Magnetic-field-induced corner states in quantum spin Hall insulators
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913058371141632 |
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| author | Krishtopenko, Sergey S. Teppe, Frédéric |
| author_facet | Krishtopenko, Sergey S. Teppe, Frédéric |
| contents | We address the problem of magnetic-field-induced corner states in quantum spin Hall insulators (QSHIs) beyond the particle-hole-symmetric limit. Starting from a realistic low-energy model for zinc-blende semiconductor quantum wells (QWs), we derive the effective edge Hamiltonian in the form of a Dirac Hamiltonian with two magnetic-field-dependent mass terms, whose structure depends on the crystallographic orientation of the edge and of the magnetic-field orientation. Our \emph{analytical} results show that magnetic-field-induced corner states are most naturally understood as in-gap bound states of the effective edge theory, controlled by the relative configuration of the edge mass vectors rather than, in general, as higher-order topological corner modes protected by a stable bulk invariant. We demonstrate that, although mirror-graded winding numbers can be defined and quantized for certain crystallographic configurations, the existence of magnetic-field-induced corner states is not restricted to regimes in which these bulk invariants are well defined. Finally, we argue that even without higher-order topological protection these corner states may remain spectrally robust under weak perturbations as isolated in-gap quasiparticle excitations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09260 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Magnetic-field-induced corner states in quantum spin Hall insulators Krishtopenko, Sergey S. Teppe, Frédéric Mesoscale and Nanoscale Physics Materials Science We address the problem of magnetic-field-induced corner states in quantum spin Hall insulators (QSHIs) beyond the particle-hole-symmetric limit. Starting from a realistic low-energy model for zinc-blende semiconductor quantum wells (QWs), we derive the effective edge Hamiltonian in the form of a Dirac Hamiltonian with two magnetic-field-dependent mass terms, whose structure depends on the crystallographic orientation of the edge and of the magnetic-field orientation. Our \emph{analytical} results show that magnetic-field-induced corner states are most naturally understood as in-gap bound states of the effective edge theory, controlled by the relative configuration of the edge mass vectors rather than, in general, as higher-order topological corner modes protected by a stable bulk invariant. We demonstrate that, although mirror-graded winding numbers can be defined and quantized for certain crystallographic configurations, the existence of magnetic-field-induced corner states is not restricted to regimes in which these bulk invariants are well defined. Finally, we argue that even without higher-order topological protection these corner states may remain spectrally robust under weak perturbations as isolated in-gap quasiparticle excitations. |
| title | Magnetic-field-induced corner states in quantum spin Hall insulators |
| topic | Mesoscale and Nanoscale Physics Materials Science |
| url | https://arxiv.org/abs/2303.09260 |