Effective Model for Bilayer Transition Metal Dichalcogenides and Quasiperiodic Anomalous Anderson Floquet Insulators



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This dissertation documents my investigation into two kinds of condensed matter materials and how they are impacted under external fields. Transition metal dichalcogenides and similar structures under optical fields and Anomalous Floquet Anderson Insulators under a chaotic Floquet drive. These two projects were conducted under two separate professors that I worked under-My supervisor, Professor Fan Zhang and Professor Michael Kolodrubetz. For the first project, I firstly conclude my studies on effective models of transition metal dichalcogenides from my proposal defense before discussing the universal optical conductivity in Graphene. I then attempt to combine these two to demonstrate that the Landau levels in transition metal dichalcogenides can be identified with an external laser source. Once the preliminaries are done, I introduce a complete version of the Kubo formula with temperature dependence and attempt to apply that to the β-Bi4X4 family materials. For the second project, I probed into a well studied cylindrical square lattice where an external Floquet drive sets it in an anomalous Anderson topological phase accompanied by chiral edge states. We attempt to push this system further by introducing temporal disorders and observe for a stable topological phase. Alongside that, we look into several methodologies that can confirm topological presence. All introductions, conclusions, and discussions in this dissertation do not reflect the viewpoints of any member of my supervisory committee.



Topological spaces, Molybdenum disulfide, Landau levels, Anderson model