In this dissertation we study the electronic properties of certain two-dimensional chiral electron systems. We study the static and dynamic screening of gapped bilayer graphene and find important qualitative differences between the dielectric screening function obtained using a simplified 2-band model and that obtained using a more sophisticated 4-band model. We also formulate a continuum model to study the low-energy electronic properties of heterostructures formed by graphene on a strong three-dimensional topological insulator (TI) both for the case of commensurate and incommensurate stacking. We find that the proximity of the TI induces a strong enhancement of the spin-orbit coupling in graphene that can be tuned via the twist angle. Additionally, we examine the effect of a spin-active interface on the symmetry of proximity-induced superconducting pairing amplitudes in topological insulators. We compare our results to those for normal metals and ferromagnetic materials finding that the nontrivial spin chirality of the TI leads to qualitatively different behavior of the pairing amplitude. Lastly, we study the many-body instabilities of the Dirac states predicted to arise on the surfaces of topological Kondo insulators identifying regions of parameter space in which the system exhibits spin density wave, and charge density wave order.
| Identifer | oai:union.ndltd.org:wm.edu/oai:scholarworks.wm.edu:etd-3686 |
| Date | 01 January 2015 |
| Creators | Triola, Christopher Lawrence Charles |
| Publisher | W&M ScholarWorks |
| Source Sets | William and Mary |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Dissertations, Theses, and Masters Projects |
| Rights | © The Author |
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