Higher-order symmetry-protected topological states for interacting bosons and fermions

Abstract

Here, the authors propose a zoology of exotic materials that are gapped in their interior and on their surfaces but support gapless mode at corners or along hinges. Exemplifying a much richer bulk-boundary correspondence, this phenomenology is now termed a higher-order topological phase. The protected corner or hinge modes are a consequence of spatial symmetry, which traps and pins the low-energy modes localized at the high symmetric point.