April 30, 2001
Thesis Committee: Harold Baranger, Gleb Finkelstein, Joshua Socolar
This research project was conducted under the supervision of Professor H.U. Baranger during my senior year. Our interest was in quantum effects of nano-size devices called quantum dots, with a focus on the probability distribution of conductance peak spacings. The dynamics of electrons within the quantum dot are believed to be chaotic, and can be well modeled by Random Matrix Theory (RMT). At very low temperatures, electron transport through the dot is strongly affected by interference of wavefunctions and electron-electron interactions; this is termed the quantum Coulomb Blockade regime. These quantum effects cause the ground state energy of the quantum dot and the conductance peak spacings, which are proportional to the second difference of the ground state energy, to vary as a function of the number of electrons. This is an example of what is termed ``mesoscopic fluctuations''.
Using the ``universal'' Hamiltonian as our starting approach, we obtained an analytic expression for the conductance peak spacing distribution, which was found to be in very good agreement with numerical results [provided by G. Usaj] when mesoscopic fluctuations are neglected. We also studied a semi-classical expansion of spin density functional theory, that serves to motivate the Hamiltonian that we used. Expanding the ground state energy as a perturbation about a ``generalized Thomas-Fermi'' model, we found a pseudo-Fock term with screening potential, that couples the spin-up to the spin-down electrons. A statistical analysis of experimental data was also carried out to determine the presence of the Even/ Odd effect in the peak spacing distributions. Statistically significant results were obtained, indicating the presence of an Even/ Odd effect in the experimental data. The statistical results also show a qualitative agreement between the numerical results and experimental data, when mesoscopic fluctuation effects are included in the simulation.
A PDF version of the entire thesis is available here: Thesis.pdf (about 560K).