Ring states in topological materials

Abstract

Ingap states in semiconductors are commonly characterized by hydrogenic models within the effective mass approximation. However, when impurities are strong, this description fails. The bound states are non-perturbative with energy pinned to a zero of the impurity-projected Green's function. We show that in the presence of Wannier obstructions, such zeros are irremovable. That is, no symmetric, gap-preserving deformation of the bulk can return the ingap state to the band continuum. We call these states ring states: their wavefunctions show a node at the impurity site, and their mixed band character is set by minimizing the level repulsion exerted by the bands above and below the gap. In Chern insulators, the band mixing endows occupied ring states with local circulating currents, remnant of a small edge mode surrounding the vacancies. Clusters of vacancies bind ring states that hybridize to form dispersive chiral edge modes, providing a real-space view of bulk-boundary correspondence.

arXiv commentUpdated to incorporate corrections made during the Newton proof stage; includes supplementary material