Theses and Dissertations
Issuing Body
Mississippi State University
Advisor
Novotny, A. Mark
Committee Member
Rupak, Gautam
Committee Member
Clay, R. Torsten
Committee Member
Kim, Seong-Gon Kim
Committee Member
Koshka, Yaroslav
Date of Degree
5-1-2010
Document Type
Dissertation - Open Access
Major
Applied Physics
Degree Name
Doctor of Philosophy
College
James Worth Bagley College of Engineering
Department
Department of Physics and Astronomy
Department
Applied Physics Program
Abstract
A general expression for quantum transmission of non-interacting spinless electrons through models of a fully connected network of sites that can be regarded as a nanoparticle is obtained using matrix algebra. This matrix algebra method leads to the same results given by the Green’s function method without requiring the mathematical sophistication as required by the later. The model of the nanoparticle in this study comprises a single linear array of atoms that profile the input and output leads connected to a fully connected blob of atoms. A simple tight-binding Hamiltonian motivates the quantum transmission in the discrete lattice system. If there are n atoms in the nanoparticle, the methodology requires the inverse of a n × n matrix. The solution is obtained analytically for different cases: a single atom in the nanoparticle, a single dangle atom, n fully connected atoms in a meanield type cluster with symmetric input and output connections, and the most general case where the n fully connected atoms can be connected arbitrarily to the input and output leads. A numerical solution is also provided for the case where the intra-bonds among the atoms in the nanoparticle are varied (a case with notully connected atoms). The expression for the transmission coefficient thus obtained using the matrix method is compared with the transmission coefficients derived using the real space Renormalization Group method and the Green’s function method.
URI
https://hdl.handle.net/11668/15200
Recommended Citation
Solomon, Lazarus, "Quantum electron transport in models of nanoparticles using matrix algebra and renormalization group methods" (2010). Theses and Dissertations. 3704.
https://scholarsjunction.msstate.edu/td/3704
Comments
Nanosystems||transport||transmission coefficient