Control over Near-Ballistic Electron Transport through Formation of Parallel Pathways in a Single-Molecule Wire

: This paper reports highly efficient coherent tunneling in single-molecule wires of oligo-ferrocenes with one to three Fc units. The Fc units were directly coupled to the electrodes, i.e. without chemical anchoring groups between the Fc units and the terminal electrodes. We found that a single Fc unit readily interacts with the metal electrodes of an STM-break junction (STM = scanning tunneling microscope) and that the zero-voltage bias conductance of an individual Fc molecular junction increased 5-fold, up to 80% of the conductance quantum G o (77.4 µS), when the length of the molecular wire was increased from one to three connected Fc units. Our compendium of experimental evidences combined with non-equilibrium Green functions calculations contemplate a plausible scenario to explain the exceedingly high measured conductance based on the electrode/molecule contact via multiple Fc units. The oligo-Fc backbone is initially connected through all Fc units and, as one of the junction electrodes is pulled away, each Fc unit is sequentially disconnected from one of the junction terminals resulting in several distinct conductance features proportional to the number of Fc units in the backbone. The conductance values are independent of the applied temperature (-10 to 85  C), which indicates that the mechanism of charge transport is coherent tunneling for all measured configurations. These measurements show the direct Fc-electrode coupling provides highly efficient molecular conduits with very low barrier for electron tunneling, and whose conductivity can be modulated near the ballistic regime through the number of Fc units able to bridge and the energy position of the frontier molecular orbital.

Ferrocene (Fc) was the first example of a metallocene and it has been attractive in molecular electronics because of its good thermal and chemical stability and low-lying highest occupied molecular orbital (HOMO). [32][33][34] Fc binds weakly to the surface of common metals substrates such as Ag, Cu, Al, Mo or Au. 33,[35][36][37][38][39][40] The Fc deposited on flat metal surfaces such as Ag (100), Cu (111) and Au (111) binds with the plane of the cyclopentadienyl moieties facing the surface. 33,36,41,42 These properties make Fc an attractive candidate in molecular electronics to provide simple electronic functions when properly linked to an electronic platform, including low resistivity and sharp gate-dependence, [43][44][45][46] or more complex operations such as negative differential resistance, 43,47 rectification 6,7,34,48 or Boolean logics. 7 A key parameter to achieve such large electrical tunability is the control over the Fc-electrode electronic coupling. Some applications require a weak Fc-electrode coupling to minimize the hybridization of the low-lying molecular orbital (here a HOMO), directly involved in the molecular charge transport, to the electrodes terminal 6,48 . Contrarily, a "high coupling" scenario could be designed by manipulating the delocalization of the low-lying HOMO level between several Fc units within the same molecular wire, 49,50 which, in turn, hybridizes to the device electrodes. 6,34 The latter is a much less studied case that could be exploited to build efficient molecular wires displaying high conductance G values close to G0. 44,51 Despite this tremendous progress in recent years, it is also well-known that molecules with the same chemical structure can yield molecular junctions with orders of magnitude differences in conductance depending on the fabrication technique that is used to construct the junctions. [52][53][54] Although the effective contact area among the different methods is largely responsible for this observation, the molecule-electrode interaction plays a crucial role. In large-area junctions, the electrodes are planar and therefore less reactive than the electrode generated in break junctions. In general, the former yields well-defined junctions that are usually resistive, while the latter yields highly conductive junctions with a wide range of possible geometries due to the dynamic way of collecting the molecular conductance. 55 Usually it is assumed that the electrodes only form a single contact with the molecules, however, the junction formation process might involve the formation and rupture of multiple contact points depending upon the chemical nature of the studied molecular backbone.
Here, we present a study of single-molecule transport in STM break junctions of a new class of molecular wires composed of oligo-ferrocenes with one, two, and three directly connected ferrocene units, namely ferrocene (Fc), biferrocene (BFc) and 1-1'-terferrocene (TFc) (Fig. 1). The Fc units strongly interact with the terminal electrodes because of the high reactivity of uncoordinated gold atoms of the STM junction, 56 without the need for additional anchoring groups such as thiolates or amines. 28,31 We show that each individual Fc moiety within the molecular wire can readily form highly conducting junctions near the conductance quantum facilitating multiple Fc-electrode contacts with well-defined conductance signatures. During the rupture process, the contact points are broken one-by-one allowing us to control the number of contacts per molecule via the number of Fc units and STM tip displacement. This new conformation in a single-molecule junction can be used to interpret unexpectedly high G features observed in previous measurements incorporating Fc units. 44,46 All our findings are supported by extensive computational calculations and our observations give rise to new insights in the dynamics of the STM-break junction formation process. This work demonstrates Fc-oligomers are an interesting class of efficient nanoscale molecular wires displaying near ballistic transport and presents Fc as a new tunable molecule/electrode anchoring group with multiple contact points (through each individual Fc unit).

Conductance signatures of the single-molecule junctions
We measured the single-molecule conductance within a high conductance range near Go (10 -2 G0 to 1G0) for the Fc, BFc, TFc and BFc-butadyine molecules (see details of the synthesis in the Supporting Information (SI) section 1) using the STM break-junction (STM-BJ) technique.
Technical details of the STM-BJ approach have been published elsewhere 3,23 (for more details see SI section 2). Briefly, a STM Au tip is firstly brought over a flat, clean Au(111) surface to a tunneling distance in a solution containing the molecule of interest. Then, the STM current feedback is turned off and the STM tip is repeatedly driven in and out of contact to and from the Au(111) surface. During the retraction stage, individual molecules that are either dissolved in the surrounding organic medium or adsorbed on the surface can be spontaneous trapped between the two electrodes. This pulling process is repeated thousands of times while the current is monitored, resulting in the collection of large amounts of current decay curves (4000-5000, see representative examples in Fig. 2 insets). Of these curves, 15-20% display plateau features corresponding to the quantum conductance of the single-molecule bridge. [57][58][59] Since not every current decay curve shows such plateau features, we designed an automatic algorithm that identifies and selects curves containing such single-molecule features. The exact same selection criteria were applied throughout all measured series (see more details in SI section 2). Conductance histograms were built by the accumulation of hundreds of selected individual current decays (displaying plateaus) and the resulting peak maxima represent the most probable conductance values of the studied single-molecule bridge. 1,2,4-Trichlorobenzene was employed as the solvent in all transport experiments (see SI sections 3 for more details and control experiments with different solvents). 60 It is worth noting from Figure 2 that each Fc unit establishes a well-defined contact geometry characterized by a single, symmetrical conductance signature (peak) as opposed to previously widely used anchoring chemistry that often result in multiple peaks, or shoulders and/or tails. [61][62][63][64] (Fig. 2a), whereas junctions with BFc and TFc (Fig. 2b-c insets) shows that as the molecular junction is stretched (the Au STM tip electrode is pulled away from the Au surface), multiple plateaus concatenate with a good correlation in number to the number of existing Fc units in the backbone (Fig. 2a-c insets). 65,66 To analyze this correlation in detail, we plotted the data in a 2D cross-correlation conductance map (see SI section 2 for additional details) 67,68 . Figure 3a shows the corresponding one for the molecular junction formed with the TFc, which is represented by a 2D histogram of the analyzed counts at a particular conductance value of the individual decay curve (Y-axis) against the full measured conductance range (X-axis). The appearance of the three red spots along both X and Y directions at the conductance values coincidental with the three conductance maxima (Fig. 2c) evidences the statistical correlation between the occurrence of the three plateaus. Given the observed high G values of such single-molecule junctions (reaching 0.8Go in the TFc case) and their sequential correlation, we hypothesize that the molecular junction forms effective parallel electron pathways by bridging multiple Fc units at the same time (Fig. 3b). The different bridging configurations for BFc and TFc will be denoted by BFcn and TFcn, where n defines the number of Fc units effectively connected between the two electrodes (Fig. 3b). It is important to stress that n denotes the number of "plugged" Fc units only and that the order in which the Fc units disconnect during the pulling sequence might occur in a totally random fashion and so Fig. 3b represents one possible scenario only. Figure 3a shows that the formation of the three molecular junction configurations, namely TFc3, TFc2 and TFc1, occurs statistically in a sequential fashion as the tip retracts while sequentially unplugging each of the three Fc units (Fig. 3b). 66,69,70 In support of this picture, the plateau length analysis of the break junction traces in Fig. 2 (see SI section 4) do not correlate with any relevant molecular length, thus reinforcing the sequential unplugging of the Fc units in the backbone, ruling out junction dynamics involving fully molecular lifting. With this picture in mind, Figure 3c summarizes the different conductance trends and the hypothesized molecular junction configurations that will be challenged in the last section by computational calculations. Fig. 3 (a) Logarithmic 2D cross-correlation conductance map of the individual traces for the TFc system. The horizontal lines are the selected conductance Bins that registered higher counting within the range of the three measured conductance plateaus for the TFc3, TFc2 and TFc1 contact configurations (see Fig. 2 for notation). The three high-counts spots appearing in all three horizontal sections evidences the high sequential correlation of the three conductance events. The diagonal line reproduces the 1D conductance histograms of Fig. 2c. The high-counts spots labelled with an asterisk and a cross signs correspond to the background and saturation lines respectively, which are equally well correlated at the opposite corners of the map. (b) Cartoon representing the pulling sequence of a TFc molecular junction. As the STM tip is retracted, the initially bridged Fc units are sequentially disconnected from one of the electrodes terminals.

Temperature-dependent single-molecule conductance
To determine the mechanism of charge transport through the Fc-based single-molecule wires, we measured their single-molecule conductance as a function of temperature T. Single-molecule transport experiments for Fc, BFc1 and TFc1 configurations with lower electrode-Fc connections were performed for varying Ts from -10 o C to 85 o C (see also SI section 5). The Arrhenius plots (Fig. 4) of the averaged conductance values (G mean) show no significant dependence on T in all cases, indicating that the mechanism of charge transport is off-resonant tunneling for all wire contact configurations. 9,10

Tuning the energy of the oligoFc frontier orbital
We can fine-tune the high conductance values of the oligo-ferrocene wires by engineering the extension of the electronic coupling between the nearest Fc neighbors units, which, in turn, modulates the energy of the frontier orbital (see the next computational section) and so the molecular device conductance. As a probe of this concept, we synthesized a diferrocenyl compound, 1,4-diferrocenyl-1,3-butadiyne (BFc-butadiyne in Fig. 1, see SI section 1 for synthetic details), where two Fc units are electrically communicated through a conjugated butadiyne spacer. Figure 5b shows the single-molecule conductance values within the high conductance region near G0 (10 -2 G0 to 1G0), which are dominated by two conductance maxima associated with the two possible bridging configurations (BFc-butadiyne)1 and (BFc-butadiyne)2 , following the same previous notation in Figure 2. Both (BFc-butadiyne)n configurations register lower conductance values, 0.08G0 and 0.23 G0, than the BFc counterpart, where the Fc units are directly connected by a single C-C bond. The BFc-butadiyne junction gives us the opportunity to challenge the proposed junction geometry shown in Fig. 3b as follow: we have explored the lower G range (10 -3 G0-10 -2 G0) to seek for possible extended junction configurations (Fig. 5a inset) where the oligoFc wire is connected with the classical wiring picture through the distal Fc units 3 . To this aim, the low conductance region was analyzed for the BFc-butadiyne compound (Fig. 5a) whose side-to-side molecular conductance can be directly compared to the conductance values of the same butadiyne backbone previously measured using different anchoring chemistry. 71,72 The obtained value in 5a, 0.0034G0, is within the range of previously measured high conductance values of the same compound using pyridine as the anchoring units 71 . This result provides qualitative evidences that the conjugated spacer between the Fc units in the BFc-butadiyne dominates the charge transport in the low current range, thus reinforcing the proposed multicontact configuration pictured within the higher G range. This result is also captured by the transmission calculations in next section.   Table I) correlates well with the high conductance features (all connected Fc units) in the histograms for the Fc, BFc2, BFc-butadiyne2 and TFc3, and suggests the HOMO frontier orbital as the transportrelevant orbital due to its close proximity in energy to the Au Fermi energy (around -5 eV), also in agreement with previous works. 48,[73][74][75][76] The correlation shows that by increasing the number of Fc units in the molecule, the EHOMO level and its degree of degenaracy increase approaching the metal Fermi energy, thus decreasing the tunneling barrier height, δE = EHOMO -EF, which is in agreement with the increase in tunneling rate with increasing the oligoFc length (Fig. 3c, purple line). The DFT-computed frontier orbitals show an extended side-to-side delocalization of the HOMO in all cases (Table I). The saturating conductance behaviour going from the Fc to the all Fc-connected TFc is captured by the HOMO-Fermi level alignment (Fig. 6). We have also performed non-equilibrium Green function (NEGF) calculations combined with DFT approaches to calculate the conductance and the transmission functions (see Computational details in SI Section 6) for the three Fc, BFc, and TFc single-molecule junctions.

DFT-orbitals and transmission functions
We have employed a model structure for the junction with two gold hillocks flanking each Fc unit to simulate the STM scenario, where all Fc units are initially connected to both junction electrodes (Fig. 7a). To simulate the sequential Fc disconnection as we pull, two Au hillocks are removed, one at a time, from one side of each of the two Fc units, and the transmission function is recalculated for each case (Fig. 7b-c). This picture is not intended to capture the pulling dynamics taking place in the experiment, but it recreates the different expected molecular connections as the junction electrodes are being separated. Figures 7d-f show the corresponding transmission curves for the three cases. The calculated conductance is extracted from the integration of the transmission curve (Landauer equation) within the experimental bias energy window (at E=0 in Fig. 7d-f) assuming linear regime. Since GGA functionals with poor HOMO-LUMO gap determination are usually employed to obtain the transmission curves in periodic systems, the obtained functions in Figures 7d-f are merely used to extract the transmission values near the Fermi level EF, with independence of whose tail, either HOMO or LUMO of the transmission function, has the largest contribution. For comparison, we have also considered a "flat electrodes" configuration where the oligoFc compound is trapped between two atomically flat surfaces (see Fig. S6.1 and S6.2). We recognize that such scenario would be much less realistic in a break-junction experiment, where a metallic quantum point contact breaks in every cycle (see the prominent 1 G0 feature in Fig. 2). The obtained much lower values for the calculated transmission in this case also reinforce that and lead us to propose the "multiple-tips" scenario represented in Fig. 7a-c as the most plausible one.   The last slight trend to be analysed from the overview Fig. 3c (grey line), can be qualitatively evaluated by plotting the transmission pathways for the two extreme cases: Fc and TFc1 (Fig. 9). The direct comparison of the transmission pathways shows a better efficiency for the Fc system, as experimentally found, than for the TFc1 case. In the latter, the lack of an effective connection through the two unbridged Fc units increases the backscattering effect in the incoming electron waves as compared to the former Fc case.

Conclusions
In conclusion, we have measured the single-molecule conductance of a series of Fc-oligomers (Fc, BFc and TFc), which efficiently couple to two metal leads in the absence of linker groups via connecting multiple Fc units in a simultaneous fashion. The result is a highly conductive molecular wire under coherent tunneling regime, whose conductance results in exceedingly high values of up to 0.8 Go, near the ballistic conductance quantum, Go. Our computed DFT orbitals show that the delocalized HOMO frontier orbital increases in energy and degeneracy in the order BFc-butadiyne<Fc<BFc<TFc, approaching the Au electrode Fermi energy and explaining the same increasing conductance trend for the configurations where all Fc units are connected. Moreover, the calculated transmission functions recreate the saturating conductance increase for each individual compound when a larger number of Fc units within the same backbone are being effectively bridged in the molecular junction.
Interestingly, this work shows that the Fc units can interact strongly with the electrodes of the STM break junction most likely via the distal uncoordinated atoms at the tips of the electrodes, as opposed to other Fc-based backbones where the Fc unit is isolated by axial linkers 44,46 or SAMbased junctions with the Fc units in van der Waals contact with the electrodes 6 . The consequence is that in the former, the molecular frontier orbitals delocalize resulting in a molecular junction displaying near ballistic transport with G=0.8G0, i.e. the junctions are in the strong coupling regime, while in the latter the molecular frontier orbital are confined in the molecule resulting in a more resistive molecular junction. These observations suggest that the properties of these classes of junctions are very different due to differences in chemical reactivity between atomic tip-shaped and flat-like electrodes. Our work also exemplifies how the junction rupture dynamics can be exploited to control the number of molecule-electrode anchoring points sequentially by simply controlling the substrate-to-tip distance.
Overall, the results show a single-molecule wire displaying near-ballistic charge transport whose conductance can be modulated through the molecularly engineered extension of the Fc lowlying molecular orbital and the number of electrode/Fc contact points. This work also suggests the use of Fc as a new tunable molecule/electrode anchoring group with a simple contact configuration (single conductance signature) and a low energy tunneling barrier for charge injection.

Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: Synthetic details, technical details of the single-molecule transport, single-molecule conductance measurements in different solvents, 2D conductance and plateau length histograms, temperature-dependent single-molecule measurement, computational methods and additional calculations, and sample preparation.