  We address the general problem of magnetic-field-induced corner states in
quantum spin Hall insulators (QSHIs). Our analytical findings reveal that when
applied to the QSHIs in zinc-blende semiconductor quantum wells (QWs), the
presence of corner states extends beyond the anticipated range of meeting
edges, surpassing the limitations imposed by crystal symmetry. We clearly
demonstrate that, in the most general scenario, magnetic field-induced corner
states in QSHIs are not topological. However, we find that the presence of
crystal symmetry can stabilize these states only under specific orientations of
the in-plane magnetic field and meeting edges. Therefore, contrary to previous
assumptions, our research unveils that QSHIs in the presence of a magnetic
field cannot be accurately considered as higher-order topological insulators.
Furthermore, the lack of an inversion center in zinc-blende semiconductor QWs
enables the emergence of corner states through the influence of a perpendicular
magnetic field.
