UC Berkeley

The dynamics of electrons governed by the Coulomb interaction determines a large portion of the observed phenomena of condensed matter. Thus, the understanding of electronic structure has played a key role in predicting the electronic and optical properties of materials. In this dissertation, I present some important applications of electronic structure theories for the theoretical calculation of these properties. In the first chapter, I review the basics necessary for two complementary electronic structure theories: model Hamiltonian approaches and first principles calculation. In the subsequent chapters, I further discuss the applications of these approaches to nanostructures (chapter II), interfaces (chapter III), and defects (chapter IV).

The abstract of each section is as follows.

Section II-1

The sensitive structural dependence of the optical properties of single-walled carbon nanotubes, which are dominated by excitons and tunable by changing diameter and chirality, makes them excellent candidates for optical devices. Because of strong many-electron interaction effects, the detailed dependence of the optical oscillator strength of excitons on nanotube diameter, chiral angle, and electronic subband index (the so-called family behavior) however has been unclear. In this study, based on results from an extended Hubbard Hamiltonian with parameters derived from ab initio GW-BSE calculations, we have obtained an explicit formula for the family behavior of the oscillator strengths of excitons in semiconducting single-walled carbon nanotubes (SWCNTs), incorporating environmental screening. The formula explains well recent measurements, and is expected to be useful in the understanding and design of possible SWCNT optical and optoelectronic devices.

Section II-2

Wave supercollimation, in which a wavepacket is guided to move undistorted along a selected direction, is a highly desirable property that is difficult to achieve for photons and has yet to be experimentally seen for electrons. Disorder in a medium would inhibit supercollimation. Here, we report a counter-intuitive phenomenon of electron supercollimation by disorder in graphene, made possible by its Dirac fermion states. We show that one can use one-dimensional disorder potentials to control electron wavepacket transport along the potential fluctuation direction. This is distinct from all known systems where the wavepacket would be further spread by the disorder and hindered in the potential fluctuating direction. This phenomenon has significant implications in the understanding and applications of transport in graphene and other Dirac fermion materials.

Section III-1

The origin of magnetic flux noise in superconducting quantum interference devices with a power spectrum scaling as 1 / f ( f is frequency) has been a puzzle for over 20 years. This noise limits the decoherence time of superconducting qubits. A consensus has emerged that the noise arises from fluctuating spins of localized electrons with an areal density of 5×10¹⁷ m^-2. We show that the physical origin of the phenomenon are localized metal-induced gap states at the interface. In the presence of potential disorder at the metal-insulator interface, some of the metal-induced gap states become localized and produce local moments. A modest level of disorder yields the observed areal density.

Section III-2

We present a microscopic theory of disorder-induced magnetic moment generation at nonmagnetic metal-insulator interfaces. Screened Hartree-Fock solution of a tight-binding Hamiltonian with electron-electron interaction, in which disorder is mimicked by the Anderson disorder model, shows that magnetic moments are originated from localized metal-induced gap states at the interface. Magnetic moment areal density becomes saturated at a maximum value of 4×10¹⁷ m^-2 as the disorder magnitude increases, consistent with the observed universality of measured local magnetic moment areal density. Dielectric screening effect is found to be essential for understanding the relatively universal behavior of the observed value.

Section IV-1

Optical initialization of the negatively charged nitrogen-vacancy (NV^-) center in diamond makes it one of the best candidates for realization of addressable spins in the solid state for quantum computing and other studies. However, its exact mechanism was not clear. We show that exact diagonalization of a many-electron Hamiltonian with parameters derived from ab initio GW calculations puts strong constraints on the mechanism. The energy surfaces of the low-energy many-body states and the relaxation processes of photo-excitation responsible for the optical initialization are calculated. Intersystem crossings are shown to be essential

Section IV-2

Graphene has been predicted to be a good test material for atomic collapse theory due to its linear band structure with a Fermi velocity 300 times slower than the speed of light. The Crommie group at UC Berkeley measured, using scanning tunneling microscopy, electrons bound to the positively charged calcium dimers on graphene, which corresponds to electrons collapsed to the super-heavy nucleus in artificial atoms. To compare measured bound states to atomic collapse theory in an artificial atom on graphene, the net charges associated with calcium dimers should be quantified. Here, we quantified the net charges associated with a calcium dimer using density function theory.