Date of Degree


Document Type


Degree Name





Godfrey Gumbs

Subject Categories

Condensed Matter Physics | Nanoscience and Nanotechnology


electron-photon interaction, graphene, Hofstadter butterfly, plasmonics, topological insulators, tunneling


Over the last five years of my research work, I, my research was mainly concerned with certain crucial tunneling, transport and optical properties of novel low-dimensional graphitic and carbon-based materials as well as topological insulators. Both single-electron and many-body problems were addressed. We investigated the Dirac electrons transmission through a potential barrier in the presence of circularly polarized light. An anomalous photon-assisted enhanced transmission is predicted and explained in a comparison with the well-known Klein paradox. It is demonstrated that the perfect transmission for nearly-head-on collision in an infinite graphene is suppressed in gapped dressed states of electrons, which is further accompanied by shift of peaks as a function of the incident angle away from the head-on collision. We calculate the energy bands for graphene monolayers when electrons move through a periodic electrostatic potential in the presence of a uniform perpendicular magnetic field. We clearly demonstrate the quantum fractal nature of the energy bands at reasonably low magnetic fields. We present results for the energy bands as functions of both wave number and magnetic flux through the unit cells of the resulting moir´e superlattice. This feature is also observed at extremely high magnetic fields. We have discovered a novel feature in the plasmon excitations for a pair of Coulomb-coupled non-concentric spherical two-dimensional electron gases (S2DEGs). Our results show that the plasmon excitations for such pairs depend on the orientation with respect to the external electromagnetic probe field. The origin of this anisotropy of the inter-sphere Coulomb interaction is due to the directional asymmetry of the electrostatic coupling of electrons in excited states which depend on both the angular momentum quantum number L and its projection M on the axis of quantization taken as the probe E-field direction. Such an effect from the plasmon spatial correlation is expected to be experimentally observable by employing circularly-polarized light or a helical light beam for incidence. The S2DEG serves as a simple model for fullerenes as well as metallic dimers, when the energy bands are far apart. Magnetoplasmons in gapped graphene have been investigated and the exchange energy dependence on magnetic field is presented.