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）

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.

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

From Wikipedia

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)

In 2004, graphene was discovered by Geim’s group.

Atom displacements due to thermal fluctuation is comparable to interatomic distance at any temperature.

Obtained by mechanical cleavage from bulk graphite. High crystal quality, as a metastable state

Electronic structure of graphene

Linear dispersion at K and K’ points.

Charge carriers behave as massless Dirac fermions, described by Dirac eq.

シュレディンガー方程式parabolicな分散関係

FkvE

Conventional metals and semiconductors have parabolic dispersion relation, ruled by Schoedinger eq.

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

– Electric field effect– High mobility – Band gap possible– Stable under ambient conditions– Easy to microfabricate (O2 plasma etc

hing)– Abundance of resource

K. S. Novoselov et al., Science 306 (2004) 666.

Also good for spintronicsSmall spin-orbit interactionSmall hyperfine interaction

Long spin relaxation length

Multilayer graphene (MLG)

single layer graphene bilayer

bulk graphite

band overlap ~ 40meV

Thickness

Multilayer graphenethickness： 1-10 nm(interlayer distance = 0.34 nm)

Electric field effect Screening of gate electric field

semimetal

interlayer screening length SC ~ 1.2 nm (3.5 layers) (Miyazaki et al., APEX 2008)

Spin transport in multi-layer graphene

FM/MLG/FM sample

Co2

Co1

Cr/Au

Cr/Au4 m

optical microscope image

Scotch tape method

Micromechanical cleavage (Scotch tape method) (Geim, Kim, Scientific American (April, 2008)）

Graphene was found in 2004 by Novoselov, Geim et al. (Manchester).

Scotch tape method

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

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


Si Substrate with 300 nm of SiO2


Scotch tape methodGraphene was found in 2004 by Novoselov, Geim et al. (Manchester).


Under optical microscope

Scotch tape methodGraphene was found in 2004 by Novoselov, Geim et al. (Manchester).


Optical microscope image

No need for MOCVD...

FM/MLG/FM sample

Co2

Co1

Cr/Au

Cr/Au4 m


1 m

Co1: 200 nm

Co2: 330 nmL = 290 nm

SEM image

I

V–+

H

thickness ~ 2.5 nm (AFM)(4 - 5 layers)

AFM image

substrate UGF

Highly doped Si substrate is used as a back gate.

F. J. Jedema et al. Nature 416, 713 (2002)Nonlocal measurement

V

I

FM/MLG/FM sample

Co2

Co1

Cr/Au

Cr/Au4 m


1 m

Co1: 200 nm

Co2: 330 nmL = 290 nm

SEM image

I

V–+

H


AFM image

substrate UGF



Ferro1 Ferro2Parallel alignment of magnetization

positive voltage

V

I

FM/MLG/FM sample

Co2

Co1

Cr/Au

Cr/Au4 m


1 m

Co1: 200 nm

Co2: 330 nmL = 290 nm

SEM image

I

V–+

H


AFM image

substrate UGF



Ferro1 Ferro2Parallel alignment of magnetization

positive voltage

Antiparallel alignment of magnetization negative voltage

V

I

Nonlocal measurement

RP ~ -RAP > 0

Rs

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-2000 -1000 0 1000 2000

V/I

(

)

H (Oe)

Vg = 0 V

RP

RAP

0.35

0.40

0.45

0.50

0.55

Rs (

)

50

100

150

200

-100 -50 0 50 100

R (

)

Vg (V)

R: 4-terminal resistance of MLG

Rs: spin signal4K

Rs: spin accumulation signal (spin signal)

Nonlocal measurement

RP ~ -RAP > 0

Rs

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-2000 -1000 0 1000 2000

V/I

(

)

H (Oe)

Vg = 0 V

RP

RAP

0

0.1

0.2

0.3

0.4

0.5

0.6

0 50 100 150 200 250

Vg > V

n

Vg < V

n

Rs (

)

R ()

Spin signal is a linearly decreasing function of resistance.

4K

Quite different from conventional spin signals

Rs: spin accumulation signal (spin signal)

General expression for spin signalTakahashi and Maekawa, PRB 67, 052409 (2003)

N

N

L

N

F

FN

i

Ji

N

F

F

F

N

i

J

J

iLNS

eRR

pRR

P

RR

p

pRR

P

P

eRR

/222

2

1

22

2

1/

1

2

1

21

114

RN

RN RN

RN RN

RF

RFRi

Ri

PJ: interfacial current polarizationpF: current polarization of F1 and F2L: separation of F1 and F2

General expression for spin signalsTakahashi and Maekawa, PRB 67, 052409 (2003)

N

N

L

N

F

FN

i

Ji

N

F

F

F

N

i

J

J

iLNS

eRR

pRR

P

RR

p

pRR

P

P

eRR

/222

2

1

22

2

1/

1

2

1

21

114

RN

RN RN

RN RN

RF

RFRi

Ri

Two limiting cases are well studied.Tunnel junctions

Co/Al2O3/Al

NLNJS eRPR /2 RN

Jedema et al., Nature 416, 713 (2002).

R1,R2 >> RN >> RF

General expression for spin signalsTakahashi and Maekawa, PRB 67, 052409 (2003)

N

N

L

N

F

FN

i

Ji

N

F

F

F

N

i

J

J

iLNS

eRR

pRR

P

RR

p

pRR

P

P

eRR

/222

2

1

22

2

1/

1

2

1

21

114

RN

RN RN

RN RN

RF

RFRi

Ri


Co/Al2O3/Al

NLNJS eRPR /2 RN

Py/Cu

Transparent junctions

NL

L

N

FN

F

FS Re

e

R

RR

p

pR

N

N 1

1)1(

4/2

/2

22

2

RN RN RN

Jedema et al., Nature 416, 713 (2002). Jedema et al., Nature 410, 345 (2001).

R1,R2 >> RN >> RF RN >> RF >> R1,R2


N

N

L

N

F

FN

i

Ji

N

F

F

F

N

i

J

J

iLNS

eRR

pRR

P

RR

p

pRR

P

P

eRR

/222

2

1

22

2

1/

1

2

1

21

114

RN

RN RN

RN RN

RF

RFRi

Ri


NL

L

N

FN

F

FS Re

e

R

RR

p

pR

N

N 1

1)1(

4/2

/2

22

2

Co/Al2O3/Al

NLNJS eRPR /2 RN

Py/Cu


RN RN RN

Jedema et al., Nature 416, 713 (2002). Jedema et al., Nature 410, 345 (2001).

R1,R2 >> RN >> RF RN >> RF >> R1,R2

Intermediate interface

RN >> R1,R2 >> RF

NS bRaR


N

N

L

N

F

FN

i

Ji

N

F

F

F

N

i

J

J

iLNS

eRR

pRR

P

RR

p

pRR

P

P

eRR

/222

2

1

22

2

1/

1

2

1

21

114

RN

RN RN

RN RN

RF

RFRi

Ri

1 2 1 22 2 2

( ) 2

1 (1 )N

N

R R R R RR R

P P

only under the following condition,

Interface resistance: R1+R2 = 540 (c.f. 490 from independent estimation)

Current polarization: PJ = 0.047 (c.f. PJ ~ 0.1 in Co/graphene[*])

From the fitting and condition (2),

(1)

. (2)

221 2 1 2

2 21 2 1 2

22

1 ( )s

R R R RPR P R

P R R R R

Rs R

Linearly decreasing asymptotic form

Fitting parameters take reasonable values, justifying the fit to eq. (1).

[*] Tombros et al. Nature 448, 571 (2007).


N

N

L

N

F

FN

i

Ji

N

F

F

F

N

i

J

J

iLNS

eRR

pRR

P

RR

p

pRR

P

P

eRR

/222

2

1

22

2

1/

1

2

1

21

114

RN

RN RN

RN RN

RF

RFRi

Ri

1 2 1 22 2 2

( ) 2

1 (1 )N

N

R R R R RR R

P P

only under the following condition,

Interface resistance: R1+R2 = 540 (c.f. 490 from independent estimation)

Current polarization: PJ = 0.047 (c.f. PJ ~ 0.1 in Co/graphene[*])

From the fitting and condition (2),

(1)

. (2)

221 2 1 2

2 21 2 1 2

22

1 ( )s

R R R RPR P R

P R R R R R

Linearly decreasing asymptotic form

Spin relaxation length: N >> 8 m RN >> R1,R2 >> RFIntermediate interfaceLonger than N of SLG, Al, and Cu.

Rs

1. Nearly perfect crystal free of structural defects

2. Origins of scattering

Long spin relaxation length in MLG

J. H. Chen et al. Nature Nanotech. (2008)

SLG on SiO2

graphite

MLG

charged impurities

1. Nearly perfect crystal free of structural defects

2. Origins of scattering

Long spin relaxation length in MLG

SiO2 layer

charge impurities, phonon

(multilayer) graphene

contaminant adsorbed molecules

modulation of carrier densitySC

SC: interlayer screening length SC ~ 1.2 nm (3.5 layers) (Miyazaki et al., APEX 2008)

Distance from contaminant and adsorbed molecules becomes larger.Ripple becomes smaller.

J. H. Chen et al. Nature Nanotech. (2008)

SLG on SiO2

graphite

MLG

Smaller scattering Longer spin relaxation length

c.f. N = 1.5 - 2 m in SLG

Tombros et al. Nature 448, 571 (2007).

charged impurities

C1C4

Contact resistance in thick MLG devices

SC

thickness: 5 nm

c1 （ L = 180 nm）c2 （ L = 290 nm）c3 （ L = 380 nm）c4 （ L = 490 nm）

c1 c2 c3 c4

Ni

contact resistance


thickness: 5 nm


c1 c2 c3 c4

SC

Ni

contact resistance

C1C4


thickness: 5 nm


c1 c2 c3 c4

SC

Ni

contact resistance

C1C4Gate-controllable intrinsic contact

resistance in thick MLG

Layered structure Screening of gate electric field


c1 c2 c3 c4

Ni

SC

Gate-controllable intrinsic contact resistance in thick MLG



c1 c2 c3 c4

Ni

SC

Gate-controllable intrinsic contact resistance in thick MLG


)(2,1 gintrinsicc

contactc VRRR

Rccontact can be reduced.


contact resistance

C1C4

thickness: 5 nm


c1 c2 c3 c4

Ni

slope: graphene resistance

)()( ggraphenegintrinsicc VRVR

If one can sufficiently reduce Rccontact,

.constR

R

N

i

Rccontact

Contact resistance and spin signalTakahashi and Maekawa, PRB 67, 052409 (2003)


N

N

L

N

F

FN

i

Ji

N

F

F

F

N

i

J

J

iLNS

eRR

pRR

P

RR

p

pRR

P

P

eRR

/222

2

1

22

2

1/

1

2

1

21

114

RN

RN RN

RN RN

RF

RFRi

Ri

NL

L

N

FN

F

FS Re

e

R

RR

p

pR

N

N 1

1)1(

4/2

/2

22

2

RN RN RN

RN >> RF >> R1,R2

Tunnel junctions

NL

NJS ReRPR N /2RN

R1,R2 >> RN >> RF

RN

Transparent junctions (Rccontact) with MLG,

NS RR

(RF ~ 1m)

.constR

R

N

i

46.48

46.49

46.50

-1500-1000 -500 0 500 1000 1500

Vg = 0 V

Magnetic field (Oe)

Sample for local measurement

_I

V+

Thickness: 9 nm

parallel – small R

MLG

antiparallel – large R

Spin valve effect

R

H

Gate voltage dependence

37.71

37.72

37.73V

g = 80 V

46.48

46.49

46.50V

g = 0 V

29.84

29.85

29.86

-1500-1000 -500 0 500 1000 1500

Vg = -80 V

Magnetic Field (Oe)

spin induced magnetoresistance (SIMR)

Oe1200

Oe0)()( dHHRHR

4K


37.71

37.72

37.73V

g = 80 V

46.48

46.49

46.50V

g = 0 V

29.84

29.85

29.86

-1500-1000 -500 0 500 1000 1500

Vg = -80 V

Magnetic Field (Oe)

spin induced magnetoresistance (SIMR)

Oe1200

Oe0)()( dHHRHR

4K

Might indicate Rs proportional to RN?

Contact resistance and spin signalTakahashi and Maekawa, PRB 67, 052409 (2003)


N

N

L

N

F

FN

i

Ji

N

F

F

F

N

i

J

J

iLNS

eRR

pRR

P

RR

p

pRR

P

P

eRR

/222

2

1

22

2

1/

1

2

1

21

114

RN

RN RN

RN RN

RF

RFRi

Ri

NL

L

N

FN

F

FS Re

e

R

RR

p

pR

N

N 1

1)1(

4/2

/2

22

2

RN RN RN

RN >> RF >> R1,R2

Tunnel junctions

NL

NJS ReRPR N /2RN

R1,R2 >> RN >> RF

RN

Transparent junctions (Rccontact) with MLG,

NS RR

(RF ~ 1m)

.constR

R

N

i

Gate controllable

Cooper pair transport in single and multi-layer graphene

Why Cooper-pairs in graphene?

Beenakker, Rev. Mod. Phys. 80, 1337 (2008).

relativity superconductivity

Single layer graphene (SLG)

Injection of Cooper-pairs by proximity effect

Andreev reflection

Intraband A. R.

Interband A. R.

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

super-conductor

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

IV characteristics

-3000 -2000 -1000 0 1000 2000 3000-0.2

-0.1

0.0

0.1

0.2

V (

mV

)

I (nA)

-75V -50V -25V 8V

VgT=200mK, B=0.00mT

sweep


Magnetic field dependence

B = 0

gap: d = 0.22 m

Temperature dependence of critical supercurrent

gap: d = 0.22 m

Vg =-75 V

-50V

75V

50V-25V

25V 0V 8V

Conventional theory for Ic(T)

Long junctions (d >> N)

))/(exp(

)/exp(

0

TT

dIc N

15.0

Nl

Dirty limit:Nl

Clean limit:



Short junctions (d << N)

ballistic, ideal interfacediffusive, ideal interface

))/(exp(

)/exp(

0

TT

dIc N

Nl

Dirty limit:Nl

(l: mean free path)15.0

Clean limit:

Two kinds of Kulik-Omel’yanchuk theory





))/(exp(

)/exp(

0

TT

dIc N

15.0

Ambegaokar-Baratoff result


Nl

Dirty limit:Nl

Clean limit:


gap: L = 0.22 m

Vg =-75 V

-50V

75V

50V-25V

25V 0V 8V


KO1 theory(short junctiondirty limit:l << d << N)

I. O. Kulick and A. N. Omel'yanchuk, JETP Lett. 21, 96 (1975).

Vg =-75 V

-50V

75V

50V-25V

25V 0V 8V


KO1 theory(short junctiondirty limit:l << d << N)

I. O. Kulick and A. N. Omel'yanchuk, JETP Lett. 21, 96 (1975).

Ballistic junction is needed for relativistic Josephson effect!

-75 -50 -25 0 25 50 750

500

1000

1500

2000

Ic(T

=0

) (n

A)

Vg (V)

Ic

-75 -50 -25 0 25 50 750.0

0.2

0.4

0.6

0.8

1.0

Tc

(K)

Vg (V)

Tc

Injection of Cooper pairs into graphene

Ic(T=0)

Tc

Vg =-75 V

-50V

75V

50V-25V

25V 0V 8V

Never seen in other SNS systems

0

50

100

150

200

250

300

-60 -40 -20 0 20 40 60

mfp

(nm

)

Vgate(V)

Making ballistic junctions

Fke

hl

22

ngF VVk 1214 Vm102.7

mean free pathAngle deposition of metals

Substrate

graphene

Resist mask

50 nm

shorter junctions

cleaner graphene

K.I. Bolotin et al., SSC 146, 351 (2008)

Multilayer graphene

Tc of Pd/Al

Temperature dependence of resistance(Inset: Vg dependence of normal-state resistance)

Current-voltage (I-V) characteristics

Vgp

supercurrent

dV/dI at 0.06 K

hole supercurrent

electron supercurrent

Ic

0.2 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

Tc of Pd/Al

Asymmetry in electron and hole supercurrents

Temperature dependence of resistance(Inset: Vg dependence of normal-state resistance)

Electron and hole supercurrents

Temperature dependence of Ic

))/(exp( 20TTIc

02

2

dT

Icd

Vg=75V

60V

45V





))/(exp(

)/exp(

0

TT

dIc N

Nl

Dirty limit:Nl

(l: mean free path)15.0

Clean limit:

02

2

dT

Icd

02

2

dT

Icd

measurement

Ambegaokar-Baratoff result


In our measurement, = 2.

Possible origin of exp(T/T0)2 behavior

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.

MLG

SC ~ 3.5 layers

SiO2 (300 nm)

Si (Back gate)

Model for Ic(T) of multilayer graphene

Regard each layer as independent single-layer graphene with different carrier density.

Assumptions



Critical supercurrent of each layer follows the KO1 theory. (Note that the results are almost the same for Ambegaoker-Baratoff or KO2 theory.)

Assumptions


Ngate: 　 gate-induced carrier density

)()( ),(0 nNnTnI gateCC


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:

Assumptions

For example

Numerical result

))/(exp( 20TTIc is reproduced in a wide temperature range.

A, B, C... : Onset of supercurrent in 1st, 2nd, 3rd... layers

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

グラフェンにおけるスピン伝導・ 超伝導近接効果

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グラフェンにおけるスピン伝導・超伝導近接効果