1

Atomic-sized Conductors: Chains of Atoms and Hydrogen Molecules

Jan van RuitenbeekKamerlingh Onnes Laboratorium

2

What will be discussed

1. Chains of metal atoms

MD simulation Au, 12 K. Sørensenet al., PRB 57, 3283 (1998)

3

What will be discussed2. Conductance of a single hydrogen molecule

R.H.M. Smit et al. Nature, in print.

4

In collaboration with ...Leiden: Helko van den Brom, Martijn Krans, Bas Ludoph,

Chris Muller, Yves Noat, Niko van der Post, Roel Smit, Carlos Untiedt, Alex Yanson.Marc van Hemert

IBM Yorktown Heights: Norton LangMadrid: Nicolas Agraït, Gabino Rubio, Juan-Carlos Cuevas,

Alfredo Levy Yeyati, Alvaro Martin-RoderoSaclay: Michel Devoret, Daniel Esteve, Cristian UrbinaKonstanz: Elke Scheer

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Mechanically Controllable Break Junction

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0 50 100 150 200 250 300012345678

Gold, 4.2 KC

ondu

ctan

ce (2

e2 /h)

Piezo-voltage (V)

7

Quantum conductance (2 dimensions)

Incoming and reflected modes

Scattering at the contact

Transmitted modes

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Conductance is transmission

Vector of incoming waves from the left, on a basis of quantum modes:

Vector of outgoing waves to the right, on a basis of quantum modes:

Matrix of transmission amplitudes:

Landauer:

lir

ror

lr itorr ˆ=

∑==n

nThett

heG

22 2)ˆˆTr(2 √

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0 1 2 3 4 50

2

4

Aluminium, T=100 mKeI

/G∆

eV/∆

1 20

2

4

Scheer et al., PRL 78, 3535 (1997)

Superconducting subgap structure

10

Fitting procedure: demonstration

11

1 2 3 40.0

0.1

0.2

0.3

5%

20%10%

x=0%

Exce

ss n

oise

(2eI

)

Conductance (2e2/h)

Gold, 4.2 K

van den Brom & JvR, PRL 82 (1999) 1526

Shot noise

12

0 1 20.00.10.20.30.40.50.60.70.80.91.0

N=3N=2

Gold

Aluminium

Exce

ss n

oise

(2eI

)

Conductance (2e2/h)

13

Conductance fluctuations: 3 examples

-50 0 501.58

1.60

1.62

1.64

1.66

1.68

1.70

G (V

) = d

I/dV

(2e2 /h

)

-50 0 50

0.99

1.01

1.03

1.05

1.07

1.09

Bias voltage (mV)-50 0 50

0.82

0.84

0.86

0.88

0.90

0.92

0.94

Au

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Principle of conductance fluctuationsin ballistic contacts

DiffusiveBank

DiffusiveBankBallistic

PointContact

ttar'rat

rtat'

γ

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RMS fluctuations measured for Au

Au

0 1 2 3 40.00.20.40.60.81.01.21.41.61.82.0

G [2e2/h]

σG

V [G

o/V]

Gold

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The modes determined by valence orbitals

Element Type ofatom

Number ofmodes

Conductance forone atom

Au s 1 1 G0

Al s-p 3 ~0.8-1.2 G

Pb s-p 3 ~2.5-3 G

Nb s-d 5 ~2.5-3 G

Cuevas et al., PRL 80 (1998) 1066

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Chains of single atoms

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Conductance curves for gold contacts at 4.2 K

0 4 8 12 16 20 24 28 320

1

2

3

4

5

6

7

8

Plateau length

Return distance

Con

duct

ance

(2e2/h

)

Electrode displacement (Å)

0 4 8 12 16 20

5

10

15

20

25

Ret

urn

dist

ance

(Å)

Plateau length (Å)

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Histogram of lengths of last plateau, Au 4.2 K

0 2 4 6 8 10 12 14 16 18 20 220

50

100

150

200

x10

Num

ber o

f tim

es e

ach

leng

th is

obs

erve

d

Length of the last plateau (Å)

14 16 18 20 22

Yanson et al., Nature 395 (1998) 783

2.5 ± 0.2 Å

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Combined TEM and STM

3.5—4 Å

Ohnishi, Kondo and Takayanagi Nature 395, 780 (1998)

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Surface reconstructions

A

B

b)

a) [001]

[10]1

(100) surface (110) surface

22-5 -4 -3 -2 -1 0 1

0

5

10

15

20

[2e2 /h

]

Con

duct

ance

Piezo Voltage [V]

-1.0 -0.5 0.0 0.5 1.0 1.5

Pt

Electrode Displacement [nm]

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

Pt

Nor

mal

ised

cou

nts

[a.u

.]Conductance [2e2/h]

stop

stop

start

start

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Test of chain formation for other metals

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40

10

20

30

Nor

mal

ized

num

ber o

f cou

nts

[a.u

.]

Plateau length [nm]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.402468

1012

Pd

Pt

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Au / AgIr / Rh

4d

5d

Pt / Pd

fract

ion

of lo

ng p

late

aus

Smit et al., PRL 87, 266102 (2001)Bahn and Jacobsen, ibid., 266101

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Relativistic effects in the bonding of Au

-0.5 0.0 0.5 1.00

1

2

3

D

ensi

ty o

f sta

tes

(arb

. un.

)

Energy

EF

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Relativistic effects in the bonding of Au

-0.5 0.0 0.5 1.00

1

2

3

D

ensi

ty o

f sta

tes

(arb

. un.

)

Energy

EFBohr radius

2

0 2

02

4

1 ( / )

aZme

mmv c

π ε0=

=−

h

N. Takeuchi et al., PRL 63, 1273 (1991)

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Chain formation in transition metals

Fe Co Ni Cu Zn

Ru Rh Pd Ag Cd

Os Ir Pt Au Hg

Smit et al., PRL 87, 266102 (2001)Bahn and Jacobsen, ibid., 266101

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Conductance of a single hydrogen molecule

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Conductance curve for Pt/H2

0.0 2.0 4.0 6.00

1

2

3

4

5

Pt/H2

Pt

C

ondu

ctan

ce (2

e2 /h)

Piezovoltage (V)

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0 1 2 3 4 5 6 7 80.0

0.2

0.4

0.6

0.8Pt/H2

Pt

N

umbe

r of c

ount

s

Conductance (2e2/h)

Conductance histogram for Pt/H2

Bias voltage 140 mV

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Principle of point contact spectroscopy

Ef+eV/2

Ef-eV/2

G decreases for eV > hν

Ener

g y

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Point contact spectrum for Pt/H2

0.92

0.93

0.94

0.95

-100 -50 0 50 100-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

Pt/H2

D

iffer

entia

l con

duct

ance

(2e2 /h

)

63.5 mV

- 63.5 mV

dG/d

V (a

.u.)

Bias voltage (mV)

Modulation: 1 mV, 7 kHzRecording time: 10 sTemperature: 4.2 K

Numerical results for Pt-H-H-Pt

Symm., longit.: 68 meVAsymm., longt.: 431 meV

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Isotope shift

30 40 50 60 70 800123456789

10Pt + HD

Pt + D2

Pt + H2

Cou

nts

Vibration mode energy [meV]

35 40 45 50

40 45 50 55 60

45 50 55 60 65 70 750

1

2

3

4

5

6

7

8

9

10

Cou

nts

Vibration mode energy [meV]

Pt-H2 not scaled Pt-D2 by √2 Pt-HD by √(3/2)

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Conductance fluctuations

0 10

1000

2000

3000

4000

5000

6000

0

1

2

3

C

ount

s

Conductance (2e2/h)

σG

V (a

.u.)

T = 0.97 (1)

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Conclusions

Universiteit Leiden