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

Mar 2023

We treat the general problem of magnetic-field-induced corner states inquantum 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 bygeneralized'' 1D Dirac equation with \emph{two mass parameters}, whose valuesdepend on crystallographic orientation of the edge and that of the magneticfield. Although the mass parameters do not vanish simultaneously, an analyticalsolution in the form of topological domain wall mode'' confirms the existenceof corner state at the intersection of two adjacent edges. Surprisingly, theexistence of the corner states induced by an in-plane magnetic field do notrequire a crystal symmetry of zinc-blende semiconductor QW, making our resultsuniversal for any quantum spin Hall insulators with isotropic edge-stateg-factor. On the contrary, the corner states induced by an out-of-planemagnetic field arise only due to the absence of an inversion center inzinc-blende semiconductor QWs.

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