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

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.

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

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  1. 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 ofChemistry, 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

  2. 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) • Low conductance peaks: • 3.3x10-4 G0 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) Full extension (~0.5 nm): just one, low-conductance peak (coupling only via the sulphur gateway) Conductance vs displacement histograms: 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

  3. 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 AB antibonding LUMO B bonding Gateway state Gateway state HOMO • Low-bias: G(2)/G(1)>2 • Resonance peak from B: 2x wider in case of molecule 2

  4. 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

  5. Probing the conductance superposition law in single-molecule circuits with parallel paths Other molecules: measurements and calculations at the EF (low bias) AB LUMO B 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

  6. 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

  7. 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, L=LUMO lowest unoccuppied m.o.) Interaction of backbone orbitals („through space coupling”): -t hopping AB antibonding LUMO EH1, EL1 EH2, EL2 B bonding Γ Γ ER EL -t (link) (link) τ τ Gateway state Gateway state Connection between backbone and gateway states: τ EL, ER gateway states (sulphur junction) HOMO (For molecule 1: 4x4 Hamiltonian) Bonding/antibonding combinations of backbone states: The relative sign of the coupling terms between each backbone state and the L or R leadscaptures the different number of nodes in the HOMO and LUMO 􀀃 states on the backbones. π Journal Club, Sept. 13. 2012, Tóvári Endre

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