Topological hierarchy matters — topological matters with superlattices of defects

He Jing¹, Kou Su-Peng^{2, †,}

(a) The illustration of square-VSLs on square lattice. (b) The DOS of the Haldane model with square-VSL for L = 3a: the mid-gap states are induced by the square-VSL. (c) The edge states of mid-gap states. The parameter is t′/t = 0.2. (d) The DOS of TFI. The insets show the DOSs of the mid-gap states. From Ref. [30].