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Breaking Down Resonance: Non-Linear Transport and the Breakdown of Coherent Tunneling Models in Single Molecule Junctions E-Dean Fung, David Gelbwaser-Klimovsky, Jeffrey Charles Taylor, Jonathan Z Low, Jianlong Xia, Fadi M. Jradi, Iryna Davydenko, Luis M. Campos, Seth R. Marder, Uri Peskin, and Latha Venkataraman Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b00316 • Publication Date (Web): 01 Mar 2019 Downloaded from http://pubs.acs.org on March 1, 2019

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Breaking Down Resonance: Non-Linear Transport and the Breakdown of Coherent Tunneling Models in Single Molecule Junctions E-Dean Fung1, David Gelbwaser2, Jeffrey Taylor1, Jonathan Low3, Jianlong Xia4, Fadi Jradi5, Iryna Davydenko5, Luis M. Campos3, Seth Marder5, Uri Peskin*6, Latha Venkataraman*1,3 1

Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, United States

2

Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 United States 3

Department of Chemistry, Columbia University, New York, New York 10027, United States

4

School of Chemistry, Chemical Engineering, and Life Science, Wuhan University of Technology, Wuhan 430070, China 5

School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States 6

Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel

*(U.P.) Tel: +972-4-8292137; Email: [email protected] *(L.V.) Tel: +1-212-854-1786; E-mail: [email protected]

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ABSTRACT The promise of the field of single-molecule electronics is to reveal a new class of quantum devices that leverages the strong electronic interactions inherent to sub-nanometer scale systems. Here, we form Aumolecule-Au junctions using a custom scanning tunneling microscope and explore charge transport through current-voltage measurements. We focus on the resonant tunneling regime of two molecules, one that is primarily an electron conductor and one that conducts primarily holes. We find that in the high bias regime, junctions that do not rupture demonstrate reproducible and pronounced negative differential resistance (NDR)-like features followed by hysteresis, with peak-to-valley ratios exceeding 100 in some cases. Furthermore, we show that both junction rupture and NDR are induced by charging of the molecular orbital dominating transport and find that the charging is reversible at lower bias and with time, with kinetic timescales on the order of hundreds of milliseconds. We argue that these results cannot be explained by existing models of charge transport and likely require theoretical advances describing the transition from coherent to sequential tunneling. Our work also suggests new rules for operating singlemolecule devices at high bias to obtain highly non-linear behavior. KEYWORDS single-molecule junctions, resonant transport, sequential tunneling, negative differential resistance, hysteresis

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Single-molecule devices enable exploration of charge transport at the sub-nanometer scale, potentially unveiling functionality with no solid-state analogues. Two-electrode systems where the molecule is chemically bound to both electrodes via anchoring groups are particularly interesting for their simplicity. Most studies on such systems thus far have focused on the low bias and non-resonant tunneling regime, leveraging chemical principles to modify the electronic structure and control transport behavior1. By contrast, two-electrode experiments on charge transport in the resonant tunneling regime, where the molecular orbital that dominates transport lies close to or within the transport window, are limited, in part because of the high biases typically required to achieve resonance but also because resonant electrons can tunnel inelastically and stimulate junction rupture2–9. Despite this challenge, transport in the resonant tunneling regime remains attractive due to the presence of strong electron-electron and electron-phonon interactions which are expected to produce non-linear effects beyond the realm of Landauer-Büttiker theory of elastic scattering. A number of pioneering studies have successfully demonstrated resonant-tunneling in singlemolecule devices10–12, and two non-linear phenomena have consistently emerged: Negative Differential Resistance13–18 (NDR) and hysteresis19–23. Although each of these phenomena has been observed in a variety of different molecules, the molecules frequently have highly-localized molecular orbitals, and the experiments are often performed at low temperature, which limits their application to devices. A variety of mechanisms have been proposed to explain the presence of NDR and hysteresis in single-molecule devices. The two theories with arguably the greatest generality are the blocking-state model24–26 and the polaron model27,28, although other explanations were also proposed for NDR and hysteresis in molecular devices13. In this work, we report both abrupt NDR and hysteresis in two molecular backbones, an oligomer of an electron-deficient thiophene-1,1-dioxide unit (TDO4) and a squaraine-based derivative with structures shown in Figure 1b. We carry out measurements in both non-polar and polar solvent 1 ACS Paragon Plus Environment

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environments. The two molecules complement one another in that electrons dominate transport in TDO4, whereas holes dominate transport in squaraine. Fitting thousands of individual single-molecule junction current-voltage (I-V) traces to the Landauer-Büttiker theory for a single level model, we show that the mechanism for NDR must be induced by charging and that the hysteresis is characterized by a shift in level alignment with little modification to the level broadening. By changing the speed at which the experiment is performed, we find that the charging mechanism is stochastic in nature and can be reversed by decreasing the bias. We explicitly rule out current formulations of the blocking-state model and the polaron model as explanations for our experimental observations and suggest that a full model requires a more detailed account of inelastic charge hopping and the time-scale of intra-molecule reorganization.

Figure 1: (a) Schematic of Scanning Tunneling Microscope break junction measurement. (b) Molecular structure of TDO4 (magenta, majority electron transport) and squaraine (blue, majority hole transport). The terminal methyl-sulfide groups serve as linkers to bind to the Au electrodes. (c) Sample currentvoltage (I-V) measurement on a TDO4 molecular junction in TCB. (d) 2-Dimensional (2D) histogram of 2 ACS Paragon Plus Environment

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over 500 selected current traces versus time demonstrating reproducible NDR and hysteresis in TDO4 molecular junctions measured in TCB. The applied bias overlaid in white. We used the Scanning Tunneling Microscope Break Junction (STM-BJ) technique described previously to form single-molecule devices29,30. In brief, a ~200 µM molecular solution is deposited on an Au substrate. An Au-wire STM tip is repeatedly brought in and out of contact with the substrate to form and break metal-molecule-metal junctions as shown schematically in Figure 1a. Each junction has slightly different structure and therefore different transport characteristics. All experiments were performed at room temperature and under ambient conditions. To explore transport in the resonant tunneling regime, we modified the STM-BJ technique to obtain a current-voltage (I-V) curve of each molecular junction. As described previously31,32, the molecular junction is held for 100 ms, during which time the current is measured as the voltage is ramped up and down. An example I-V trace, along with the piezo and voltage ramp, is shown in Figure 1c. Thousands of traces are typically collected and analyzed. The result from an I-V experiment for junctions of TDO4 in a solution of 1,2,4-Trichlorobenzene (TCB) is shown as a two-dimensional histogram in Figure 1d where we show only half of the voltage ramp. The voltage was ramped from 0 to 1.8 Volts and back down over the course of 50 ms. During the ramp up, the current follows a curve characteristic of elastic single-level charge transport up to approximately 1.5 Volts. After 1.5 Volts, the current drops, even as the bias is increased further. In other words, the junctions display NDR-like behavior. As the bias is ramped down, many junctions rupture and are therefore lost. The traces included in the 2D histogram shown in Figure 1d are the ~500 that do not rupture; the full histogram, which includes about 3000 traces, is shown in the supporting information (SI) Figure S6b (see SI for selection algorithm). What is clearly visible in Figure 1d is that the current displays hysteresis, following a different path during the ramp down compared to the ramp up. We also collected analogous data for squaraine, shown in SI Figure S3a.


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To acquire a more detailed account of the underlying mechanism for the observed NDR and hysteresis, we performed non-linear least-squares fitting to the I-V data using a single channel model of charge transport within the Landauer-Büttiker theory, which is commonly used in describing coherent charge transport in single-molecule devices33–35. This theory assumes elastic tunneling such that the electrons or holes do not interact with each other or with the vibrational modes of the molecule. Although the Landauer-Büttiker theory cannot capture NDR and hysteresis, it is a reasonable approximation when the transport is dominated by coherent single-particle tunneling. The fittings to our experimental results suggest that this is indeed the case for small biases, before the NDR feature appears. Within this approximation, the properties of the junction are captured by the transmission function T(E), which describes the probability of charge transfer across the molecule as function of the carrier energy E. The current, I, is then given by Equation 1, where f(E) is the Fermi-Dirac distribution and the energy E is written with respect to the Fermi energy. e and h are the elementary charge and Planck’s constant, respectively, and the bias across the junction is V. ∞

2𝑒 𝑒𝑉 𝑒𝑉 𝐼(𝑉) = ∫ 𝑑𝐸 𝑇(𝐸) ⋅ [𝑓 (𝐸 − ) − 𝑓 (𝐸 + )] ℎ 2 2

(1)

−∞

In the simplest case, a single molecular orbital dominates transport in the junction. We have shown in previous work that in the case of TDO4, this is the Lowest Unoccupied Molecular Orbital (LUMO)36,37, and the same reasoning is applied to squaraine to infer that the Highest Occupied Molecular Orbital (HOMO) dominates transport (Sections S1.4 and S3.3 of the SI). This is also confirmed by Density Functional Theory (DFT)-based transport calculations (Section S4 of SI). For this reason, we say that electrons (holes) dominate transport in TDO4 (squaraine) or, equivalently, that TDO4 is LUMO-conducting and squaraine is HOMO-conducting. The transmission function can then be approximated using a single Lorentzian function with only two parameters (Equation 2): the level alignment ε and level broadening Γ. We assume symmetric coupling and define Γ = ΓL = ΓR38. 4 ACS Paragon Plus Environment

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𝑇(𝐸) =

Γ2 (𝐸 − 𝜀)2 + Γ 2

(2)

In fitting I-V data to the coherent transport model, we use the Fermi-Dirac distribution at roomtemperature instead of taking the 0 Kelvin approximation, which is necessary in order to capture the more gradual increase in current near resonance at room temperature. To compensate for the increase in computational complexity, we only fit 200 points per junction, which is 20% of the total data available. We fit log10(I) instead of I as a function of bias to give points at all biases equal weight since I spans over three orders of magnitude. The fitting algorithm is described in full in the SI.

Figure 2: Analysis of TDO4 molecular junctions measured in TCB. (a) Sample I-V trace with forward bias sweep in red and backward bias sweep in orange. Fits to single-level model within the Landauer-Büttiker formalism overlaid in dashed blue and green for forward and backward bias sweeps, respectively. The threshold bias as determined by locating the maximum current is indicated by the vertical dashed line. 5 ACS Paragon Plus Environment

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The black arrows indicate the sweep direction. (b) 2D histogram of threshold bias and level alignment ε. Dotted line represents bias at which the transport level enters the bias window. Histograms of fitted (c) level alignment ε and (d) level broadening Γ, with the results before and after charging shown in blue and green, respectively. An exemplary I-V trace is shown in solid colors on a semi-log plot in Figure 2a, where the ramp up is drawn in red and the ramp down is drawn in orange. The NDR feature, seen during the ramp up, is abrupt, which is not obvious in the 2D histogram. We identify the threshold bias at which NDR occurs (dashed vertical line in Figure 2a) by selecting the point of maximum current. By fitting the curve up to the threshold bias to the coherent transport model given in Eq. 1, we extract ε and Γ. We plot the threshold bias against ε for these same junctions in a 2D histogram (Figure 2b). Not only is there a strong correlation between the threshold bias and ε, but, with few exceptions, the threshold bias is always just below 2ε. The significance of this becomes clear upon closer inspection of Equation 1. Because the bias window opens symmetrically about the Fermi energy, in the limit of T=0, V=2ε is the condition necessary for achieving resonant transport. From the strong correlation between threshold bias and ε, we infer that charging the molecular orbital that dominates transport induces the NDR. In the case of TDO4, this corresponds to the molecule being reduced, whereas for squaraine, it is oxidized. Upon charging, the junctions either rupture or sustain, and we find that approximately 20% of junctions found in Figure 1d sustain. From these junctions, we can extract a peak-to-valley ratio for each trace, which is around 10 for most junctions, but can be as high as 200 (Fig. S1). In addition, we also fit the I-V on the return bias sweep to the single-level coherent transport model. We emphasize that this fitting assumes coherence and, therefore, only represents models where coherent tunneling is preserved upon charging. The fitted values for ε and Γ before and after charging are summarized in the histograms in Figure 2c,d. The mean value of ε increases by around 0.3 eV, whereas any change in Γ is negligible. Both the NDR and hysteresis, therefore, clearly result in an increase in ε, at least within a coherent tunneling model. The same qualitative behavior is observed for squaraine in TCB, as shown in SI Figure S3. 6 ACS Paragon Plus Environment

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To test if the solvent environment alters these results, we repeated the experiment in propylene carbonate (PC). As described in previous work, STM-BJ measurements performed in polar solvents like PC utilize a tip coated with an insulating layer in order to reduce capacitive and Faradaic background currents39. Because the surface area of the tip is much smaller than the surface area of the substrate, the density of the electric double layer is asymmetric, resulting in junctions that rectify according to the dominant transport orbital. More explicitly, in the limit that the electric double layer is much denser at the tip than at the substrate, the voltage drops almost entirely across the tip-molecule interface. We model this effect as a linear dependence of ε on the applied bias, i.e. we replace ε in Equation 2 with ε(V)= ε0+αeV. The effect of the solvent is parameterized by α, which ranges from 0 (in the case of a non-polar solvent) to 0.5 (for the case where the molecular orbital is completely pinned to the substrate). Although we had previously concluded that α was 0.536, this conclusion was derived from a zero-temperature approximation. The present work shows that α can vary from junction to junction when considering that measurements are at 300 K and is therefore used as a third fitting parameter. We extract ε and Γ before and after charging for TDO4 and squaraine in PC as shown in Figures S2 and S4, respectively. Again, ε increases upon charging, accompanied by a small change in Γ. Furthermore, the peak-to-valley ratio is even higher in PC than in TCB and is easily on the order of 100. We obtain greater insight into the mechanism for charging by changing the bias ramp speed. We repeat the experiment depicted in Figure 1c, changing only the duration over which the bias is ramped. The result for squaraine in PC is shown in Figure 3a. At slow speeds, the threshold bias is consistently around 0.5±0.1V. The large spread of values accounts for variations in ε. As the speed increases, the threshold bias increases logarithmically with ramp speed. We infer from this trend that the charging event is stochastic in nature. Assuming that the probability of charging the molecule increases the closer the bias is to the resonant tunneling condition, only at sufficiently slow ramp speeds is there enough time for


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the molecule to charge at lower bias. The same behavior is observed for squaraine in TCB and TDO4 in TCB and PC (Figure S5). Finally, we investigate whether the shift in level alignment, which we attribute to a charging event, can be reversed by discharging the molecule. We begin by simply adding a second I-V sweep following the first, and we find that most junctions (collected in Figure 3b) display a second NDR feature, thus ruling out any irreversible chemical reactions. To explore the kinetics further, we designed a modified STM-BJ experiment as depicted for squaraine in PC in Figure 3c. The experiment starts with a ramp up to 1 V in order to charge the molecule, with the ramp speed fixed at 20 V/s. The bias is then ramped down to some hold bias over the course of 50 ms. This bias is then maintained for some time before the bias is again ramped up to 1 V. Since we know that the ramp speed can affect the charging statistics, this second ramp is also performed at 20 V/s. Lastly, the bias is ramped down to 0 V, also at a 20 V/s rate. By varying the hold bias and hold time, we control the likelihood that the molecule reverts to the neutral state. The experiments are analyzed as follows: first, we select for traces that sustain a molecular junction to the end of the bias hold (100 ms in Fig. 3c). Next, we select those traces which display hysteresis after the first ramp. Such traces also typically display NDR. Of these traces, we select those that display a second hysteresis feature after the second ramp to 1 V. Because a second hysteresis feature is only expected of those molecules that return to the neutral state, we infer that junctions have reversed their charge state during the hold. In this way, we measured the percent of junctions that discharge as a function of hold bias and hold time. Figures 3d and 3e show the dependence of the reversibility on the hold bias and the hold time, respectively. In Figure 3d, the hold time is kept fixed at 100 ms as the hold bias is varied. As the hold bias increases, the number of junctions which reverse decreases, suggesting that the charged state can be sustained under a high bias. Below a hold bias of around 0.4 V, the reversibility plateaus. This means that


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to discharge the molecule, the bias must be sufficiently far from the resonant tunneling condition, but the rate of discharge does not increase below a certain threshold bias. In Figure 3e, the hold bias is set to 0.3 V as the hold time is varied. This bias is deliberately chosen to be just below where the bias dependence becomes negligible. As the hold time increases, the percent of junctions which reverse increases logarithmically, indicating that discharging, like charging, is a stochastic process. Again, these results are reproduced for squaraine in TCB and for TDO4 (Figure S5).

Figure 3: All figures represent results of squaraine molecular junctions measured in PC. (a) Threshold bias as a function of ramp speed. Error bars depict the standard deviation of threshold bias values. (b) 2D histogram of current vs time of selected traces (2795 traces) from experiment with two sequential bias sweeps, overlaid in white, from -0.5 to 1.0 V. NDR and hysteresis are repeated in second bias sweep, indicating that the molecule discharges. (c) 2D histogram of current versus time of custom experiment testing stability of charged state. Applied bias overlaid in white. Percent of junctions reversed as a function of (d) hold bias and (e) hold time. Before analyzing these results based on existing theories, we briefly summarize the key results that must be explained. (A) Charging the molecular orbital which dominates transports results in an abrupt 9 ACS Paragon Plus Environment

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drop in current. (B) Many junctions are lost upon charging, indicating significant coupling to molecular nuclear motion. (C) Insofar as the charged system can be characterized by a single-level model within the Landauer-Büttiker formalism, the level of the charged system moves further away from Fermi, whereas the change in level broadening, if any, is small compared to variance. (D) Both charging and discharging are not driven solely by bias but occur stochastically, with 100 ms timescale kinetics.

Figure 4: Models for simultaneous NDR and hysteresis represented as energy-level diagrams. Electrodes are drawn as a continuous density of states filled up to the chemical potential. Single-electron levels are drawn as horizontal lines, with dashed (solid) lines indicating the levels before (after) charging and vertical arrows indicting the level dynamics upon charging. Charging of the level suggested by arched arrows from the left electrode to the electronic level. All models are depicted for LUMO conducting systems. (a) Blocking-state model: LUMO+1 is poorly coupled to the electrodes, whereas LUMO is well coupled to the electrodes. Upon charging LUMO+1, LUMO shifts up by U, the Coulomb charging energy, resulting in a drop in current. (b) Polaron model: upon charging the LUMO, the charge on the molecule is stabilized by both nuclear motion and the solvent environment, parameterized by the reorganization energy 𝜆. The level moves down such that the charged level is further from Fermi than the empty level, resulting in a drop in current. 𝜀0 and 𝜀̃ are the level alignment before and after charging, respectively. (c) Sequential tunneling: due to strong interaction with molecular vibrations and the environment, electrons no longer tunnel elastically. In the context of Marcus charge transfer, sequential tunneling is modelled by the charge transfer rates k1 and k2 for transfer to and from the molecule, respectively. Charge transfer in the opposite direction is omitted for clarity. We first consider applying the blocking-state model to our results.24–26 This model, shown in Figure 4a, assumes that an electronic level which does not contribute significantly to transport (LUMO+1 in the 10 ACS Paragon Plus Environment

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Figure 4a) is occupied at high bias. Occupation of this higher level shifts the alignment of the transport level (LUMO in this case) away from the Fermi energy due to Coulomb interactions, which can be captured by a Hubbard-like parameter U. The condition for NDR in this model is that the higher level be weakly coupled to the electrodes compared to the coupling of the transport level. By contrast, in our experiments, we find that NDR occurs upon charging of the level that dominates transport (Fig. 2b), not a second, weakly coupled orbital. Furthermore, DFT-based transport calculations of TDO4 junctions do not show higher-energy levels with significantly weaker coupling as required by this model36. The second model we consider is the polaron mean-field model, advanced by Galperin and coworkers27,28, which is depicted in Figure 4b. According to this model, transport involves a single electronic level whose coupling to phonon modes stabilizes the charge on the molecule. In a non-polar solvent environment, where the bias falls symmetrically across the substrate- and tip-molecule interfaces, NDR occurs if the reorganization energy, λ, is greater than ε such that the charged level is further from the Fermi energy than the neutral level. In order to discharge the level, the bias polarity must be either increased further or reversed. In our measurements, however, we observe that the junction discharges even without further increasing or reversing the bias polarity. In a non-polar solvent, the polaron model is consistent with this result only if λ is smaller than ε, which is incompatible with NDR as the charged level would then be closer to the Fermi energy, resulting in an increase in current upon charging. We obtain further evidence against the polaron model by more careful analysis of the data measured in the polar solvent. The fitting applied to measurements in PC summarized in Figures S2 and S4 implicitly assumed a blocking-state-like model. This is because the fitting applied there required that TDO4 (squaraine) remain LUMO (HOMO) conducting upon charging. In the polaron model, however, the observation of NDR implies that a LUMO-conducting molecule becomes HOMO-conducting upon charging and vice versa. After correcting the fitting to apply to the polaron model (Figure S9), the reorganization energy λ can be calculated using the relation 2𝜆 = |𝜀̃ − 𝜀0 |, where 𝜀0 and 𝜀̃ are the level alignment before 11 ACS Paragon Plus Environment

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and after charging, respectively (Figure 4b). Surprisingly, the results from this calculation imply that λ is smaller in PC than in TCB despite PC being significantly more polar (Section S3.4 of SI). This is counterintuitive, since polar solvents are expected to better screen the charge and, consequently, result in a larger reorganization energy than non-polar solvents40–42. Since this result derives directly from imposing a simple polaron model, we conclude that this model, at least in its current formulation, cannot explain our experimental results. In principle, the polaron model can be modified by introducing a second transport channel. The reorganization energy would then cause the frontier orbital to drop out of transport bias window, allowing the second channel to dominate transport. Although we cannot entirely rule out such a model, we suspect that such a model would be extremely sensitive to the exact reorganization energies and level alignment. Furthermore, such a model would violate the Aufbau principle, which is unlikely for conjugated organic molecules without highly localized molecular orbitals25,26 or radical character43. We also note briefly that there are a class of theories which explain NDR by biased-induced deformation of the molecular orbitals that, in turn, result in changes in the level broadening13,44–46. Similarly, theories which implicate chargeinduced conformational change47,48 also manifest as decreases in level broadening49,50. However, biasinduced orbital deformation predicts more gradual NDR than is observed here, and curve-fitting does not show any consistent change in level broadening. Instead, we interpret our observations as a transition from predominately coherent tunneling, as described by the Landauer-Büttiker model, to sequential tunneling where inelastic processes damp the current in the resonant tunneling regime. Theoretical work exploring this transition has shown that the introduction of incoherence decreases the transmission through a single level at resonance51–53. Our results demonstrate, however, that the transition from coherent to sequential tunneling is abrupt even at room temperature and that the relevant timescales are long, at least compared to the characteristic timescales of molecular motion. We propose that advances in theories incorporating Marcus charge 12 ACS Paragon Plus Environment

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transfer rates and its possible extensions, where the reorganization energy asymmetrically affects charge transfer to and from the molecule (k1 and k2, respectively in Fig. 4c), may account for this extraordinary result54,55. We reemphasize that the I-V curve-fitting during the reverse bias sweep using the LandauerBüttiker formalism as performed in our analysis is only valid within the context of coherent tunneling and should only be used to evaluate models where this is applicable. Consequently, a model of incoherent tunneling will not be constrained to the interpretation presented in Figure 2 of level alignment shift, and a blocking-state or polaron-like model that relaxes the assumptions stated in the preceding paragraphs may still provide a good foundation for exploration56. This will be the subject of future investigations and is beyond the scope of this work. To conclude, we have explored the rich phenomena that occur in the resonant tunneling regime. First, we have shown that the widely ignored junction rupture at high bias is not entirely impervious to study and is directly attributable to redox events. Furthermore, junctions that do not rupture display highly reproducible and pronounced NDR and hysteresis with kinetic timescales on the order of 100 milliseconds. We argue that existing models cannot describe our results and suggest that a deeper understanding of the interplay between molecular reorganization rates and both coherent and incoherent tunneling is the key to resolving the mystery. Finally, this work opens the possibility of a new mode of operation of single-molecule devices at high bias to achieve highly non-linear behavior even at room temperature. Corresponding Authors *(U.P.) Tel: +972-4-8292137; Email: [email protected] *(L.V.) Tel: +1-212-854-1786; E-mail: [email protected] Acknowledgements


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E.F. and L.V. would like to acknowledge Michael Galperin for fruitful discussions regarding the applicability of the polaron model. The work at Columbia University was primarily funded by the Columbia University’s Research Initiatives in Science and Engineering and the National Science Foundation (grant number CHE1404922 and CHE-1764256). J. L. thanks the A*STAR Graduate Academy in Singapore for a graduate fellowship. J.X. acknowledges the financial support from the National Natural Science Foundation of China (NSFC, 51773160). U.P. acknowledges the Israel Science Foundation grant #1243/18. The work at the Georgia Institute of Technology was supported by the Air Force Office of Scientific Research through the COMAS MURI program (Agreement no. FA9550-10-1-0558) and the Georgia Power Foundation through a Georgia Power Chair for Energy Efficiency for S.R.M. ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website. Additional Analysis and Data, Selection Algorithms, Non-Linear Least-Squares Fitting Methods, Density Functional Theory-Based Transport Calculation of Squaraine, Synthesis and Characterization of Squaraine (PDF) Notes The authors declare no competing financial interest. REFERENCES (1)

Su, T. A.; Neupane, M.; Steigerwald, M. L.; Venkataraman, L.; Nuckolls, C. Nature Reviews Materials 2016, 1, 16002.

(2)

Stipe, B. C.; Rezaei, M. A.; Ho, W.; Gao, S.; Persson, M.; Lundqvist, B. I. Phys. Rev. Lett. 1997, 78 (23), 4410–4413.

(3)

Seideman, T. J. Phys.: Condens. Matter 2003, 15 (14), R521–R549.


Page 16 of 21

Page 17 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

(4)

Smit, R. H. M.; Untiedt, C.; Ruitenbeek, J. M. van. Nanotechnology 2004, 15 (7), S472–S478.

(5)

Koch, J.; Semmelhack, M.; von Oppen, F.; Nitzan, A. Phys. Rev. B 2006, 73 (15), 155306.

(6)

Suzuki, M.; Ominami, Y.; Ngo, Q.; Yang, C. Y.; Cassell, A. M.; Li, J. Journal of Applied Physics 2007, 101 (11), 114307.

(7)

Taniguchi, M.; Tsutsui, M.; Yokota, K.; Kawai, T. Nanotechnology 2009, 20 (43), 434008.

(8)

Li, H.; Su, T. A.; Zhang, V.; Steigerwald, M. L.; Nuckolls, C.; Venkataraman, L. J. Am. Chem. Soc. 2015, 137 (15), 5028–5033.

(9)

Li, H.; Kim, N. T.; Su, T. A.; Steigerwald, M. L.; Nuckolls, C.; Darancet, P.; Leighton, J. L.; Venkataraman, L. J. Am. Chem. Soc. 2016, 138 (49), 16159–16164.

(10)

Elbing, M.; Ochs, R.; Koentopp, M.; Fischer, M.; Hänisch, C. von; Weigend, F.; Evers, F.; Weber, H. B.; Mayor, M. PNAS 2005, 102 (25), 8815–8820.

(11)

Perrin, M. L.; Verzijl, C. J. O.; Martin, C. A.; Shaikh, A. J.; Eelkema, R.; Esch, J. H. van; van Ruitenbeek, J. M.; Thijssen, J. M.; van der Zant, H. S. J.; Dulić, D. Nat Nano 2013, 8 (4), 282–287.

(12)

Kuang, G.; Chen, S.-Z.; Wang, W.; Lin, T.; Chen, K.; Shang, X.; Liu, P. N.; Lin, N. J. Am. Chem. Soc. 2016, 138 (35), 11140–11143.

(13)

Xu, B.; Dubi, Y. J. Phys.: Condens. Matter 2015, 27 (26), 263202.

(14)

Xiao, X.; Nagahara, L. A.; Rawlett, A. M.; Tao, N. J. Am. Chem. Soc. 2005, 127 (25), 9235–9240.

(15)

Kang, N.; Erbe, A.; Scheer, E. Applied Physics Letters 2010, 96 (2), 023701.

(16)

Perrin, M. L.; Frisenda, R.; Koole, M.; Seldenthuis, J. S.; Gil, J. A. C.; Valkenier, H.; Hummelen, J. C.; Renaud, N.; Grozema, F. C.; Thijssen, J. M.; et al. Nat Nano 2014, 9 (10), 830–834.

(17)

Kuang, G.; Chen, S. Z.; Yan, L.; Chen, K. Q.; Shang, X.; Liu, P. N.; Lin, N. J. Am. Chem. Soc. 2018, 140 (2), 570–573.

(18)

Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Science 1999, 286 (5444), 1550–1552.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(19)

Blum, A. S.; Kushmerick, J. G.; Long, D. P.; Patterson, C. H.; Yang, J. C.; Henderson, J. C.; Yao, Y.; Tour, J. M.; Shashidhar, R.; Ratna, B. R. Nature Materials 2005, 4 (2), 167–172.

(20)

Lörtscher, E.; Ciszek, J. W.; Tour, J.; Riel, H. Small 2006, 2 (8–9), 973–977.

(21)

Schwarz, F.; Kastlunger, G.; Lissel, F.; Riel, H.; Venkatesan, K.; Berke, H.; Stadler, R.; Lörtscher, E. Nano Lett. 2014, 14 (10), 5932–5940.

(22)

Schwarz, F.; Kastlunger, G.; Lissel, F.; Egler-Lucas, C.; Semenov, S. N.; Venkatesan, K.; Berke, H.; Stadler, R.; Lörtscher, E. Nat Nano 2016, 11 (2), 170–176.

(23)

Schwarz, F.; Koch, M.; Kastlunger, G.; Berke, H.; Stadler, R.; Venkatesan, K.; Lörtscher, E. Angew. Chem. Int. Ed. 2016, 55 (39), 11781–11786.

(24)

Muralidharan, B.; Datta, S. Phys. Rev. B 2007, 76 (3), 035432.

(25)

Migliore, A.; Nitzan, A. ACS Nano 2011, 5 (8), 6669–6685.

(26)

Migliore, A.; Nitzan, A. J. Am. Chem. Soc. 2013, 135 (25), 9420–9432.

(27)

Galperin, M.; Ratner, M. A.; Nitzan, A. Nano Lett. 2005, 5 (1), 125–130.

(28)

Yeganeh, S.; Galperin, M.; Ratner, M. A. J. Am. Chem. Soc. 2007, 129 (43), 13313–13320.

(29)

Xu, B.; Tao, N. J. Science 2003, 301 (5637), 1221–1223.

(30)

Kamenetska, M.; Koentopp, M.; Whalley, A. C.; Park, Y. S.; Steigerwald, M. L.; Nuckolls, C.; Hybertsen, M. S.; Venkataraman, L. Phys. Rev. Lett. 2009, 102 (12), 126803.

(31)

Reed, M. A.; Zhou, C.; Muller, C. J.; Burgin, T. P.; Tour, J. M. Science 1997, 278 (5336), 252–254.

(32)

Ulrich, J.; Esrail, D.; Pontius, W.; Venkataraman, L.; Millar, D.; Doerrer, L. H. J. Phys. Chem. B 2006, 110 (6), 2462–2466.

(33)

Lörtscher, E.; Weber, H. B.; Riel, H. Phys. Rev. Lett. 2007, 98 (17), 176807.

(34)

Cuevas, J. C.; Scheer, E. Molecular Electronics, 2nd ed.; World Scientific Series in Nanoscience and Nanotechnology, Vol. 15; World Scientific: Singapore, 2017.


Page 18 of 21

Page 19 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

(35)

Hayakawa, R.; Karimi, M. A.; Wolf, J.; Huhn, T.; Zöllner, M. S.; Herrmann, C.; Scheer, E. Nano Lett. 2016, 16 (8), 4960–4967.

(36)

Capozzi, B.; Xia, J.; Adak, O.; Dell, E. J.; Liu, Z.-F.; Taylor, J. C.; Neaton, J. B.; Campos, L. M.; Venkataraman, L. Nature Nanotechnology 2015, 10 (6), 522–527.

(37)

Dell, E. J.; Capozzi, B.; Xia, J.; Venkataraman, L.; Campos, L. M. Nature Chemistry 2015, 7 (3), 209– 214.

(38)

Peskin, U. J. Phys. B: At. Mol. Opt. Phys. 2010, 43 (15), 153001.

(39)

Nagahara, L. A.; Thundat, T.; Lindsay, S. M. Review of Scientific Instruments 1989, 60 (10), 3128– 3130.

(40)

Dzhioev, A. A.; Kosov, D. S. Phys. Rev. B 2012, 85 (3), 033408.

(41)

Matyushov, D. V. J. Chem. Phys. 2004, 120 (16), 7532–7556.

(42)

Marcus, R. A. J. Chem. Phys. 1956, 24 (5), 979–989.

(43)

Slipchenko, L. V.; Munsch, T. E.; Wenthold, P. G.; Krylov, A. I. Angewandte Chemie International Edition 2004, 43 (6), 742–745.

(44)

Pati, R.; McClain, M.; Bandyopadhyay, A. Phys. Rev. Lett. 2008, 100 (24), 246801.

(45)

Cardamone, D. M.; Kirczenow, G. Phys. Rev. B 2008, 77 (16), 165403.

(46)

Capozzi, B.; Low, J. Z.; Xia, J.; Liu, Z.-F.; Neaton, J. B.; Campos, L. M.; Venkataraman, L. Nano Lett. 2016, 16 (6), 3949–3954.

(47)

Emberly, E. G.; Kirczenow, G. Phys. Rev. B 2001, 64 (12), 125318.

(48)

Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122 (13), 3015–3020.

(49)

Solomon, G. C.; Andrews, D. Q.; Duyne, R. P. V.; Ratner, M. A. ChemPhysChem 2009, 10 (1), 257– 264.

(50)

Woitellier, S.; Launay, J. P.; Joachim, C. Chemical Physics 1989, 131 (2), 481–488.

(51)

Buttiker, M. IBM Journal of Research and Development 1988, 32 (1), 63–75.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(52)

Golizadeh-Mojarad, R.; Datta, S. Phys. Rev. B 2007, 75 (8), 081301(R).

(53)

Peskin, U. J. Chem. Phys. 2000, 113 (17), 7479–7487.

(54)

Kuznetsov, A. M.; Ulstrup, J. J. Phys. Chem. A 2000, 104 (49), 11531–11540.

(55)

Sowa, J. K.; Mol, J. A.; Briggs, G. A. D.; Gauger, E. M. J. Chem. Phys. 2018, 149 (15), 154112.

(56)

Ryndyk, D. A.; D’Amico, P.; Cuniberti, G.; Richter, K. Phys. Rev. B 2008, 78 (8), 085409.


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