Raquel QUEIROZ
Weizmann Institute of Science
Symmetry protected topological (SPT) phases are gapped phases of matter that cannot be deformed to a trivial phase without breaking the symmetry or closing the bulk gap. In this talk I will introduce a new notion of a topological obstruction that is not captured by bulk energy gap closings in periodic boundary conditions. More specifically, we say two bulk Hamiltonians belong to distinct boundary obstructed topological `phases' (BOTPs) if they can be deformed to each other on a system with periodic boundaries, but cannot be deformed to each other for symmetric open boundaries without closing the gap at at least one high symmetry region on the surface. I will discuss the double-mirror quadrupole model [Science, 357(6346), 2018] and a dimerized weak topological insulator [arxiv 1809.03518] as examples of BOTPs. I will describe the general framework to study boundary obstructions in free-fermion systems in terms of Wannier band representations (WBR), an extension of the recently-developed band representation formalism to Wannier bands. WBRs capture the notion of topological obstructions in the Wannier bands which can then be used to study topological obstructions in the boundary spectrum by means of the correspondence between the Wannier and boundary spectra. This establishes a form of bulk-boundary correspondence for BOTPs by relating the bulk band representation to the boundary topology.