A local view on topology

Raquel Queiroz

Assistant Professor of Physics Department of Physics

Columbia University, New York, NY

Abstract:

In this talk, I revisit the notion of topology in solid-state materials from a local perspective. This view highlights qualitative differences in the physical response to local perturbations between topological and trivial systems, from topological semimetals to topological insulators. I will introduce the notion of ring states as a precursor of boundary states in topological materials and show how they give rise to the celebrated bulk-boundary correspondence. This perspective provides a unifying framework for topology centered on symmetry, from local symmetry to crystalline symmetry. I will make the discussion concrete by analyzing the effect of local defects from the well-known Chern insulators to more exotic new topological phases, such as fragile topological insulators protected by lattice symmetries.