CMT Forum Prof. Raquel Quieroz

Topological obstructions in quantum matter prevent the construction of symmetric and exponentially localized Wannier states from Bloch bands. We show that a topological obstruction leads to bound states at finite ingap energies for local symmetric potentials that exceed the Bloch Hamiltonian's bandwidth, such as lattice vacancies. The resulting ingap states, which we call ring states, are the precursors of topological boundary modes and can serve as a local probe of topology. We demonstrate the origin of ring states as well as boundary states from the pole structure of the local Green's function, present in topological phases protected by internal or spatial symmetries.