Probing the conductance superposition law in single-molecule circuits with parallel paths H. Vazquez 1, R. Skouta 2, S. Schneebeli 2, M. Kamenetska 1,

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1 Probing the conductance superposition law in single-molecule circuits with parallel paths H. Vazquez 1, R. Skouta 2, S. Schneebeli 2, M. Kamenetska 1, R. Breslow 2, L. Venkataraman 1 and M.S. Hybertsen 3 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 1,4-bis(methyl(thio)methyl)–benzene (1) 2,11-dithia(3,3)paracyclophane (2) sulphur groups bind to the gold leads

2 Low conductance peaks: 3.3x10 -4 G 0 for 1; 2.9 for 1a; 9.0 for 2 Broad features: enhanced coupling between the gold and the π-system (when not fully extended) Journal Club, Sept. 13. 2012, Tóvári Endre STM-based break-junction technique Au tip over Au surface: repeatedly forming and breaking Au point contacts in solution of the molecules 12 1a (C 4 H 8 branch) Conductance vs displacement histograms: All counts for an interval of 0.1 nm around 0.5 nm extension 9.7x10 -4 G 0 3.5x10 -4 G 0 2.8x10 -4 G 0 Full extension (~0.5 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 ratio: G(2)/G(1)=2.8

3 Resonances: contributions of gateway, bonding (B) and antibonding (AB) states LUMO HOMO AB antibonding B bonding Gateway state A simple model for electron transmission: Green’s function approach Journal Club, Sept. 13. 2012, Tóvári Endre BAB Low-bias: G(2)/G(1)>2 Resonance peak from B: 2x wider in case of molecule 2 Probing the conductance superposition law in single-molecule circuits with parallel paths Bonding/antibonding: combinations of backbone states

4 Extensive DFT studies Journal Club, Sept. 13. 2012, Tóvári Endre 1c2 1 Probing the conductance superposition law in single-molecule circuits with parallel paths G(2)/G(1c)=3.3 1 1 instead of 1c: to eliminate the role of junction structure (in comparing 1 and 2) 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)=8.2x10 -3 G 0 G(1c)=2.5x10 -3 G 0 G(2)/G(1c)=3.3 Larger than measured (2.8) Correction doesn’t change the ratio by more than 20%

5 Journal Club, Sept. 13. 2012, Tóvári Endre Probing the conductance superposition law in single-molecule circuits with parallel paths Transmission spectra are qualitatively similar. Conductance ratio: sensitive to relative placement of energy levels (E F, gateway, backbone states): LUMO HOMO AB B Gateway Other molecules: measurements and calculations at the E F (low bias) for some molecules AB resonances are near the gateway states’ energy  reduced transmission (and cond. ratio) for E<E F

6 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

7 A simple model for electron transmission: Green’s function approach Journal Club, Sept. 13. 2012, Tóvári Endre Probing the conductance superposition law in single-molecule circuits with parallel paths 2 levels for each molecular backbone (1.,2.): E H1, E L1 E H2, E L2 (same for 1 and 2, if backbones are equivalent) (H=HOMO highest occuppied molec. orbital, L=LUMO lowest unoccuppied m.o.) E H1, E L1 E H2, E L2 Interaction of backbone orbitals („through space coupling”): -t hopping -t (link) E L, E R gateway states (sulphur junction) ELEL ERER 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 states on the backbones. Bonding/antibonding combinations of backbone states: Γ Γ LUMO HOMO AB antibonding B bonding (For molecule 1: 4x4 Hamiltonian) Gateway state π


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