  The search for exotic new topological states of matter in widely accessible
materials, for which the manufacturing process is mastered, is one of the major
challenges of the current topological physics. Here we predict higher order
topological insulator state in quantum wells based on the most common
semiconducting materials. By successively deriving the bulk and boundary
Hamiltonians, we theoretically prove the existence of topological corner states
due to cubic symmetry in quantum wells with double band inversion. We show that
the appearance of corner states does not depend solely on the crystallographic
orientation of the meeting edges, but also on the growth orientation of the
quantum well. Our theoretical results significantly extend the application
potential of topological quantum wells based on IV, II-VI and III-V
semiconductors with diamond or zinc-blende structures.
