Dissertation/Thesis Abstract

Quantum Dragon Solutions for Electron Transport through Single-Layer Planar Rectangular Crystals
by Inkoom, Godfred, Ph.D., Mississippi State University, 2017, 205; 10641651
Abstract (Summary)

When a nanostructure is coupled between two leads, the electron transmission probability as a function of energy, E, is used in the Landauer formula to obtain the electrical conductance of the nanodevice. The electron transmission probability as a function of energy, T( E), is calculated from the appropriate solution of the time independent Schrödinger equation. Recently, a large class of nanostructures called quantum dragons has been discovered. Quantum dragons are nanodevices with correlated disorder but still can have electron transmission probability unity for all energies when connected to appropriate (idealized) leads. Hence for a single channel setup, the electrical conductivity is quantized. Thus quantum dragons have the minimum electrical conductance allowed by quantum mechanics. These quantum dragons have potential applications in nanoelectronics.

It is shown that for dimerized leads coupled to a simple two-slice ( l = 2, m = 1) device, the matrix method gives the same expression for the electron transmission probability as renormalization group methods and as the well known Green's function method. If a nanodevice has m atoms per slice, with l slices to calculate the electron transmission probability as a function of energy via the matrix method requires the solution of the inverse of a (2 + ml) × (2 + ml) matrix. This matrix to invert is of large dimensions for large m and l. Taking the inverse of such a matrix could be done numerically, but getting an exact solution may not be possible. By using the mapping technique, this reduces this large matrix to invert into a simple (l + 2) × (l + 2) matrix to invert, which is easier to handle but has the same solution. By using the map-and-tune approach, quantum dragon solutions are shown to exist for single-layer planar rectangular crystals with different boundary conditions. Each chapter provides two different ways on how to find quantum dragons. This work has experimental relevance, since this could pave the way for planar rectangular nanodevices with zero electrical resistance to be found. In the presence of randomness of the single-band tight-binding parameters in the nanodevice, an interesting quantum mechanical phenomenon called Fano resonance of the electron transmission probability is shown to be observed.

Indexing (document details)
Advisor: Novotny, Mark A.
Commitee: Arnoldus, Hendrik F., Clay, R. Torsten, Kim, Seong-Gon, Miller, Vivien G.
School: Mississippi State University
Department: Physics and Astronomy
School Location: United States -- Mississippi
Source: DAI-B 79/03(E), Dissertation Abstracts International
Subjects: Physics
Keywords: Electron transmission, Fano resonances, Perron-Frobenius theorem, Quantum dragons, Single-band tight binding model, Single-layer rectangular crystals
Publication Number: 10641651
ISBN: 978-0-355-51391-2
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