  The discovery and realization of topological insulators, a phase of matter
which hosts metallic boundary states when the $d$-dimension insulating bulk is
confined 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- and
two-dimensional systems, respectively. These nontrivial materials are named
higher-order topological insulators (HOTIs). Here we show a connection between
spin Hall effect and HOTIs using a combination of {\it ab initio} calculations
and tight-binding modeling. The model demonstrates how a non-zero bulk midgap
spin Hall conductivity (SHC) emerges within the HOTI phase. Following this, we
performed high-throughput density functional theory calculations to find
unknown HOTIs, using the SHC as a criterion. We calculated the SHC of 693
insulators resulting in seven stable two-dimensional HOTIs. Our work guides
novel experimental and theoretical advances towards higher-order topological
insulators realization and applications.
