Probing the conductance superposition law in single-molecule circuits with parallel paths

H Vazquez1 R Skouta2 S Schneebeli2 M Kamenetska1 R Breslow2 L Venkataraman1 and MS Hybertsen3

1Department of Applied Physics and Applied Mathematics Columbia University 500 W 120th Street New York New York 10027 USA 2Department of Chemistry Columbia University 3000 Broadway New York 10027 USA 3Center for Functional Nanomaterials Brookhaven National Laboratory Upton New York 11973 USA

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

14-bis(methyl(thio)methyl)ndashbenzene (1)

211-dithia(33)paracyclophane (2)

sulphur groups bind to the gold leads

bull Low conductance peaks33x10-4 G0 for 1 29 for 1a 90 for 2bull Broad features enhanced coupling

between the gold and the π-system (when not fully extended)

Journal Club Sept 13 2012 Toacutevaacuteri Endre

STM-based break-junction techniqueAu tip over Au surface repeatedly forming and breaking Au point contacts in solution of the molecules

1 21a

(C4H8 branch)

Conductance vs displacement histograms

All counts for an interval of 01 nm around 05 nm extension

97x10-4 G0

35x10-4 G028x10-4 G0

Full extension (~05 nm) just one low-conductance peak(coupling only via the sulphur gateway)

Probing the conductance superposition law in single-molecule circuits with parallel paths

conductance ratioG(2)G(1)=28

Resonances contributions of gateway bonding (B) and antibonding (AB) states

LUMO

HOMO

AB antibondingB bonding

Gateway state

Gateway state

A simple model for electron transmission Greenrsquos function approach

Journal Club Sept 13 2012 Toacutevaacuteri Endre

B AB

bull Low-bias G(2)G(1)gt2bull Resonance peak from B 2x wider in case of molecule 2

Probing the conductance superposition law in single-molecule circuits with parallel paths

Bondingantibonding combinations of backbone states

2121 ABB

Extensive DFT studies

Journal Club Sept 13 2012 Toacutevaacuteri Endre

1c 2

1

1c

Probing the conductance superposition law in single-molecule circuits with parallel paths

G(2)G(1c)=33

1 1 instead of 1c to eliminate the role of junction structure (in comparing 1 and 2)

The LUMO (B) peak (at 19 eV) is 18x broader than the original LUMO at 21 eVdue to coherent lincomb of backbone states (interference)

G(2)=82x10-3 G0

G(1c)=25x10-3 G0

G(2)G(1c)=33Larger than measured (28)Correction doesnrsquot change the ratio by more than 20

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

bull Transmission spectra are qualitatively similarbull Conductance ratio sensitive to relative placement of

energy levels (EF gateway backbone states)LUMO

HOMO

AB B

GatewayGateway

Other molecules measurements and calculations at the EF (low bias)

for some molecules AB resonances are near the gateway statesrsquo energyreduced transmission (and cond ratio) for EltEF

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

In conclusion

bull synthesizing single and double-backbone molecules

bull STM-based break junctionconductance histograms

bull DFT transport calculations

Constructive interference in molecules with two backbonesbullmore than double conductance measured (mostly)bullbroader transmission resonances calculatedbullsensitive to electronic structure of the linker group

A simple model for electron transmission Greenrsquos function approach

Journal Club Sept 13 2012 Toacutevaacuteri EndreProbing the conductance superposition law in single-molecule circuits with parallel paths

2 levels for each molecular backbone (12)EH1 EL1

EH2 EL2 (same for 1 and 2 if backbones are equivalent)(H=HOMO highest occuppied molec orbital L=LUMO lowest unoccuppied mo)

EH1 EL1

EH2 EL2

Interaction of backbone orbitals (bdquothrough space couplingrdquo)-t hopping

-t(link)(link)

EL ER gateway states (sulphur junction)

EL ER

τ τ

Connection between backbone and gateway states τ

The relative sign of the coupling terms between each backbone state and the L or R leads captures the different number of nodes in the HOMO and LUMO 1048579 states on the backbones

R

L

L

H

H

L

EEttE

EttE

E

H

00000

0000

0

2

1

2

1

Bondingantibonding combinations of backbone states

2121 ABB

AB

B

EE

EttE

00

2

1

ΓΓLUMO

HOMO

AB antibondingB bonding

(For molecule 1 4x4 Hamiltonian)

Gateway state

Gateway state

π

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7

bull Low conductance peaks33x10-4 G0 for 1 29 for 1a 90 for 2bull Broad features enhanced coupling

between the gold and the π-system (when not fully extended)

Journal Club Sept 13 2012 Toacutevaacuteri Endre

STM-based break-junction techniqueAu tip over Au surface repeatedly forming and breaking Au point contacts in solution of the molecules

1 21a

(C4H8 branch)

Conductance vs displacement histograms

All counts for an interval of 01 nm around 05 nm extension

97x10-4 G0

35x10-4 G028x10-4 G0

Full extension (~05 nm) just one low-conductance peak(coupling only via the sulphur gateway)

Probing the conductance superposition law in single-molecule circuits with parallel paths

conductance ratioG(2)G(1)=28

Resonances contributions of gateway bonding (B) and antibonding (AB) states

LUMO

HOMO

AB antibondingB bonding

Gateway state

Gateway state

A simple model for electron transmission Greenrsquos function approach

Journal Club Sept 13 2012 Toacutevaacuteri Endre

B AB

bull Low-bias G(2)G(1)gt2bull Resonance peak from B 2x wider in case of molecule 2

Probing the conductance superposition law in single-molecule circuits with parallel paths

Bondingantibonding combinations of backbone states

2121 ABB

Extensive DFT studies

Journal Club Sept 13 2012 Toacutevaacuteri Endre

1c 2

1

1c

Probing the conductance superposition law in single-molecule circuits with parallel paths

G(2)G(1c)=33

1 1 instead of 1c to eliminate the role of junction structure (in comparing 1 and 2)

The LUMO (B) peak (at 19 eV) is 18x broader than the original LUMO at 21 eVdue to coherent lincomb of backbone states (interference)

G(2)=82x10-3 G0

G(1c)=25x10-3 G0

G(2)G(1c)=33Larger than measured (28)Correction doesnrsquot change the ratio by more than 20

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

bull Transmission spectra are qualitatively similarbull Conductance ratio sensitive to relative placement of

energy levels (EF gateway backbone states)LUMO

HOMO

AB B

GatewayGateway

Other molecules measurements and calculations at the EF (low bias)

for some molecules AB resonances are near the gateway statesrsquo energyreduced transmission (and cond ratio) for EltEF

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

In conclusion

bull synthesizing single and double-backbone molecules

bull STM-based break junctionconductance histograms

bull DFT transport calculations

Constructive interference in molecules with two backbonesbullmore than double conductance measured (mostly)bullbroader transmission resonances calculatedbullsensitive to electronic structure of the linker group

A simple model for electron transmission Greenrsquos function approach

Journal Club Sept 13 2012 Toacutevaacuteri EndreProbing the conductance superposition law in single-molecule circuits with parallel paths

2 levels for each molecular backbone (12)EH1 EL1

EH2 EL2 (same for 1 and 2 if backbones are equivalent)(H=HOMO highest occuppied molec orbital L=LUMO lowest unoccuppied mo)

EH1 EL1

EH2 EL2

Interaction of backbone orbitals (bdquothrough space couplingrdquo)-t hopping

-t(link)(link)

EL ER gateway states (sulphur junction)

EL ER

τ τ

Connection between backbone and gateway states τ

The relative sign of the coupling terms between each backbone state and the L or R leads captures the different number of nodes in the HOMO and LUMO 1048579 states on the backbones

R

L

L

H

H

L

EEttE

EttE

E

H

00000

0000

0

2

1

2

1

Bondingantibonding combinations of backbone states

2121 ABB

AB

B

EE

EttE

00

2

1

ΓΓLUMO

HOMO

AB antibondingB bonding

(For molecule 1 4x4 Hamiltonian)

Gateway state

Gateway state

π

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7

Resonances contributions of gateway bonding (B) and antibonding (AB) states

LUMO

HOMO

AB antibondingB bonding

Gateway state

Gateway state

A simple model for electron transmission Greenrsquos function approach

Journal Club Sept 13 2012 Toacutevaacuteri Endre

B AB

bull Low-bias G(2)G(1)gt2bull Resonance peak from B 2x wider in case of molecule 2

Probing the conductance superposition law in single-molecule circuits with parallel paths

Bondingantibonding combinations of backbone states

2121 ABB

Extensive DFT studies

Journal Club Sept 13 2012 Toacutevaacuteri Endre

1c 2

1

1c

Probing the conductance superposition law in single-molecule circuits with parallel paths

G(2)G(1c)=33

1 1 instead of 1c to eliminate the role of junction structure (in comparing 1 and 2)

The LUMO (B) peak (at 19 eV) is 18x broader than the original LUMO at 21 eVdue to coherent lincomb of backbone states (interference)

G(2)=82x10-3 G0

G(1c)=25x10-3 G0

G(2)G(1c)=33Larger than measured (28)Correction doesnrsquot change the ratio by more than 20

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

bull Transmission spectra are qualitatively similarbull Conductance ratio sensitive to relative placement of

energy levels (EF gateway backbone states)LUMO

HOMO

AB B

GatewayGateway

Other molecules measurements and calculations at the EF (low bias)

for some molecules AB resonances are near the gateway statesrsquo energyreduced transmission (and cond ratio) for EltEF

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

In conclusion

bull synthesizing single and double-backbone molecules

bull STM-based break junctionconductance histograms

bull DFT transport calculations

Constructive interference in molecules with two backbonesbullmore than double conductance measured (mostly)bullbroader transmission resonances calculatedbullsensitive to electronic structure of the linker group

A simple model for electron transmission Greenrsquos function approach

Journal Club Sept 13 2012 Toacutevaacuteri EndreProbing the conductance superposition law in single-molecule circuits with parallel paths

2 levels for each molecular backbone (12)EH1 EL1

EH2 EL2 (same for 1 and 2 if backbones are equivalent)(H=HOMO highest occuppied molec orbital L=LUMO lowest unoccuppied mo)

EH1 EL1

EH2 EL2

Interaction of backbone orbitals (bdquothrough space couplingrdquo)-t hopping

-t(link)(link)

EL ER gateway states (sulphur junction)

EL ER

τ τ

Connection between backbone and gateway states τ

The relative sign of the coupling terms between each backbone state and the L or R leads captures the different number of nodes in the HOMO and LUMO 1048579 states on the backbones

R

L

L

H

H

L

EEttE

EttE

E

H

00000

0000

0

2

1

2

1

Bondingantibonding combinations of backbone states

2121 ABB

AB

B

EE

EttE

00

2

1

ΓΓLUMO

HOMO

AB antibondingB bonding

(For molecule 1 4x4 Hamiltonian)

Gateway state

Gateway state

π

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7

Extensive DFT studies

Journal Club Sept 13 2012 Toacutevaacuteri Endre

1c 2

1

1c

Probing the conductance superposition law in single-molecule circuits with parallel paths

G(2)G(1c)=33

1 1 instead of 1c to eliminate the role of junction structure (in comparing 1 and 2)

The LUMO (B) peak (at 19 eV) is 18x broader than the original LUMO at 21 eVdue to coherent lincomb of backbone states (interference)

G(2)=82x10-3 G0

G(1c)=25x10-3 G0

G(2)G(1c)=33Larger than measured (28)Correction doesnrsquot change the ratio by more than 20

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

bull Transmission spectra are qualitatively similarbull Conductance ratio sensitive to relative placement of

energy levels (EF gateway backbone states)LUMO

HOMO

AB B

GatewayGateway

Other molecules measurements and calculations at the EF (low bias)

for some molecules AB resonances are near the gateway statesrsquo energyreduced transmission (and cond ratio) for EltEF

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

In conclusion

bull synthesizing single and double-backbone molecules

bull STM-based break junctionconductance histograms

bull DFT transport calculations

Constructive interference in molecules with two backbonesbullmore than double conductance measured (mostly)bullbroader transmission resonances calculatedbullsensitive to electronic structure of the linker group

A simple model for electron transmission Greenrsquos function approach

Journal Club Sept 13 2012 Toacutevaacuteri EndreProbing the conductance superposition law in single-molecule circuits with parallel paths

2 levels for each molecular backbone (12)EH1 EL1

EH2 EL2 (same for 1 and 2 if backbones are equivalent)(H=HOMO highest occuppied molec orbital L=LUMO lowest unoccuppied mo)

EH1 EL1

EH2 EL2

Interaction of backbone orbitals (bdquothrough space couplingrdquo)-t hopping

-t(link)(link)

EL ER gateway states (sulphur junction)

EL ER

τ τ

Connection between backbone and gateway states τ

The relative sign of the coupling terms between each backbone state and the L or R leads captures the different number of nodes in the HOMO and LUMO 1048579 states on the backbones

R

L

L

H

H

L

EEttE

EttE

E

H

00000

0000

0

2

1

2

1

Bondingantibonding combinations of backbone states

2121 ABB

AB

B

EE

EttE

00

2

1

ΓΓLUMO

HOMO

AB antibondingB bonding

(For molecule 1 4x4 Hamiltonian)

Gateway state

Gateway state

π

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

bull Transmission spectra are qualitatively similarbull Conductance ratio sensitive to relative placement of

energy levels (EF gateway backbone states)LUMO

HOMO

AB B

GatewayGateway

Other molecules measurements and calculations at the EF (low bias)

for some molecules AB resonances are near the gateway statesrsquo energyreduced transmission (and cond ratio) for EltEF

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

In conclusion

bull synthesizing single and double-backbone molecules

bull STM-based break junctionconductance histograms

bull DFT transport calculations

Constructive interference in molecules with two backbonesbullmore than double conductance measured (mostly)bullbroader transmission resonances calculatedbullsensitive to electronic structure of the linker group

A simple model for electron transmission Greenrsquos function approach

Journal Club Sept 13 2012 Toacutevaacuteri EndreProbing the conductance superposition law in single-molecule circuits with parallel paths

2 levels for each molecular backbone (12)EH1 EL1

EH2 EL2 (same for 1 and 2 if backbones are equivalent)(H=HOMO highest occuppied molec orbital L=LUMO lowest unoccuppied mo)

EH1 EL1

EH2 EL2

Interaction of backbone orbitals (bdquothrough space couplingrdquo)-t hopping

-t(link)(link)

EL ER gateway states (sulphur junction)

EL ER

τ τ

Connection between backbone and gateway states τ

The relative sign of the coupling terms between each backbone state and the L or R leads captures the different number of nodes in the HOMO and LUMO 1048579 states on the backbones

R

L

L

H

H

L

EEttE

EttE

E

H

00000

0000

0

2

1

2

1

Bondingantibonding combinations of backbone states

2121 ABB

AB

B

EE

EttE

00

2

1

ΓΓLUMO

HOMO

AB antibondingB bonding

(For molecule 1 4x4 Hamiltonian)

Gateway state

Gateway state

π

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7

Journal Club Sept 13 2012 Toacutevaacuteri Endre Probing the conductance superposition law in single-molecule circuits with parallel paths

In conclusion

bull synthesizing single and double-backbone molecules

bull STM-based break junctionconductance histograms

bull DFT transport calculations

Constructive interference in molecules with two backbonesbullmore than double conductance measured (mostly)bullbroader transmission resonances calculatedbullsensitive to electronic structure of the linker group

A simple model for electron transmission Greenrsquos function approach

Journal Club Sept 13 2012 Toacutevaacuteri EndreProbing the conductance superposition law in single-molecule circuits with parallel paths

2 levels for each molecular backbone (12)EH1 EL1

EH2 EL2 (same for 1 and 2 if backbones are equivalent)(H=HOMO highest occuppied molec orbital L=LUMO lowest unoccuppied mo)

EH1 EL1

EH2 EL2

Interaction of backbone orbitals (bdquothrough space couplingrdquo)-t hopping

-t(link)(link)

EL ER gateway states (sulphur junction)

EL ER

τ τ

Connection between backbone and gateway states τ

The relative sign of the coupling terms between each backbone state and the L or R leads captures the different number of nodes in the HOMO and LUMO 1048579 states on the backbones

R

L

L

H

H

L

EEttE

EttE

E

H

00000

0000

0

2

1

2

1

Bondingantibonding combinations of backbone states

2121 ABB

AB

B

EE

EttE

00

2

1

ΓΓLUMO

HOMO

AB antibondingB bonding

(For molecule 1 4x4 Hamiltonian)

Gateway state

Gateway state

π

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7

A simple model for electron transmission Greenrsquos function approach

Journal Club Sept 13 2012 Toacutevaacuteri EndreProbing the conductance superposition law in single-molecule circuits with parallel paths

2 levels for each molecular backbone (12)EH1 EL1

EH2 EL2 (same for 1 and 2 if backbones are equivalent)(H=HOMO highest occuppied molec orbital L=LUMO lowest unoccuppied mo)

EH1 EL1

EH2 EL2

Interaction of backbone orbitals (bdquothrough space couplingrdquo)-t hopping

-t(link)(link)

EL ER gateway states (sulphur junction)

EL ER

τ τ

Connection between backbone and gateway states τ

The relative sign of the coupling terms between each backbone state and the L or R leads captures the different number of nodes in the HOMO and LUMO 1048579 states on the backbones

R

L

L

H

H

L

EEttE

EttE

E

H

00000

0000

0

2

1

2

1

Bondingantibonding combinations of backbone states

2121 ABB

AB

B

EE

EttE

00

2

1

ΓΓLUMO

HOMO

AB antibondingB bonding

(For molecule 1 4x4 Hamiltonian)

Gateway state

Gateway state

π

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7