Two-dimensional (2D) layered transition metal dichalcogenides (TMDs) have recently attracted tremendous interest as potential valleytronic and nanoelectronic materials, in addition to being well-known as excellent lubricants in the bulk. The interlayer van der Waals (vdW) coupling and low-frequency phonon modes and how they evolve with the number of layers are important for both the mechanical and the electrical properties of 2D TMDs. Here we uncover the ultralow frequency interlayer breathing and shear modes in few-layer MoS2 and WSe2, prototypical layered TMDs, using both Raman spectroscopy and first principles calculations. Remarkably, the frequencies of these modes can be perfectly described using a simple linear chain model with only nearest-neighbor interactions. We show that the derived in-plane (shear) and out-of-plane (breathing) force constants from experiment remain the same from two-layer 2D crystals to the bulk materials, suggesting that the nanoscale interlayer frictional characteristics of these excellent lubricants should be independent of the number of layers.

In this work, we focus on 4,4'-bipyridine-gold junctions, where we find two reproducible and distinct conductance states that can be controllably switched by mechanical manipulation of the electrode separation. The conductance is measured by repeatedly forming and breaking Au point contacts with a modified STM in a solution of the molecules at room temperature 13,14 . The current is recorded at a fixed bias while the junction is elongated to generate conductance traces (see Methods Typical conductance traces, shown in Fig. 1B, exhibit a High G step that precedes a Low G step. To statistically analyze this step sequence in our entire data set, we compute a two dimensional (2D) conductance-displacement histogram of all measured traces (see Methods). The 2D histogram generated from the same 10000 traces (Fig. 1c) shows two clear regions with a large number of counts. The counts within the Low G range occur ~2Å after the break of the gold point contact (x=0). This is in contrast to the counts in the High G range, which start right after the break of the gold point-contact. This indicates that the High G steps start as soon as the gold contact breaks, and Low G steps follow High G steps (see SI for more details).Since the Low G steps occur only upon elongation of the junction, a natural question is whether junction compression would restore the High G state. To investigate this possibility, we measure the conductance between the tip and substrate while applying two types of ramps (dashed trace in Fig. 2a The properties of the pyridine-gold link naturally explain the observed switching behavior. The bonding mechanism, elucidated by our density functional theory (DFT)calculations detailed below, consists of donation from the N lone pair orbital into the partially empty s-orbital on a specific undercoordinated Au atom on the electrode. Since the N lone pair in bipyridine is parallel to the bipyridine backbone, we expect the N-Au bond to be along the bipyridine backbone. While such a structure is difficult to achieve initially given the geometric constraints, it may be easily accommodated after elongation by several Å. Previous conductance calculations [19][20][21] , in agreement with our own, haveshown that the essential orbital channel supporting transmission is the lowest unoccupied π * -orbital (LUMO; Fig. 3a). Since the π * -orbital is orthogonal to the N lone pair in this case, it is plausible to expect that an elongated junction, with the N-Au bond aligned to the backbone, will have low electronic coupling and hence low conductance. On the other hand, the constraints imposed by the compressed junctions will drive strong tilting of the N-Au bond, which can result in stronger coupling and higher conductance.Our DFT calculations (see Methods) indicate that bipyridine molecules bind selectively to undercoordinated atop Au sites. To investigate the sensitivity of conductance to N-Au bond orientation, we compute the transmission for a series of model junctions ( Fig. 3b) with identical geometric features except for the...

A combination of theory and experiment is used to quantitatively understand the conductance of single-molecule benzenediamine-gold junctions. A newly developed analysis is applied to a measured junction conductance distribution, based on 59 000 individual conductance traces, which has a clear peak at 0.0064 G0 and a width of +/-47%. This analysis establishes that the distribution width originates predominantly from variations in conductance across different junctions rather than variations in conductance during junction elongation. Conductance calculations based on density functional theory (DFT) for 15 distinct junction geometries show a similar spread. We show explicitly that differences in local structure have a limited influence on conductance because the amine-Au bonding motif is well-defined and flexible, explaining the narrow distributions seen in the experiments. The minimal impact of junction structure on conductance permits an unambiguous comparison of calculated and measured conductance values and a direct assessment of the widely used DFT theoretical framework. The average calculated conductance (0.046 G0) is found to be seven times larger than experiment. This discrepancy is explained quantitatively in terms of electron correlation effects to the molecular level alignments in the junction.