On the Electronic and Magnetic Properties of Nanostructures

In this work we calculate the properties of several condensed matter systems using a combination of empirical model Hamiltonian approaches and methods from computational condensed matter physics such as density functional theory and numerical solutions of the mean-field Gross-Pitaevskii equations. This work has been organized into 7 chapters as follows. (1) In the first chapter we motivate the discussion for the rest of the thesis and discuss the theoretical ideas that underly the work. (2) In the second chapter we discuss the approaches and approximations such as density functional theory and many-body perturbation theory that have been used in this research to make the many-electron problem a tractable one. (3) In the third chapter we discuss the application of density functional theory calculations to the analysis of scanning tunneling microscope (STM) images of boron nitride nanotubes. It is found experimentally and confirmed theoretically that the electric field of the STM can be used to lower the gap of the nanotube in a controllable fashion and also the modify the shape of the electronic states on the nanotube. (4) In the fourth chapter we extend the idea of modifying electronic properties of boron nitride nanotubes with an STM and apply the principle to carbon nanotube bundles. In this study a combination of density functional theory and model Hamiltonian calculations is used to derive a theoretical prediction where the application of an electric field through an STM can drive a transition of a nanotube bundle from a semiconductor to an excitonic system where the ground state is populated with a density of excitons that is tunable by the electric field strength. (5) In the fifth chapter we discuss another class of nanosystems, and focus on molecules on metallic substrates. These systems have been the subject of a large number of studies because of their technological relevance to solar-cells and molecular electronic devices. In this chapter we develop a technique to determine the level alignment and gaps of a molecule in the neighborhood of a substrate. We then test our method by quantitatively comparing the results of this method applied to the C 60 molecule on Au and Ag substrates to experimental scanning tunneling spectroscopy results on these systems. (6) In chapter six we move our focus to bulk systems and use a combination of density functional theory and empirical pseudopotential methods to study the transport properties of Ge-Sn alloy systems. Using the empirical pseudopotential method we find a combination of strain and alloying that turns Ge-Sn into a direct gap semiconductor with low electron and hole masses. The low effective masses implies an increased carrier mobility for the alloy. Using density functional theory calculations we calculate the effect of alloy scattering from Sn in Ge and show that even after taking into account substitutional disorder from alloy scattering Ge-Sn alloys are expected to exhibit higher mobilities than Ge. (7) In the final chapter we apply the combination of a model Hamiltonian and a computational solution of mean field equations that we have been applying to solid state systems to understand and predict the properties of ultra-cold spinor Bose Eintein Condensates. In this study we study the effect of how dipole-dipole interactions between spin-1 Rubidium atoms can directly affect the dynamics of quantum noise induced domain formation and predict ways to directly observe the dipole-dipole interactions between 87Rb.