Electron transport in interacting quantum wires

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Hoffmann, James A.
Cosby, Ronald M.
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Thesis (M.S.)
Department of Physics and Astronomy
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Nanoscale wires and molecules have remarkable electrical properties that make them well suited for new electronic devices. The projected device densities result in very small separation distances and therefore the possibility of device-device interactions. However, we do not know what impacts wire-wire interactions might have on the properties of closely spaced devices. If two quantum wires interact, what types of effects will there be on transport properties such as conductance? How would the coupling strength, length of wire, position of contact, or the energy of the electrons affect conductance? Understanding the effects of the interactions will assist the construction of efficient nanoscale devices.This thesis examined the effects of interaction on the low-field conductance using a simple classical model and two quantum models of coupled quantum wires fabricated electrostatically in the two-dimensional electron gas at the interface of the heterostructure A1GaAs/GaAs. We considered the effect of position and length of an interaction between two parallel quantum wires formed by hard wall boundaries and connected to electron reservoirs. Our second model consisted of two artificial molecular wires, i.e., parallel chains of quantum dots. We used a one-electron Schrodinger equation in the envelope approximation, a tight-binding Hamiltonian, and a recursive Green's function method to study the electron transport properties. Multi-parameter computations using a fortran-95 computer model provided data for an analysis of the relationships among conductance, the interaction strength, interaction location, and electron energy.In contrast to the monotonic changes predicted by the classical model, the lowfield conductance of interacting hard wall quantum wires varies in an oscillatory manner with the perturbing interaction strength and position. For electron energies below the first conductance plateau, Breit-Wigner resonances appear as a consequence of coupling. These conductance properties are explained with reference to quasi-bound states created by reflections at the end boundaries of the wires and the separating wall.At low electron energies, the conductance signature of a symmetric artificial molecule composed of serial quantum dots is a band of resonances. Coupled artificial molecular wires display a split-off molecular band with an energy separation that grows with the coupling strength and a bandwidth that narrows. The position of the Fermi energy relative to the molecular band states plays a dominant role in determining the lowfield conductance of interacting artificial molecules. The conductance variation with coupling ranges from oscillatory to monotonic, depending on the Fermi energy. Varying the atom-atom coupling position in the molecular wires causes a relatively small shift in the resonance band energies.