I'm a graduate student, and my focus is understanding how disorder affects topological phenomena. In our research, we're looking at how Landau levels react to disorder that keeps certain symmetries intact, like chiral symmetry. Interestingly, the zeroth Landau level of a Dirac particle stays strong even when faced with chiral disorder. This resilience is connected to a math concept called an index theorem of elliptical differential operators. We're working to apply this idea to different real-world situations. Our first application involves studying two-dimensional transition metal dichalcogenides, comparing them to graphene. We're also exploring twisted bilayer graphene's Moire potential to understand the implications of the index theorem.
In another aspect of our research, we're looking at disorder-induced phase transitions in topological systems. In the quantum Hall system, we observe critical delocalized states that separate different quantum Hall plateaus due to both disorder and topology. The variety of topological materials nowadays adds an interesting layer to studying these transitions. Depending on a material's symmetry class and its specific topological features, we see different critical behaviors, such as multifractal critical states or even a whole critical phase.