Magnetic-field-induced corner states in quantum spin Hall insulators

We treat the general problem of magnetic-field-induced corner states in quantum spin Hall insulators based on zinc-blende semiconductor quantum wells (QWs). An analysis performed within the \emph{continuous} Bernevig-Hughes-Zhang (BHZ) model reveals that the gapped edge states are described by ``generalized'' 1D Dirac equation with \emph{two mass parameters}, whose values depend on crystallographic orientation of the edge and that of the magnetic field. Although the mass parameters do not vanish simultaneously, an analytical solution in the form of ``topological domain wall mode'' confirms the existence of corner state at the intersection of two adjacent edges. Surprisingly, the existence of the corner states induced by an in-plane magnetic field do not require a crystal symmetry of zinc-blende semiconductor QW, making our results universal for any quantum spin Hall insulators with isotropic edge-state g-factor. On the contrary, the corner states induced by an out-of-plane magnetic field arise only due to the absence of an inversion center in zinc-blende semiconductor QWs.