Doctoral Dissertations

Date of Award

5-1999

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Physics

Major Professor

Gerald D. Mahan

Committee Members

Tom Callcott, Ted Barnes, John Quinn, Bob Compton

Abstract

New effects due to the electron-phonon interaction in some low-dimensional tight-binding systems are discussed. A sheet of graphite which is two dimensional and an armchair single wall carbon nanotube (SWNT) which is quasi-one dimensional are taken as examples. The geometrical structure and the linear dispersion of the energy with respect to the electron wave vector are expected to play a significant role. For the ordinary electron-phonon coupling which includes modulated hopping and linear electron-phonon interaction the matrix elements for both systems are derived in the context of a two parameter model for the phonon vibrational spectrum. It is found that they (for both structures) strongly depend on the geometry, display a deformation type of potential and are reduced by a factor of (1 — R), where R depends uniquely on the introduced phonon parameters.Next a new type of interaction is derived; it arises from the phonon modulation of the electron-electron interaction. After writing the matrix elements for the new Hamiltonian, the problem is considered in the context of many body physics.There are two contributions. One of them is the random phase approximation with one phonon line. The electron self-energy for it is calculated. It is shown that, in general, one might expect that this is not a large effect. Analytical expressions are obtained for the armchair single wall carbon nanotube. The exchange interaction in the one-phonon approximation is another term that arises and is also considered. One is able to write four new Feynman diagrams and derive an expression for —ImΣ(k⃗). It is found that the contribution from this type of coupling could be large and comparable to the one from the modulated hopping. These results are supported by numerical estimates of some characteristics of graphene and SWNT.The values of the electron-phonon coupling constant. λ, and the electron lifetime,τ, could be compared between the traditional electron-phonon interaction and thephonon modulated electron-electron interaction. Finally, it is realized that for a perfect (defect-free) armchair SWNT the diffusion thermopower and the phonon drag thermopower should be zero because of the complete symmetry of the energy bands of the system.

Download
Files over 3MB may be slow to open. For best results, right-click and select "save as..."

Share

COinS