Bound states in the continuum of higher-order topological phases

In this talk, we connect the study of bound states in the continuum (BICs) with the field of topological band theory. Specifically, we show that lattices with higher-order topology can support corner-localized BICs: topological, symmetry-protected states that remain localized to corners even though they are not spectrally isolated within an energy gap. We propose a method for the direct identification of BICs in condensed matter settings and use it to demonstrate the existence of BICs in a concrete lattice model. Although symmetry-protected, corner-induced filling anomalies give rise to these states, additional symmetries protect them from hybridizing with their degenerate bulk states. We demonstrate the protection mechanism for BICs in this model as arising from the simultaneous presence of chiral and C4v symmetries. We further show how breaking this mechanism transforms the BICs into higher-order topological resonances.