Intrinsic second-order topological insulators in two-dimensional polymorphic graphyne with sublattice approximation

In two dimensions, intrinsic second-order topological insulators (SOTIs) are characterized by topological corner states that emerge at the intersections of distinct edges with reversed mass signs, enforced by spatial symmetries. Here, we present a comprehensive investigation within the class BDI to clarify the symmetry conditions ensuring the presence of intrinsic SOTIs in two dimensions. We reveal that the (anti-)commutation relationship between spatial symmetries and chiral symmetry is a reliable indicator of intrinsic corner states. Through first-principles calculations, we identify several ideal candidates within carbon-based polymorphic graphyne structures for realizing intrinsic SOTIs under sublattice approximation. Furthermore, we show that the corner states in these materials persist even in the absence of sublattice approximation. Our findings not only deepen the understanding of higher-order topological phases but also open new pathways for realizing topological corner states that are readily observable.