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Comprehensive suppression of single-molecule conductance using destructive σ-interference

Abstract

The tunnelling of electrons through molecules (and through any nanoscale insulating and dielectric material1) shows exponential attenuation with increasing length2, a length dependence that is reflected in the ability of the electrons to carry an electrical current. It was recently demonstrated3,4,5 that coherent tunnelling through a molecular junction can also be suppressed by destructive quantum interference6, a mechanism that is not length-dependent. For the carbon-based molecules studied previously, cancelling all transmission channels would involve the suppression of contributions to the current from both the π-orbital and σ-orbital systems. Previous reports of destructive interference have demonstrated a decrease in transmission only through the π-channel. Here we report a saturated silicon-based molecule with a functionalized bicyclo[2.2.2]octasilane moiety that exhibits destructive quantum interference in its σ-system. Although molecular silicon typically forms conducting wires7, we use a combination of conductance measurements and ab initio calculations to show that destructive σ-interference, achieved here by locking the silicon–silicon bonds into eclipsed conformations within a bicyclic molecular framework, can yield extremely insulating molecules less than a nanometre in length. Our molecules also exhibit an unusually high thermopower (0.97 millivolts per kelvin), which is a further experimental signature of the suppression of all tunnelling paths by destructive interference: calculations indicate that the central bicyclo[2.2.2]octasilane unit is rendered less conductive than the empty space it occupies. The molecular design presented here provides a proof-of-concept for a quantum-interference-based approach to single-molecule insulators.

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Acknowledgements

G.C.S. and M.H.G. received funding from the Danish Council for Independent Research | Natural Sciences and the Carlsberg Foundation. We thank the National Science Foundation (NSF) for the support of experimental studies under grant no. CHE-1404922 (Ha.L.) and Columbia University’s Research Initiatives in Science and Engineering. Y.C., Z.S., T.L. and S.X. are sponsored by the National Natural Science Foundation of China (grant nos 21473113 and 51502173), the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning (no. 2013-57), the “Shuguang Program” supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (14SG40), the Program of Shanghai Academic/Technology Research Leader (no. 16XD1402700), the National Natural Science Foundation of Shanghai (no. 15ZR1431100), the Ministry of Education of China (PCSIRT_16R49) and the International Joint Laboratory of Resource Chemistry (IJLRC). T.A.S. was supported by an NSF Graduate Research Fellowship under grant no. 11-44155. We thank B. Fowler for mass spectrometry characterization. Single-crystal X-ray diffraction was performed at the Shared Materials Characterization Laboratory (SMCL) at Columbia University. Use of the SMCL was made possible by funding from Columbia University.

Author information

M.H.G., Ha.L., T.A.S., C.N., L.V. and G.C.S. conceived the idea for the paper. M.H.G. conducted the theoretical calculations under the supervision of G.C.S. Ha.L. did the conductance, noise and thermopower measurements under the supervision of L.V. Y.C., T.A.S., Z.S, D.W.P. and T.L. synthesized and characterized the molecules under the supervision of F.N., He.L., C.N. and S.X. M.H.G., Ha.L., L.V. and G.C.S. analysed the data and wrote the paper with contributions from all authors.

Competing interests

The authors declare no competing financial interests.

Correspondence to Shengxiong Xiao or Colin Nuckolls or Latha Venkataraman or Gemma C. Solomon.

Extended data figures and tables

  1. Extended Data Fig. 1 The three conformations of Si222 and Si2-Si222-Si2, and their transmission data.

    a, Optimized structures of the three conformations of Si222. b, c, Calculated Landauer transmission for the ortho (b) and cis (c) conformations, which are very similar to that of the anti-conformation shown in Fig. 2. dg, Transmission pathways for: (d) Si222-ortho-cut, (e) Si222-cis-cut, (f) Si222-ortho and (g) Si222-cis.

  2. Extended Data Fig. 2 Transmission data for Si222, Si222-short (a compressed junction of Si222) and Si2-Si222-Si2 anti-conformations.

    a, Transmission plot; bd, transmission pathways of (b) Si222-short, (c) Si2-Si222-Si2 and (d) Si222 calculated at 0 eV (the Fermi energy); e, Si2-Si222-Si2 calculated at –0.6 eV; f, Si222 calculated at –1.6 eV. Through-space injection dominates on one side of the molecule in Si222-short at 0 eV and a flattened transmission function around the Fermi energy is observed. This coexistence implies that through-space injection can change the slope of the transmission (and thus the thermopower), without a substantial change in the magnitude of the conductance. Si2-Si222-Si2 at −0.6 eV and Si222 at −1.6 eV both show reversed ring current direction in comparison with that calculated at 0 eV, a clear signature of destructive quantum interference.

  3. Extended Data Fig. 3 Transmission of the partially cut versions of Si222.

    a, Chemical structures of Si222-1bridge and Si222-2bridge. b, Transmission data of Si222 in anti-conformation with different number of bridges being cut. ce, Transmission pathways are shown for (c) Si222-1bridge (one bridge remains, two were cut), (d) Si222-2bridge (two bridges remain, one was cut) and (e) Si222. The transmission of the Si222-2bridge junction is almost as high as Si222-cut junction where all three bridges are cut, because the bridge where the interference signature appears is cut (d). If we instead cut the other two bridges simultaneously (c, Si222-1bridge), the ring current pathways and the antiresonance in the transmission persist.

  4. Extended Data Fig. 4 Transmission of linear tetrasilane (Si4) with one bridging unit cut.

    a, Transmission plot of Si4 and Si4-cut, where one Si(CH3)2 unit has been cut away and the bridgehead silicon atoms passivated with hydrogen atoms. b, c, Transmission pathways are shown for (b) Si4 and (c) Si4-cut. d, Transmission at the Fermi energy plotted against bridgehead silicon distance of Si4 and Si4-cut. Solid red line is a linear fit to the data of Si4-cut.

  5. Extended Data Fig. 5 Experimental 2D conductance versus displacement histograms.

    a, Si4; b, Si222; c, Si2-Si222-Si2. d, Two-dimensional histogram of normalized flicker noise power against average junction conductance for Si4 along with a 2D Gaussian fit of the data. We see almost no correlation between flicker noise power and the conductance and the noise power scales as G1.1.

  6. Extended Data Fig. 6 Thermopower data of Si2-Si222-Si2 and Si8.

    a, Chemical structures of Si8 and Si2-Si222-Si2. b, c, Two-dimensional histograms of thermoelectric current measured while Si2-Si222-Si2 junctions are held at ΔT = 0 K and 37 K, respectively. d, Histogram of the measured thermoelectric current for Si8, which has the same number of Si atoms across the molecule as Si2-Si222-Si2, with ΔT = 0 K and 27 K. Inset: Histogram of thermopower determined from the thermoelectric current for Si8 junctions. After subtracting the thermopower of Au of 2 μV K−1 (to account for the thermoelectric current between the hot substrate and the cold set-up), the average thermopower for Si8 is 35 ± 17 μV K−1, smaller than that of Si2-Si222-Si2. e, Transmission curves for Si8 junction along with Si2-Si222-Si2 junction showing different slopes at the Fermi level. f, Thermopower calculated as the slope of the transmission as a function of energy. Theory underestimates the thermopower of both Si2-Si222-Si2 and Si8 by approximately an order of magnitude. Furthermore, the energy alignment between the antiresonance and the Fermi energy is not exact because of inherent errors of DFT31,42, which results in the opposite sign of the thermopower at the Fermi energy compared to the experimental value.

  7. Extended Data Fig. 7 Further comparison of experimental conductance of thiomethyl- and amine-terminated molecules.

    a, b, Experimental conductance is plotted against calculated (a) sulfur–sulfur distance for thiomethyl-linked molecules and (b) nitrogen–nitrogen distance for amine linked molecules; dashed lines are linear fits to the data. All conductance values are determined from log-binned conductance histograms created from data taken from references and reproduced in Extended Data Fig. 814,33,43,44,45,46,47,48.

  8. Extended Data Fig. 8 Logarithmically binned 1D conductance histograms for control molecules.

    a, Molecules 9 and 10; b, molecules 12 to 15; c, amine-terminated alkanes C2 to C12.

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Further reading

Fig. 1: Schematic illustration of coherent electron transport and model transmission.
Fig. 2: Calculated transport properties of Si4, Si222, Si222-cut and Si2-Si222-Si2.
Fig. 3: Synthesis scheme and experimental single-molecule conductance, thermopower and noise data.
Fig. 4: Experimental single Au–molecule–Au junction conductance against molecular length.
Extended Data Fig. 1: The three conformations of Si222 and Si2-Si222-Si2, and their transmission data.
Extended Data Fig. 2: Transmission data for Si222, Si222-short (a compressed junction of Si222) and Si2-Si222-Si2 anti-conformations.
Extended Data Fig. 3: Transmission of the partially cut versions of Si222.
Extended Data Fig. 4: Transmission of linear tetrasilane (Si4) with one bridging unit cut.
Extended Data Fig. 5: Experimental 2D conductance versus displacement histograms.
Extended Data Fig. 6: Thermopower data of Si2-Si222-Si2 and Si8.
Extended Data Fig. 7: Further comparison of experimental conductance of thiomethyl- and amine-terminated molecules.
Extended Data Fig. 8: Logarithmically binned 1D conductance histograms for control molecules.

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