Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915715117744128 |
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| author | Kang, Myungjun Sung, Wonjun Verma, Sonu Cheon, Sangmo |
| author_facet | Kang, Myungjun Sung, Wonjun Verma, Sonu Cheon, Sangmo |
| contents | Symmetry and topology are essential principles in topological physics. Recently, the idea of sub-symmetry-protected topology -- where some of the original symmetries are broken while a remaining subset, called sub-symmetries, continues to protect specific boundary states -- has been developed. Here, we extend sub-symmetry-protected topology to higher-order topological systems from second-order topological insulators to semimetals. By introducing a sub-symmetry-protecting perturbation that acts on a single sublattice and selectively preserves specific topological boundary states, we track the evolution of these states and their topological features using numerical and analytical methods, and we show that state-resolved quadrupole moments diagnose which corner or hinge modes remain topological. As a representative example of a second-order topological insulator, we begin with the Benalcazar-Bernevig-Hughes model. We demonstrate that, under a sub-symmetry-protecting perturbation, sub-symmetry-protected corner states remain pinned at zero energy and maintain quantized state-resolved quadrupole moments. In contrast, corner states on sub-symmetry-broken boundaries shift away from zero energy and lose their quantized character. We further extend this framework to a three-dimensional second-order topological semimetal, constructed by stacking second-order topological insulator layers, and analyze how second-order Fermi arc states -- hinge-localized modes that link the projections of bulk Dirac points, in contrast to conventional surface Fermi arcs -- evolve under a sub-symmetry-protecting perturbation. While one second-order Fermi arc becomes dispersive and loses its quadrupolar character under a sub-symmetry-breaking perturbation, the remaining second-order Fermi arcs retain chiral symmetry and preserve quantized quadrupolar characters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17694 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology Kang, Myungjun Sung, Wonjun Verma, Sonu Cheon, Sangmo Mesoscale and Nanoscale Physics Symmetry and topology are essential principles in topological physics. Recently, the idea of sub-symmetry-protected topology -- where some of the original symmetries are broken while a remaining subset, called sub-symmetries, continues to protect specific boundary states -- has been developed. Here, we extend sub-symmetry-protected topology to higher-order topological systems from second-order topological insulators to semimetals. By introducing a sub-symmetry-protecting perturbation that acts on a single sublattice and selectively preserves specific topological boundary states, we track the evolution of these states and their topological features using numerical and analytical methods, and we show that state-resolved quadrupole moments diagnose which corner or hinge modes remain topological. As a representative example of a second-order topological insulator, we begin with the Benalcazar-Bernevig-Hughes model. We demonstrate that, under a sub-symmetry-protecting perturbation, sub-symmetry-protected corner states remain pinned at zero energy and maintain quantized state-resolved quadrupole moments. In contrast, corner states on sub-symmetry-broken boundaries shift away from zero energy and lose their quantized character. We further extend this framework to a three-dimensional second-order topological semimetal, constructed by stacking second-order topological insulator layers, and analyze how second-order Fermi arc states -- hinge-localized modes that link the projections of bulk Dirac points, in contrast to conventional surface Fermi arcs -- evolve under a sub-symmetry-protecting perturbation. While one second-order Fermi arc becomes dispersive and loses its quadrupolar character under a sub-symmetry-breaking perturbation, the remaining second-order Fermi arcs retain chiral symmetry and preserve quantized quadrupolar characters. |
| title | Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2512.17694 |