グラフェンにおけるスピン伝導・ 超伝導近接効果

1. 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 KandaUniversity of Tsukuba, Japan Collaborators U. Tsukuba H. Goto, S. Tanaka, H. Tomori, Y. OotukaMANA, NIMS K. Tsukagoshi, H. MiyazakiAkita U. M. HayashiNara Women’s U. H. YoshiokaSupported 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. 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 Relativistic Josephson effect Klein paradox (propagation of relativistic particlesthrough a barrier) Superconducting proximity effect O. Klein, Z. Phys53,157 (1929); 41, 407 (1927) Geim & Kim, Scientific American, April, 2008

6. Graphene as a nanoelectronics material Also good for spintronics Small spin-orbit interactionSmall hyperfine interaction 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 Long spin relaxation length

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

8. Spin transport in multi-layer graphene

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

10. 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)）

11. 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））

12. 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

13. 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

14. 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

15. 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...

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

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

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

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

20. Nonlocal measurement Rs: spin signal Rs R: 4-terminal resistance of MLG 4K 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 RN RN RN RN RF RF Ri Ri Takahashi and Maekawa, PRB 67, 052409 (2003) RN PJ: interfacial current polarizationpF: current polarization of F1 and F2L: separation of F1 and F2

23. General expression for spin signals Tunnel junctions RN RN RN RN RN R1,R2 >> RN >> RF RF RF Ri Ri Co/Al2O3/Al Jedema et al., Nature416, 713 (2002). Takahashi and Maekawa, PRB 67, 052409 (2003) RN Two limiting cases are well studied.

24. General expression for spin signals RN RN RN RN RN RN RN RN RF RF Ri Ri Takahashi and Maekawa, PRB 67, 052409 (2003) RN Two limiting cases are well studied. Tunnel junctions Transparent junctions R1,R2 >> RN >> RF RN >> RF >> R1,R2 Py/Cu Co/Al2O3/Al Jedema et al., Nature416, 713 (2002). Jedema et al., Nature410, 345 (2001).

25. General expression for spin signal RN RN RN RN RN RN RN RN RF RF Ri Ri Takahashi and Maekawa, PRB 67, 052409 (2003) RN Two limiting cases are well studied. Tunnel junctions Transparent junctions R1,R2 >> RN >> RF RN >> RF >> R1,R2 Py/Cu Co/Al2O3/Al Jedema et al., Nature416, 713 (2002). Jedema et al., Nature410, 345 (2001). Intermediate interface RN >> R1,R2>> RF

26. General expression for spin signal RN RN RN RN RF RF Ri Ri Takahashi and Maekawa, PRB 67, 052409 (2003) 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 = 0.047 (c.f. PJ ~ 0.1in Co/graphene[*]) Fitting parameters take reasonable values, justifying the fit to eq. (1). [*] Tombros et al. Nature448, 571 (2007).

27. General expression for spin signal RN RN RN RN RN RF RF Ri Ri Takahashi and Maekawa, PRB 67, 052409 (2003) 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 = 0.047 (c.f. PJ ~ 0.1in 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 graphite SLG on SiO2 J. H. Chen et al. Nature Nanotech. (2008) 1. Nearly perfect crystal free of structural defects 2. Origins of scattering MLG charged impurities

29. Long spin relaxation length in MLG graphite contaminant adsorbed molecules SLG on SiO2 lSC modulation of carrier density J. H. Chen et al. Nature Nanotech. (2008) Smaller scattering  Longer spin relaxation length c.f. N = 1.5 - 2 m in SLG Tombros et al. Nature448, 571 (2007). 1. Nearly perfect crystal free of structural defects 2. Origins of scattering MLG (multilayer) graphene charge impurities, phonon charged impurities SiO2 layer lSC: interlayer screening length lSC ~ 1.2 nm (3.5 layers) (Miyazaki et al., APEX 2008) Distance from contaminant and adsorbed molecules becomes larger.Ripple becomes smaller.

30. 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 C4 C1 contact resistance lSC

31. 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 C4 lSC C1 contact resistance

32. 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 C4 lSC C1 contact resistance

33. 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 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 devices Gate-controllable intrinsic contact resistance in thick MLG Layered structure Screening of gate electric field lSC c1 c2 c3 c4 Ni

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

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

37. Contact resistance and spin signal RN R1,R2 >> RN >> RF Tunnel junctions RN RN RN RN RN RN RN RN RN RF RF Ri Ri Takahashi and Maekawa, PRB 67, 052409 (2003) Transparent junctions (Rccontact) with MLG, Transparent junctions (RF ~ 1mW) RN >> RF >> R1,R2

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

39. Gate voltage dependence spin induced magnetoresistance (SIMR) 4K

40. Gate voltage dependence spin induced magnetoresistance (SIMR) 4K Might indicate Rs proportional to RN?

41. Contact resistance and spin signal RN R1,R2 >> RN >> RF Tunnel junctions RN RN RN RN RN RN RN RN RN RF RF Ri Ri Takahashi and Maekawa, PRB 67, 052409 (2003) Transparent junctions (Rccontact) with MLG, Transparent junctions (RF ~ 1mW) RN >> RF >> R1,R2 Gate controllable

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

43. Why Cooper-pairs in graphene? superconductivity relativity Single layer graphene (SLG) 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 ≈ 0.2 - 0.6 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