| Summary: | A dissertation submitted to the department of physics of the University of the Witwatersrand towards fulfillment of the requirements for the degree of doctor of philosophy
February 2018 === In this work investigations into the quantum transport of two different low dimensional carbon systems are presented. Heavily boron-doped nanocrystalline diamond is known to be superconducting and has attracted much research attention as it forms a new class of superconductor; the doped semiconductor superconductor. The system follows a Mott transition with doping concentration and has thus lead to various proposed pairing mechanisms forming the Cooper pair, this includes phonon mediated as well as resonating valence band mechanisms for pairing. Although generally considered a three dimensional system to date very few reports exist on determining the dimensionality of the quantum conduction channels in the system.
I investigate the dimensional crossovers in transport using the well-known scaling analysis such as Azlomazov-Larkn and Lerner-Varlomov-Vinokur models to establish the characteristic dimensionality within the fluctuation regime and establish a two dimensional phase that occurs before Josephson coupling between grains becomes significant. The field induced superconductor to insulator transition is then investigated in light of the previously proposed charge-glass state that has been observed in other 2D superconducting systems. It is shown that there the predicted universal scaling analysis can in fact be applied to this system with critical exponents that follow the expected values Further supporting the claim of a 2D system. Subsequently one of the result of the two dimensionality, the Berezinskii-Kosterlitz-Thouless transition is observed through both current-voltage scaling as well as temperature dependent resistance. In addition to these aspects of low dimensional transport the possibility of Andreev bound states is exhibited in the differential resistance, these resonant features are related to the mid gap states observed in layered cuprate systems with anisotropic order parameter (d-wave).
Novel magnetoresistance features such as a change from negative to positive magnetoresistance (weak localization to anti-localization) is observed to occur in the fluctuation regime near the established BKT transition point, this is related to normal state electrons that undergo spontaneous time reversal symmetry breaking as the superconducting stage is reach. Such novel transport features are often related to signatures of topological non-trivial phases which can be of use for various quantum computation technologies. This work also investigates the effect of strain deformation on the transport in graphene. Raman annealing is proposed as a non-destructive tool for the formation of nano-scaled deformations, the effect
of the deformation on the phonon modes is discussed and related to possible psuedomagnetic field Landau quantization. A novel method utilizing nanomanipulators is employed for fabricating wrinkled multilayer graphene devices allowing for transport features to be compared to flat quasi-2D devices. The magnetoresistance shows a conversion from the 2DEG to a linear positive magnetoresistance with large deformation. These processes can be of interest for carbon based quantum technology. The suitability and possible fabrication methods for creating diamond based superconducting circuit elements are discussed. === MT 2018
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