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

Nature Nanotechnology volume 7, pages 663–667 (2012)Cite this article

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Abstract

According to Kirchhoff's circuit laws, the net conductance of two parallel components in an electronic circuit is the sum of the individual conductances. However, when the circuit dimensions are comparable to the electronic phase coherence length, quantum interference effects play a critical role1, as exemplified by the Aharonov–Bohm effect in metal rings2,3. At the molecular scale, interference effects dramatically reduce the electron transfer rate through a meta-connected benzene ring when compared with a para-connected benzene ring4,5. For longer conjugated and cross-conjugated molecules, destructive interference effects have been observed in the tunnelling conductance through molecular junctions6,7,8,9,10. Here, we investigate the conductance superposition law for parallel components in single-molecule circuits, particularly the role of interference. We synthesize a series of molecular systems that contain either one backbone or two backbones in parallel, bonded together cofacially by a common linker on each end. Single-molecule conductance measurements and transport calculations based on density functional theory show that the conductance of a double-backbone molecular junction can be more than twice that of a single-backbone junction, providing clear evidence for constructive interference.

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Figure 1: Single-molecule circuits containing one and two conducting backbones connected in parallel.
Figure 2: STM break-junction measurements of single-molecule conductance.
Figure 3: Calculated transmission properties comparing a double-backbone circuit with an idealized, single-backbone circuit.

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Acknowledgements

This work was supported primarily by the Nanoscale Science and Engineering Initiative of the National Science Foundation (NSF, CHE-0641523), the New York State Office of Science, Technology, and Academic Research (NYSTAR) and an NSF Career Award to L.V. (CHE-07-44185). L.V. also thanks the Packard Foundation for support. This work was carried out in part at the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the US Department of Energy, Office of Basic Energy Sciences (contract no. DE-AC02-98CH10886). R.S. acknowledges financial support from the Canadian postdoctoral fellowship FQRNT programme. S.T.S. acknowledges support from an Arun Guthikonda Memorial graduate fellowship. The authors thank the NSF (CHE-0619638) for the acquisition of an X-ray diffractometer, and G. Parkin and W. Sattler for obtaining our crystal structures.

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Author notes

  1. M. Kamenetska

    Present address: Present address: Department of Molecular Biophysics & Biochemistry and the Department of Physics, Yale University,

  2. H. Vazquez and R. Skouta: These authors contributed equally to this work

Authors and Affiliations

  1. Department of Applied Physics and Applied Mathematics, Columbia University, 500 W. 120th Street, New York, New York 10027, USA

    H. Vazquez, M. Kamenetska & L. Venkataraman

  2. Department of Chemistry, Columbia University, 3000 Broadway, New York 10027, USA

    R. Skouta, S. Schneebeli & R. Breslow

  3. Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA,

    M.S. Hybertsen

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  1. H. Vazquez
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Contributions

The experiments were conceived by R.S., S.S., M.K., R.B. and L.V. Theory and calculations were conceived by H.V. and M.S.H. Synthesis and chemical analysis were performed by R.S. and S.S. Conductance measurements and analysis were performed by M.K and L.V. Calculations were performed by H.V. The manuscript was written by H.V., L.V. and M.S.H., with comments and input from all other authors.

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Correspondence to R. Breslow, L. Venkataraman or M.S. Hybertsen.

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The authors declare no competing financial interests.

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Vazquez, H., Skouta, R., Schneebeli, S. et al. Probing the conductance superposition law in single-molecule circuits with parallel paths. Nature Nanotech 7, 663–667 (2012). https://doi.org/10.1038/nnano.2012.147

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