Highly nonlinear transport across single-molecule junctions via destructive quantum interference

Abstract

To rival the performance of modern integrated circuits, single-molecule devices must be designed to exhibit extremely nonlinear current–voltage (I–V) characteristics1,2,3,4. A common approach is to design molecular backbones where destructive quantum interference (QI) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) produces a nonlinear energy-dependent tunnelling probability near the electrode Fermi energy (EF)5,6,7,8. However, tuning such systems is not straightforward, as aligning the frontier orbitals to EF is hard to control9. Here, we instead create a molecular system where constructive QI between the HOMO and LUMO is suppressed and destructive QI between the HOMO and strongly coupled occupied orbitals of opposite phase is enhanced. We use a series of fluorene oligomers containing a central benzothiadiazole10 unit to demonstrate that this strategy can be used to create highly nonlinear single-molecule circuits. Notably, we are able to reproducibly modulate the conductance of a 6-nm molecule by a factor of more than 104.

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Fig. 1: Destructive QI between two MOs at the Fermi energy, EF.
Fig. 2: Structure and electronic properties of molecules 1–3.
Fig. 3: Conductance and current–voltage (IV) measurements of 1–3.
Fig. 4: Transmission function calculations for Au–molecule–Au junctions.

Data availability

Data associated with the synthesis and characterization of 13 and C1 are available at https://doi.org/10.5525/gla.researchdata.1062. Additional data that support the findings of this study not included in the Supplementary Information are available from the corresponding authors upon reasonable request.

Code availability

The data that support the findings were acquired using a custom instrument controlled by custom software (Igor Pro, Wavemetrics). The software is available from the corresponding author upon reasonable request.

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Acknowledgements

J.E.G and S.G. are supported by National Science Foundation (NSF) Graduate Research Fellowships under grant no. DGE-1644869. T.F. is supported by the NSF under award grant no. CHE-1764256. J.E.G. and L.V. acknowledge financial support from the NSF under grant no. DMR-1807580. J.C., N.J.F. and P.J.S. thank the EPSRC for funding under grant nos. EP/P02744X/2 and EP/N035496/2.

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Contributions

J.E.G performed all STM measurements. J.C. and N.J.F synthesized all compounds. T.F. and S.G. carried out all calculations. J.E.G. and L.V. wrote the paper with contributions from all authors. L.V. and P.J.S. oversaw the project.

Corresponding authors

Correspondence to Peter J. Skabara or Latha Venkataraman.

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The authors declare no competing interests.

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Peer review information Nature Nanotechnology thanks Colin Lambert and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Synthesis of the longest analogue, 3.

Scheme representing the synthetic strategy used to form the benzothiadiazole-based molecular wires. Suzuki cross coupling reactions were used to introduce fluorene groups to modify the molecular length and to cap the molecules with 4-(thiomethyl)phenyl groups for binding to gold.

Extended Data Fig. 2 Redox properties of 1–3.

Cyclic voltammetry of compounds 1 (light blue), 2 (blue) and 3 (dark blue) using glassy carbon, platinum wire and silver wire as the working, counter and pseudo-reference electrodes, respectively, with (nBu4N)PF6 in dichloromethane as supporting electrolyte (0.1 M) at a scan rate of 100 mV s−1. Reduction (a) and oxidation (b) data were referenced to the Fc/Fc+ redox couple, which has a HOMO of −4.8 eV.

Extended Data Fig. 3 I-V characteristics of 1 and 2.

Current versus time histograms for 1 (a) and 2 (b). In each histogram, the top panel is the bias applied across a 100 kΩ resistor in series with the junction while the tip-substrate distance is held constant. Current is logarithmically-binned (57 bins dec−1) and time is linearly binned (4000 bins s−1). Histogram (a) compiled from 242/1200 selected traces with ± 1.8 V maximum applied bias. Histogram (b) compiled from 389/2000 selected traces with ± 2.0 V maximum applied bias. Number of counts increases from red to yellow. Note: Since the maximum applied bias for 1 is only ± 1.8 V, the hold time is shortened to maintain the same voltage sweep rate.

Extended Data Fig. 4 Single I-t traces for 2 and 3.

Sample I-t traces for 2 (a) and 3 (b) from bias switching measurements. In (a) and (b), the top panel is the bias applied across a 100 kΩ resistor in series with the junction while the tip-substrate distance is held constant. The high bias current for 2 is a factor of ~ 10,000 greater than the low bias current. The high bias current for 3 is a factor of ~ 30,000 greater than the low bias current. Since the low bias current for 3 is through-solvent current (see Supplementary Figs. 5 and 7) and the through-molecule current is even lower, we stress ~ 30,000 represents a lower bound for the enhancement factor at high bias. The switching speed should be instantaneous since transport is ballistic, but the RC time constant associated with the experimental circuit limits the measurement speed.

Extended Data Fig. 5 Bias switching measurements for 1 and 2.

Logarithmically-binned current (100 bins dec−1) versus linearly-binned time (2.86 bin ms−1) histograms for 1 (a) and 2 (b). In each histogram, the top panel is the bias applied across a 100 kΩ resistor in series with the junction while the tip-substrate gap is held fixed. The high bias currents for 1 and 2 are, respectively, ~ 500 and ~ 10,000 times greater than the low bias currents. Counts increase blue (0 counts) to red to yellow. See Supplementary Fig. 7 for full histograms showing formation and rupture of molecular junctions as a function of time.

Extended Data Fig. 6 Visualizations of QI for 1–3.

a–c) Transmission functions for 13 calculated using the B3LYP functional and assuming the wide-band limit . The coupling of each MO, γ, (green circles, right axis) is extracted from the DFT-based calculations and plotted against MO energy. Notably, non-frontier orbitals are better coupled than frontier orbitals for all three molecules. d-f) Visualizations of quantum interference (QI map) at EF for 13. All three QI maps show the LUMO is decoupled and does not contribute to transmission or interfere with other MOs at EF. The QI maps also show that strongly-coupled occupied MOs of opposite phase destructively interfere. As molecular length increases, more occupied MOs contribute to transmission at EF and the destructive interference between these MOs increases, resulting in highly nonlinear transmission. See Ref. 16 for more details on QI map.

Extended Data Fig. 7 Comparison of electronic properties of molecules with and without central BT unit.

a) Molecular structure of the control molecule C1. The structure of C1 is the same as 1 except without the central BT unit. b) Molecular orbitals of C1 calculated using DFT with B3LYP functional. Note the HOMO and LUMO have opposite phases and straddle EF, which suggests these two MOs will constructively interfere near EF. c) Energy level diagram for 1 and C1 constructed from DFT calculations. d) Normalised absorption spectra for 1 and C1 recorded in dichloromethane (10−5 M). Both (c) and (d) show the BT unit considerably lowers the energy of the LUMO of 1, whereas the energies of the HOMO and HOMO-1 are roughly equal for 1 and C1.

Extended Data Fig. 8 Two-electrode gating experiments for 1 and C1.

1D conductance histograms of 1 (a) at positive (+ 0.75 V, red) and negative (− 0.75 V, blue) bias and C1 (b) at positive (+ 0.75 V, green) and negative (− 0.75 V, purple) bias. 2D conductance-displacement histograms for 1 (c) and C1 (d) corresponding to positive bias data presented in (a) and (b), respectively. Measurements performed in ~ 40 μM solution of PC with ~ 0.1 M TBAPF6. Conductance is logarithmically binned (1D: 100 bins dec−1, 2D: 89 bins dec−1) and displacement is linearly binned (300 bins nm−1). All histograms compiled from 1,000 traces without data selection.

Extended Data Fig. 9 Destructive QI between the HOMO and lower energy MOs of opposite phase suppresses transmission at EF.

Transmission functions for junctions of 13 (a–c) overlaid with a single-level model derived from the coupling and position of the HOMO. The single-level model shows that although the LUMO is decoupled, transport is not simply dominated by the HOMO. The ratio of HOMO-dominated transmission to DFT-based transmission at EF is 13, 84 and 350 for 1, 2 and 3, respectively (ratios displayed in inset to Fig. 4c). The disparity between the DFT-based transmission and the single-level model increases with length due to an increase in destructive QI between the HOMO and non-frontier orbitals.

Supplementary information

Supplementary Information

Synthesis details and characterization data, Supplementary Figs. 1–9, Tables 1 and 2 and Discussion.

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Greenwald, J.E., Cameron, J., Findlay, N.J. et al. Highly nonlinear transport across single-molecule junctions via destructive quantum interference. Nat. Nanotechnol. (2020). https://doi.org/10.1038/s41565-020-00807-x

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