Journal Club, Sept. 13. 2012, Tóvári Endre
Probing the conductance superposition law in
single-molecule circuits with parallel paths
Probing the conductance superposition law in
single-molecule circuits with parallel paths
1,4-bis(methyl(thio)methyl)–benzene (1)
sulphur groups bind to the gold leads
2,11-dithia(3,3)paracyclophane (2)
H. Vazquez1, R. Skouta2, S. Schneebeli2, M. Kamenetska1, R. Breslow2, L.
Venkataraman1 and M.S. 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, Tóvári Endre
Probing the conductance superposition law in
single-molecule circuits with parallel paths
STM-based break-junction technique
Au tip over Au surface: repeatedly forming and breaking
Au point contacts in solution of the molecules
1a
1
2
(C4H8 branch)
Conductance vs displacement histograms:
• Low conductance peaks:
-4 G for 1;(~0.5
Full extension
nm):
3.3x10
2.9 for
1a; 9.0 for 2
0
one,
low-conductance
• just
Broad
features:
enhanced peak
coupling
(coupling
sulphur
gateway)
betweenonly
the via
goldthe
and
the π-system
(when not fully extended)
All counts for an interval
of 0.1 nm around 0.5 nm
extension
conductance ratio:
G(2)/G(1)=2.8
9.7x10-4 G0
3.5x10-4 G0
2.8x10-4 G0
Journal Club, Sept. 13. 2012, Tóvári Endre
Probing the conductance superposition law in
single-molecule circuits with parallel paths
A simple model for electron transmission: Green’s function approach
B AB
Resonances: contributions of gateway,
bonding (B) and antibonding (AB) states
Bonding/antibonding:
combinations of
backbone states
LUMO
Gateway
state
HOMO
• Low-bias: G(2)/G(1)>2
• Resonance peak from B: 2x wider in case of molecule 2
B , AB 
1
1
 2
2
AB antibonding
B bonding
Gateway
state

Journal Club, Sept. 13. 2012, Tóvári Endre
Probing the conductance superposition law in
single-molecule circuits with parallel paths
Extensive DFT studies
1c
2
1c
1
1 instead of 1c: to eliminate the
role of junction structure (in
comparing 1 and 2)
1
The LUMO (B) peak (at 1.9 eV)
is 1.8x broader than the
original LUMO at 2.1 eV:
due to coherent lin.comb. of
backbone states
(interference).
G(2)/G(1c)=3.3
G(2)=8.2x10-3 G0
G(1c)=2.5x10-3 G0
G(2)/G(1c)=3.3
Larger than measured (2.8)
Correction doesn’t change
the ratio by more than 20%
Journal Club, Sept. 13. 2012, Tóvári Endre
Probing the conductance superposition law in
single-molecule circuits with parallel paths
Other molecules: measurements and calculations at the EF (low bias)
AB
B
LUMO
Gateway
Gateway
HOMO
• Transmission spectra are qualitatively similar.
• Conductance ratio: sensitive to relative placement of
energy levels (EF, gateway, backbone states):
for some molecules AB resonances
are near the gateway states’
energyreduced transmission (and
cond. ratio) for E<EF
Journal Club, Sept. 13. 2012, Tóvári Endre
Probing the conductance superposition law in
single-molecule circuits with parallel paths
In conclusion:
• synthesizing single and double-backbone
molecules
• STM-based break junctionconductance
histograms
• DFT transport calculations
Constructive interference in molecules with two
backbones:
• more than double conductance measured
(mostly)
• broader transmission resonances calculated
• sensitive to electronic structure of the linker
group
Journal Club, Sept. 13. 2012, Tóvári Endre
Probing the conductance superposition law in single-molecule circuits with parallel paths
A simple model for electron transmission: Green’s function approach
2 levels for each molecular backbone (1.,2.):
EH1, EL1
EH2, EL2 (same for 1 and 2, if backbones are equivalent)
(H=HOMO highest occuppied molec. orbital,
Interaction of backbone orbitals
L=LUMO lowest unoccuppied m.o.)
(„through space coupling”):




0 
 EL
AB antibonding


-t
hopping
LUMO
E ,E
B bonding
0
 
   E H 1 H1 t L1 0
Γ
 E  t

Γ
E
E
0
0

R
L
H2
H 
   (link)0


0

 0


0
E L(link)
t
1
0
t
EL2

 



E R 
EH2, EL2    
EL, ER gateway states (sulphur junction)
(For molecule 1: 4x4 Hamiltonian)
-t
τ
τ
Gateway
state
Connection
between
Gateway
state
backbone and gateway states:
HOMO
τ
Bonding/antibonding combinations of backbone states:
The relative sign of the
 t backbone
1 coupling terms between
 E 1 each
 E B state0and the L or

  and LUMO􀀃πstates
B ,captures
AB the different
1  number
2
R leads
of nodes
in theHOMO
E AB 
on the backbones. 2
  t E2 
 0

