spin signal)

22. General expression for spin signal
Takahashi and Maekawa, PRB 67, (2003) Ri RF RN RN RN Ri RF RN RN
PJ: interfacial current polarization pF: current polarization of F1 and F2 L: separation of F1 and F2

23. General expression for spin signals
Takahashi and Maekawa, PRB 67, (2003) Ri RF RN RN RN Ri RF RN RN
Two limiting cases are well studied.
Tunnel junctions
Co/Al2O3/Al RN
Jedema et al., Nature 416, 713 (2002).
R1,R2 >> RN >> RF

24. General expression for spin signals
Takahashi and Maekawa, PRB 67, (2003) Ri RF RN RN RN Ri RF RN RN
Two limiting cases are well studied.
Tunnel junctions
Transparent junctions
R1,R2 >> RN >> RF
RN >> RF >> R1,R2
Co/Al2O3/Al
Py/Cu
Jedema et al., Nature 416, 713 (2002).
Jedema et al., Nature 410, 345 (2001). RN RN

25. General expression for spin signal
Takahashi and Maekawa, PRB 67, (2003) Ri RF RN RN RN Ri RF RN RN
Two limiting cases are well studied.
Tunnel junctions
Transparent junctions
R1,R2 >> RN >> RF
RN >> RF >> R1,R2
Co/Al2O3/Al
Py/Cu
Jedema et al., Nature 416, 713 (2002).
Jedema et al., Nature 410, 345 (2001).
Intermediate interface
RN >> R1,R2 >> RF RN RN RN RN

26. General expression for spin signal
Takahashi and Maekawa, PRB 67, (2003) Ri RF RN RN RN Ri RF RN RN
Linearly decreasing asymptotic form Rs R
(1)
only under the following condition,
. (2)
From the fitting and condition (2),
Interface resistance: R1+R2 = 540  (c.f. 490  from independent estimation)
Current polarization: PJ = (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).

27. General expression for spin signal
Takahashi and Maekawa, PRB 67, (2003) RN RF Ri
Linearly decreasing asymptotic form Rs R
(1)
only under the following condition,
. (2)
From the fitting and condition (2),
Interface resistance: R1+R2 = 540  (c.f. 490  from independent estimation)
Current polarization: PJ = (c.f. PJ ~ 0.1 in Co/graphene[*])
RN >> R1,R2 >> RF
Spin relaxation length: N >> 8 m
Intermediate interface
Longer than lN of SLG, Al, and Cu.

28. Long spin relaxation length in MLG
1. Nearly perfect crystal free of structural defects
2. Origins of scattering
J. H. Chen et al. Nature Nanotech. (2008)
SLG on SiO2
graphite
MLG
charged impurities

29. Long spin relaxation length in MLG
1. Nearly perfect crystal free of structural defects
2. Origins of scattering
J. H. Chen et al. Nature Nanotech. (2008)
SLG on SiO2
graphite
contaminant
adsorbed molecules
MLG
(multilayer) graphene
modulation of carrier density
lSC
charge impurities, phonon
charged impurities
SiO2 layer
lSC: interlayer screening length lSC ~ 1.2 nm (3.5 layers) (Miyazaki et al., APEX 2008)
Smaller scattering  Longer spin relaxation length
c.f. N = m in SLG
Tombros et al. Nature 448, 571 (2007).
Distance from contaminant and adsorbed molecules becomes larger. Ripple becomes smaller.

30. Contact resistance in thick MLG devices
thickness: 5 nm
c1 （L = 180 nm）
c2 （L = 290 nm）
c3 （L = 380 nm）
c4 （L = 490 nm） c1 c2 c3 c4 Ni C1 C4
contact resistance
lSC

31. Contact resistance in thick MLG devicesNi
c1 （L = 180 nm）
c2 （L = 290 nm）
c3 （L = 380 nm）
c4 （L = 490 nm）
thickness: 5 nm C4
lSC C1
contact resistance

32. Contact resistance in thick MLG devicesNi
c1 （L = 180 nm）
c2 （L = 290 nm）
c3 （L = 380 nm）
c4 （L = 490 nm）
thickness: 5 nm C4
lSC C1
contact resistance

33. Contact resistance in thick MLG devicesNi
c1 （L = 180 nm）
c2 （L = 290 nm）
c3 （L = 380 nm）
c4 （L = 490 nm）
thickness: 5 nm
Gate-controllable intrinsic contact resistance in thick MLG
Layered structure Screening of gate electric field C4
lSC C1
contact resistance

34. Contact resistance in thick MLG devicesNi
lSC
Gate-controllable intrinsic contact resistance in thick MLG
Layered structure Screening of gate electric field

35. Contact resistance in thick MLG devices
lSC
Gate-controllable intrinsic contact resistance in thick MLG
Layered structure Screening of gate electric field c1 c2 c3 c4 Ni
Rccontact can be reduced.

36. Contact resistance in thick MLG devices
thickness: 5 nm
c1 （L = 180 nm）
c2 （L = 290 nm）
c3 （L = 380 nm）
c4 （L = 490 nm） c1 c2 c3 c4 Ni
Rccontact
contact resistance C1 C4
slope: graphene resistance
If one can sufficiently reduce Rccontact,

37. Contact resistance and spin signal
Takahashi and Maekawa, PRB 67, (2003) RN RF Ri
Tunnel junctions RN
R1,R2 >> RN >> RF
Transparent junctions (Rccontact) with MLG,
Transparent junctions
(RF ~ 1mW)
RN >> RF >> R1,R2 RN

38. Sample for local measurement_ I V +
Thickness: 9 nm
Spin valve effect
parallel – small R R
MLG H
antiparallel – large R

39. Gate voltage dependence4K
spin induced magnetoresistance (SIMR)

40. Gate voltage dependence4K
spin induced magnetoresistance (SIMR)
Might indicate Rs proportional to RN?

41. Contact resistance and spin signal
Takahashi and Maekawa, PRB 67, (2003) RN RF Ri
Tunnel junctions RN
R1,R2 >> RN >> RF
Transparent junctions (Rccontact) with MLG,
Transparent junctions
(RF ~ 1mW)
RN >> RF >> R1,R2 RN
Gate controllable

42. Cooper pair transport in single and multi-layer graphene

43. 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).

44. 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

45. S/graphene/S junctions
super-conductor
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 ≈ mm
Doped Si is used as a back gate.
super-conductor
graphene
graphene

46. Josephson effect in SLG
Gate voltage dependence
gap: d = 0.22 mm
IV characteristics
B = 0
Magnetic field dependence
sweep

47. Temperature dependence of critical supercurrent
Vg = -75 V -50V
75V
50V -25V
25V 0V 8V
gap: d = 0.22 mm

48. Conventional theory for Ic(T)
Long junctions (d >> xN)
Clean limit:
Dirty limit:

49. Conventional theory for Ic(T)
Long junctions (d >> xN)
Clean limit:
Dirty limit:
(l: mean free path)
Short junctions (d << xN)
Two kinds of Kulik-Omel’yanchuk theory
ballistic, ideal interface
diffusive, ideal interface

50. Conventional theory for Ic(T)
Long junctions (d >> xN)
Clean limit:
Dirty limit:
Short junctions (d << xN)
Two kinds of Kulik-Omel’yanchuk theory
ballistic, ideal interface
diffusive, ideal interface
Ambegaokar-Baratoff result

51. Temperature dependence of critical supercurrent
Vg = -75 V -50V
75V
50V -25V
25V 0V 8V
gap: L = 0.22 mm

52. Temperature dependence of critical supercurrent
Vg = -75 V -50V
75V
50V -25V
25V 0V 8V
KO1 theory (short junction dirty limit: l << d << xN)
I. O. Kulick and A. N. Omel'yanchuk, JETP Lett. 21, 96 (1975).

53. Temperature dependence of critical supercurrent
Injection of Cooper pairs into graphene
Vg = -75 V -50V
75V
50V -25V
25V 0V 8V
KO1 theory (short junction dirty limit: l << d << xN)
Ic(T=0) Tc
Never seen in other SNS systems
Ballistic junction is needed for relativistic Josephson effect!
I. O. Kulick and A. N. Omel'yanchuk, JETP Lett. 21, 96 (1975).

54. Making ballistic junctions
mean free path
shorter junctions
Angle deposition of metals
Resist mask
graphene
Substrate
50 nm
cleaner graphene
K.I. Bolotin et al., SSC 146, 351 (2008)

55. Multilayer graphene
Temperature dependence of resistance (Inset: Vg dependence of normal-state resistance)
Tc of Pd/Al

56. electron supercurrent
Current-voltage (I-V) characteristics
hole supercurrent
electron supercurrent
0.2 K Ic
Vgp
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.

57. Electron and hole supercurrents
Relation between Ic and Rn

58. 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

59. Temperature dependence of Ic
Vg=75V
60V
45V

60. Conventional theory for Ic(T)
Long junctions (d >> xN)
Clean limit:
Dirty limit:
(l: mean free path)
In our measurement, a = 2.
Short junctions (d << xN)
Two kinds of Kulik-Omel’yanchuk theory
measurement
ballistic, ideal interface
diffusive, ideal interface
Ambegaokar-Baratoff result

61. 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.

62. Model for Ic(T) of multilayer graphene
Assumptions
Regard each layer as independent single-layer graphene with different carrier density.

63. 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.)

64. 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
Ngate:　gate-induced carrier density

65. Numerical result is reproduced in a wide temperature range.
A, B, C... : Onset of supercurrent in 1st, 2nd, 3rd... layers
is reproduced in a wide temperature range.

66. 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