Theory of molecular-scale transport in graphene nanojunctions

A molecular junction consists of a single molecule or self-assembled monolayer (SAM) placed between two electrodes. It has varieties of functionalities due to quantum interference in nanoscale. Although there exist issues, advantages could still appeal to scientists who wish to investigate transport properties in many aspects such as electronics, thermoelectronics, spintronics, and optotronics. Recent studies of single-molecule thermoelectricity have identified families of high-performance molecules. However, controlled scalability might be used to boost electrical and thermoelectric performance over the current single-junction paradigm. In order to translate this discovery into practical thin-film energyharvesting devices, there is a need for an understanding of the fundamental issues arising when such junctions are placed in parallel. As a first step in this direction, we investigate here the properties of two C60 molecules placed in parallel and sandwiched between top and bottom graphene electrodes. It is found that increasing the number of parallel junctions from one to two can cause the electrical conductance to increase by more than a factor of 2 and furthermore, the Seebeck coefficient is sensitive to the number of parallel molecules sandwiched between the electrodes, whereas classically it should be unchanged. This non-classical behaviour of the electrical conductance and Seebeck coefficient are due to interjunction quantum interference, mediated by the electrodes, which leads to an enhanced response in these vertical molecular devices. Except the study of thermoelectricity, on the other hand, stable, single-molecule switches with high on-off ratios are an essential component for future molecularscale circuitry. Unfortunately, devices using gold electrodes are neither complementary metal-oxide-semiconductor (CMOS) compatible nor stable at room temperature. To overcome these limitations, several groups are developing electroburnt graphene electrodes for single molecule electronics. Here, in anticipation of these developments, we examine how the electrical switching properties of a series of porphyrin molecules with pendant dipoles can be tuned by systematically increasing the number of spacer units between the porphyrin core and graphene electrodes. The porphyrin is sandwiched between a graphene source and drain and gated by a third electrode. The associated rotation of porphyrin referred to graphene plane leads to the breaking of conjugation and a decrease in electrical conductances. As the number of spacers is increased, the conductance ratio can increase from 100 with one spacer to 200 with four spacers, and further enhanced by decreasing the temperature, reaching approximately 2200 at 100K. This design for a molecular switch using graphene electrodes could be extended to other aromatic systems. As mentioned in the design of 퐶60 -based thermoelectric vertical junction with graphene layers as electrodes and porphyrin-based switch in graphene nanogap, graphene provides a two-dimensional platform for contacting individual molecules, which enables transport spectroscopy of molecular orbital, spin, and vibrational states. Next, we report single-electron tunnelling through a molecule that has been anchored to two graphene leads. It is found that quantum interference within the graphene leads gives rise to an energy-dependent transmission and fluctuations in the sequential tunnelling. The lead states are electrostatically tuned by a global back-gate due to the weak screening effect compared to the metal electrodes, resulting in a distinct pattern of varying intensity in the measured conductance maps. This pattern could potentially obscure transport features that are intrinsic to the molecule under investigation. Finally, using ensemble averaged magneto-conductance measurements, lead and molecule states are disentangled, enabling spectroscopic investigation of the single molecule. As the above describes, there are varieties of research on the charge transport properties of molecular devices. It is noticed that noise exists in all electronic devices, and the investigation on noise could help us understand more fundamental information of the device, i.e. the imperfections and configurational changes in the system, the correlation of the transmission conduction channels or even exploit the noise characteristics for biosensing. In electroburnt graphene nanogaps, our collaborators observe that 1/f noise and random telegraph noise at room temperature and 77K respectively. Here, I employ a simple one-dimensional tight binding model to gauge the effect of two-level fluctuations in the electrostatic environment in the tunnel junctions. Two types of models are investigated. Model I describes the case that the environmental traps drive the tunnel barrier locally and differently. Model II is the case that the collective effect of all the environmental traps drives the tunnel barrier synchronously. It is concluded that the 77 K data is best described by a single environmental fluctuator influencing the transmission through the tunnel barrier. This may either occur via a local perturbation of the barrier potential, or via an overall modulation of the barrier height. A 1/푓 signal emerges as more fluctuators with different lifetime 휏 are added to the environment, corresponding to the thermal activation of multiple random telegraph noises (RTNs) at room temperature