グラフェンにおけるスピン伝導・ 超伝導近接効果 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. 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

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).

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

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 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)

Spin transport in multi-layer graphene

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

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...

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

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

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

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)

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)

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)

General expression for spin signal Takahashi and Maekawa, PRB 67, 052409 (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

General expression for spin signals Takahashi and Maekawa, PRB 67, 052409 (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

General expression for spin signals Takahashi and Maekawa, PRB 67, 052409 (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

General expression for spin signal Takahashi and Maekawa, PRB 67, 052409 (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

General expression for spin signal Takahashi and Maekawa, PRB 67, 052409 (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 = 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) 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 = 0.047 (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.

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

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 = 1.5 - 2 m in SLG Tombros et al. Nature 448, 571 (2007). Distance from contaminant and adsorbed molecules becomes larger. Ripple becomes smaller.

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

Contact resistance in thick MLG devices 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

Contact resistance in thick MLG devices 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

Contact resistance in thick MLG devices 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

Contact resistance in thick MLG devices Ni lSC Gate-controllable intrinsic contact resistance in thick MLG Layered structure Screening of gate electric field

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.

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,

Contact resistance and spin signal Takahashi and Maekawa, PRB 67, 052409 (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

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

Gate voltage dependence 4K spin induced magnetoresistance (SIMR)

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

Contact resistance and spin signal Takahashi and Maekawa, PRB 67, 052409 (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

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 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

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

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

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

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

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

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

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).

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).

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)

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

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.

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

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

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 Ngate:　gate-induced carrier density

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.

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