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Over the past few decades, significant advancements in nanotechnology have enabled scientists to investigate and understand single-molecule electronics. These advances have allowed the integration of single molecules as different electronic components within macroscale circuits. Specifically, techniques such as the scanning tunneling microscope-based break junction (STM-BJ) technique and the mechanically controllable break junction (MCBJ) technique have made it possible to create single-molecule junctions, where a single molecule bridges the gap between two bulk electrodes. By applying an external bias, electrons can be driven through these single-molecule junctions. The observed transport properties are dictated by both the molecules themselves and the interfacial coupling between the molecules and the electrodes. These experiments therefore provide a fundamental understanding of how chemical design affects electronic behavior of single-molecule junctions. Because of the small dimension of single molecules, electrons behave as waves when traveling through molecular junctions. Therefore, the conductance of a molecular junction is directly related to the electron transmission probability. The transmission through molecular junctions is typically coherent without scattering or loss of phase information of the electrons, indicating that the wave properties of the electrons are preserved throughout the transmission. In coherent and off-resonant transport, the conductance of an oligomeric molecular wire decays exponentially with increasing number of repeating units, which can be quantified by a decay factor. Although different repeating units exhibit different decay factors, the trend of experimental decay in conductance stays for most molecular series. Consequently, the conductance of a long oligomeric molecular wire is inevitably lower than that of its shorter analogs. Nevertheless, scientists have been making great efforts to mitigate the exponential conductance decay, as long and highly conducting molecular wires are more desired for constructing molecule-based electronic circuits because they can decrease power loss and maintain signal integrity over long distances. One popular approach to address this problem is using conjugated building blocks, which feature small decay factor values. However, a more effective solution is to design molecular series to exhibit a reversed conductance decay, in which conductance increases exponentially with the number of repeating units. This dissertation aims to demonstrate that a special class of molecules, known as one-dimensional topological insulators (1D TIs), can exhibit anomalous conductance-length relationships, such as reversed conductance decay, due to their non-trivial edge states. The body of this dissertation is divided into six chapters. Chapter 1 introduces the experimental and theoretical concepts required to understand the subsequent chapters. In Chapter 2, we investigate the Su-Schrieffer-Heeger (SSH) model of 1D TIs. Using a tight-binding approach, we demonstrate that polyacetylene and other diradicaloid 1D TIs exhibit a reversed conductance decay at the short chain limit. We then analyze the impact of edge states on electron transmission through these 1D wires. Additionally, we discuss the role of the electrode-molecule coupling and the on-site energy of the edge sites in modulating the reversed conductance decay. The next two chapters both present experimental studies of 1D TIs using the STM-BJ technique. In Chapter 3, we study an oligophenylene-bridged bis(triarylamines) series with tunable and stable mono- or di-radical character. The doubly oxidized wires are 1D TIs and exhibit reversed conductance decay with increasing length, consistent with the SSH model. These wires display quasi-metallic transport properties in molecular junctions. In Chapter 4, using the same molecular series, we demonstrate how electron transport through a single edge state can be modulated by the other edge state through a topological gating effect. We show that this quantum phenomenon within 1D TIs can be harnessed to achieve a long-range gating in molecular conductors. These works provide a deep understanding of the electronic transport properties of 1D TIs. However, throughout the studies of 1D TIs, we find that reversed conductance decay can only be observed at the short chain limit. Beyond this limit, conductance starts to decrease. To extend the length at which anomalous conductance-length relationships persist, Chapter 5 introduces a new design using short 1D TIs as building blocks to create long topological oligo[n]emeraldine wires. As the wire length increases, the number of topological states also increases, enhancing electronic transmission along the wire. As a result, the transport performance of the longest wire significantly surpasses that of previously reported long wires. In Chapter 6, we use theoretical tools to investigate wires with 1D TIs in series. Additionally, we explore cyclic systems to show that unit transmission and zero transmission can be switched upon transitioning between their topological and trivial forms, making them excellent molecular switches. Finally, we summarize the entire body of works on electron transport through single 1D TIs and 1D TIs in series. We conclude this dissertation by acknowledging that there is still a long journey from fundamental research to the practical implementation of molecule-based devices using 1D TIs. However, I hope my works will encourage and inspire other researchers to continue pursuing advances in this field. |
