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The discovery and realization of topological insulators, a phase of matterwhich hosts metallic boundary states when the $d$-dimension insulating bulk isconfined to ($d-1$)-dimensions, led to several potential applications.Recently, it was shown that protected topological states can manifest in($d-2$)-dimensions, such as hinge and corner states for three- andtwo-dimensional systems, respectively. These nontrivial materials are namedhigher-order topological insulators (HOTIs). Here we show a connection betweenspin Hall effect and HOTIs using a combination of {\it ab initio} calculationsand tight-binding modeling. The model demonstrates how a non-zero bulk midgapspin Hall conductivity (SHC) emerges within the HOTI phase. Following this, weperformed high-throughput density functional theory calculations to findunknown HOTIs, using the SHC as a criterion. We calculated the SHC of 693insulators resulting in seven stable two-dimensional HOTIs. Our work guidesnovel experimental and theoretical advances towards higher-order topologicalinsulators realization and applications.

Discovery of Higher-Order Topological Insulators using the Spin Hall Conductivity as a Topology Signature