>Magister Scientiae - MSc / Perovskite solar cells have attracted a tremendous amount of research interest in the scientific community recently, owing to their remarkable performance reaching up to 22% power conversion efficiency (PCE) in merely 6 to 7 years of development. Numerous advantages such as reduced price of raw materials, ease of fabrication and so on, have contributed to their increased popularity.

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A general exact matrix renormalization group method is developed for solving quantum transmission through networks. Using this method transmission of spinless electrons is calculated for a Hanoi network and a (newly introduced) fully connected Bethe lattice. Plots of the transmission and wavefunctions are obtained through application of the derived Renormalization Group recursion relations. The plots reveal band gaps (which has possible application in nano devices) in HN3 networks while no band gaps are observed in HN5 networks. With the fully connected Bethe lattice a drastic reduction in the transmission (in comparison to the normal Bethe lattice) is observed. This reduction can be found to be a purely quantum mechanical effect.

This thesis explores electron transport across single-molecule circuits via a combination of theory and experiment. Chapter 1 begins by introducing the diverse motivations for studying single-molecule electronics within engineering, chemistry and physics. Key aspects of the theory of electron transport across single-molecule circuits are summarized, before describing the modified scanning tunneling microscope technique used to measure single-molecule circuits. Chapter 2 presents a new theoretical approach to calculating quantum interference, which allows interference effects to be easily visualized within a matrix. The approach demonstrates that interference is vital to molecular-scale transport and accounts for conductance decay with length across molecular wires. In Chapter 3, a novel chemical design strategy is used to exploit destructive quantum interference in a series of long molecular wires containing a central benzothiadiaole unit. Scanning tunneling microscope-break junction measurements show the wires exhibit extremely nonlinear current-voltage characteristics, and the conductance of a six-nanometer molecule can be modulated by a factor of 10,000. Chapter 4 details how the scanning tunneling microscope setup may be modified to incorporate electrochemical impedance spectroscopy. Impedance measurements are then used to interrogate the solvent environment and measure capacitance. Chapter 5 demonstrates solvent-induced shifts in molecular conductance can be correlated with changes in junction capacitance. Together, the chapters in this thesis provide a framework for using chemical design to develop single-molecule circuits with functional properties.

Reduced graphene oxide (RGO) sheet, a chemically functionalized atomically thin carbon sheet, provides a convenient pathway for producing large quantities of graphene via solution processing. The easy processibility of RGO sheet and its composites offer interesting electronic, chemical and mechanical properties that are currently being explored for advanced electronics and energy based materials. However, a clear understanding of electron transport properties of RGO sheet is lacking which is of great significance for determining its potential application. In this dissertation, I demonstrate fabrication of high-yield solution based graphene field effects transistor (FET) using AC dielectrophoresis (DEP) and investigate the detailed electronic transport properties of the fabricated devices. The majority of the devices show ambipolar FET properties at room temperature. However, the mobility values are found to be lower than pristine graphene due to a large amount of residual defects in RGO sheets. I calculate the density of these defects by analyzing the low temperature (295 to 77K) charge transport data using space charge limited conduction (SCLC) with exponential trap distribution. At very low temperature (down to 4.2 K), I observe Coulomb blockade (CB) and Efros-Shklovskii variable range hopping (ES VRH) conduction in RGO implying that RGO can be considered as a graphene quantum dots (GQD) array, where graphene domains act like QDs while oxidized domains behave like tunnel barriers between QDs. This was further confirmed by studying RGO sheets of varying carbon sp 2 fraction from 55 – 80 % and found that both the localization length and CB can be tuned. From the localization length and using confinement effect, we estimate tunable band gap of RGO sheets with varying carbon sp 2 fraction. I then studied one dimensional RGO nanoribbon iv (RGONR) and found ES VRH and CB models are also applicable to the RGONR. However, in contrast to linear behavior of decrease in threshold voltage (Vt) with increasing temperature (T) in the RGO, sub linear dependence of Vt on T was observed in RGONR due to reduced transport pathways. Finally, I demonstrate synthesis and transport studies of RGO/nanoparticles (CdS and CeO2) composite and show that the properties of RGO can be further tuned by attaching the nanoparticles.

The understanding and study of electron transport in semiconductor systems has been the instigation behind the growth of semiconductor electronics industry which has enabled technological developments that are part of our everyday lives. However, most materials exhibit diffusive electron transport where electrons scatter off disorder (impurities, phonons, defects, etc.) inevitably present in the system, and lose their momentum. Advances in material science have led to the discovery of materials which are essentially disorder-free and exhibit exceptionally high mobilities, enabling transport physics beyond diffusive transport. In this work, we explore non-diffusive transport regimes, namely, the ballistic and hydrodynamic regimes in a high-mobility two-dimensional electron system in a GaAs quantum well in a GaAs/AlGaAs heterostructure. The hydrodynamic regime exhibits collective fluid-like behavior of electrons which leads to the formation of current vortices, attributable to the dominance of electron-electron interactions in this regime. The ballistic regime occurs at low temperatures, where electron-electron interactions are weak, constraining the electrons to scatter predominantly against the device boundaries. To study these non-diffusive regimes, we fabricate mesoscopic devices with multiple point contacts on the heterostructure, and perform variable-temperature (4.1 K to 40 K) zero-field nonlocal resistance measurements at various locations in the device to map the movement of electrons. The experiments, along with interpretation using kinetic simulations, demarcate hydrodynamic and ballistic regimes and establish the dominant role of electron-electron interactions in the hydrodynamic regime. To further understand the role of electron-electron interactions, we perform nonlocal resistance measurements in the presence of magnetic field in transverse magnetic focusing geometries under variable temperature (0.39 K to 36 K). Using our experimental results and insights from the kinetic simulations, we quantify electron-electron scattering length, while also highlighting the importance of electron-electron interactions even in ballistic transport. At a more fundamental level, we reveal the presence of current vortices in both hydrodynamic and surprisingly, ballistic regimes both in the presence and absence of magnetic field. We demonstrate that even the ballistic regime can manifest negative nonlocal resistances which should not be considered as the hallmark signature of hydrodynamic regime. The work sheds a new light on both hydrodynamic and ballistic transport in high-mobility solid-state systems, highlighting the similarities between these non-diffusive regimes and at the same time providing a way of effectively demarcating them using innovative device design, measurement schemes and one-to-one modeling. The similarities stem from total electron system momentum conservation in both the hydrodynamic and ballistic regimes. The work also presents a sensitive and precise experimental technique for measuring electron-electron scattering length, which is a fundamental quantity in solid-state physics. / Doctor of Philosophy / Electrons are the charged particles that are bound around the nuclei of atoms. But sometimes in a solid material electrons break free away from the nuclei and wander around. They are then the carriers of electric current ubiquitous in our daily lives as in our homes, and in our electronic devices such as smartphones and computers. Often an analogy is made between the flow of electric current in a material and the flow of water in a stream. However, the analogy does not hold well for most materials. In most materials the motion of electrons can be thought of as balls in a pinball machine - their movement hindered and randomized by collisions with the countless defects and impurities present in the material they travel through. However, recently scientists have been able to synthesize ultraclean materials, where electrons can indeed mimic the flow of water under the right conditions. In this aptly-named hydrodynamic regime, electrons predominantly interact with each other and that leads to the formation of current whirlpools or vortices similar to those forming in water. A telling signature of this regime is a negative electrical resistance appearing near the location of the vortex. When the interactions between electrons are weak, such as at very low temperatures, electrons move along straight-line trajectories until they hit and bounce off the device edges, similar to billiard balls. This low-temperature phenomenon is called ballistic transport. In this work we reveal that measurement of negative resistance and formation of current vortices are not unique to the hydrodynamic regime but can occur in the ballistic regime as well. It is indeed counterintuitive that electrons moving like billiards balls can behave similarly to electrons flowing like water. The similarities can be traced back to a fundamental physics conservation law active in both situations, namely momentum conservation. To experimentally realize the tests, we use a very high purity semiconductor material GaAs/AlGaAs and fabricate tiny devices on the material with a cutting-edge design, capable of precisely measuring resistance at various locations along the device to map the movement of electrons. The simulations of the novel physics indeed reveal current vortices of various sizes in the ballistic regime, in agreement with the experimental data showing negative resistance. In another experiment, we apply a magnetic field, making the electrons move in circular paths. If uninterrupted, electrons complete half circles and are collected through an opening in the device, giving resistance peaks in experiments. Due to electron-electron interactions, the electrons on their circular trajectory are interrupted by other electrons which leads to a decay in resistance peaks. This decay is utilized to measure the strength of electron-electron interactions. The work has both fundamental and applied implications. The existence of whirlpools shows that the electron momentum is not lost by collisions, and that in turn means that the conduction of electrical current in these regimes is inherently efficient. This opens up avenues for electronic devices which are faster, more functional and more power efficient than present electronic devices.

In this dissertation, we study the most important microscopic aspects that grant molecules such as Single Molecule Magnets (SMMs) their preferential spin direction. We do so by proposing and solving a model that includes correlations between electrons occupying atomic orbitals. In addition, we study the relation between the non-equilibrium electronic transport signatures in a SMM model weakly coupled to a three-terminal single electron transistor device, and the interference features of the SMM model in the presence of a magnetic field. Finally, we investigate the equilibrium transport features in a giant-spin model of a SMM in the Kondo regime. We study how the magnetic field modulation of the energy in a highly anisotropic molecule can affect the conductance of the molecule in the Kondo regime.

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Methanosarcina are methanogens capable of growth and methanogenesis from H₂/CO₂, formate, methanol, methylamines, and acetate. Methanosarcina conserve energy by coupling electron transport and methyl transfer to the generation of ion gradients during acetoclastic growth. This work focuses on cytochrome b and heterodisulfide reductase, two proteins involved in energy conservation by electron transport. A procedure was developed for mass cultivation of Methanosarcina thermophila strain TM-1 in 12-liter fermentations which produced up to 10 grams wet weight/liter, in order to facilitate biochemical studies. Cytochromes occurring in Methanosarcina thermophila were characterized spectrophotometrically using chemical and physiological reactants. This analysis revealed two heme centers, one of which was only reduced by Na₂S₂O₄ or carbon monoxide. Partially purified cytochromes were found to be present in a complex and were characterized by electrophoretic and spectrophotometric analysis. The cytochrome-containing protein was found to contain two hemes and had an M_r of 28,000 Da. Heterodisulfide reductase was isolated from the soluble fraction by anion exchange chromatography and assayed using methyl viologen as an artificial electron donor. Electron transport from CO to the heterodisulfide of 2-mercaptoethanesulfonic acid (HS-CoM) and 7- mercaptoheptanoylthreonine phosphate (HS-HTP) was reconstituted using carbon monoxide dehydrogenase, ferredoxin, membranes, and heterodisulfide reductase. Both membranes and ferredoxin were required for reduction of the heterodisulfide. / Master of Science

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.