Ting, Chin-Sen2018-07-242018-07-24May 20182018-05May 2018Portions of this document appear in: Roy, Bitan, Sayed Ali Akbar Ghorashi, Matthew S. Foster, and Andriy H. Nevidomskyy. "Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal." arXiv preprint arXiv:1708.07825 (2017); and in: Ghorashi, Sayed Ali Akbar, Seth Davis, and Matthew S. Foster. "Disorder-enhanced topological protection and universal quantum criticality in a spin-3 2 topological superconductor." Physical Review B 95, no. 14 (2017): 144503; and in: Ghorashi, Sayed Ali Akbar, Yunxiang Liao, and Matthew S. Foster. "Critical Percolation without Fine-Tuning on the Surface of a Topological Superconductor." Physical Review Letters 121, no. 1 (2018): 016802; and in: Ghorashi, Sayed Ali Akbar, Pavan Hosur, and Chin-Sen Ting. "Irradiated three-dimensional Luttinger semimetal: A factory for engineering Weyl semimetals." Physical Review B 97, no. 20 (2018): 205402.http://hdl.handle.net/10657/3302In this dissertation, we have studied the effect of disorder and interaction on some classes of topological superconductors and semimetals. In the superconducting phase, we studied various phases and critical phenomena that arise by the effect of disorder on the surface states of topological superconductors with different and higher winding numbers. In particular, we investigated topological protection of topological superconductors with effective spin-3/2 systems. Moreover, we have shown that the almost all the nite-energy states at the surface of topological superconductors in the presence of disorder are also protected (delocalized) and sit at the spin quantum plateau transition point without ne tuning. Finally, through the Floquet formalism we showed that the irradiated Luttinger semimetal is a suitable platform for engineering various Weyl semimetals, from Type-I to type-II as well as single and double Weyl semimetals.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. UH Libraries has secured permission to reproduce any and all previously published materials contained in the work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Topological superconductorsDisorderCritical phenomenaTopological semimetalsWeyl semimetals2018-07-24Thesisborn digital