Condensed-Matter Physics & Materials Science Seminar

Topological insulators are a new breed of materials for which the topology of the bulk quantum states has
highly nontrivial physical consequences, such as the emergence of metallic states at the edges of a sample. Another
characteristic is the existence of robust metallic states in the bulk and on the edges, even in the presence of strong
disorder. In this talk I will present a theoretical framework that allows one to define and characterize bulk and edge
topological invariants for systems without translational symmetry (as is the case of disordered materials). I will explain
how the robustness of these invariants against disorder implies the existence of metallic states at large disorder. This
framework also leads to extremely efficient numerical techniques for the evaluation of the topological invariants,
which I used in the past to explore the behavior of the topological materials and to map their phase diagrams in the
presence of strong disorder. I plan to share with you the results of many numerical experiments and to discuss the
implications of all the above for the experimental characterization of these materials.