Disorder, Interface, and Discovery of Topological Insulators
Topological materials are characterized by a topological invariant, a discrete quantity that is preserved through adiabatic transformations. Most topological materials studied in the literature are quantum spin Hall insulators (QSHIs) classified by a Z2 invariant and topologically protected by time-reversal symmetry. Other symmetries, or the lack of symmetries, may result in non-trivial topology. Examples are the topological crystalline insulators (TCIs), dual topological insulators (DTIs), high-order topological insulators (HOTI), and amorphous topological phases. The interest in these systems has increased in recent years due to novel physics and open questions regarding their properties and protection under realistic conditions. Also, how one could rationally predict topological materials. To tackle these questions, we use density functional theory to investigate topological systems' electronic and transport properties with broken crystalline symmetries. This includes edge vacancies of Na3Bi, amorphous flat bismuthene, and three-dimensional amorphous Bi2Se3. Also, we are employing machine learning methodologies to predict the topological classification of QSHIs, which can be later generalized to other systems.