Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917028847157248 |
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| author | Chen, Yuxiao Xu, Zhiming Wang, Citian Huang, Huaqing |
| author_facet | Chen, Yuxiao Xu, Zhiming Wang, Citian Huang, Huaqing |
| contents | We propose that three-dimensional layered octagonal quasicrystals can host magnetic-field-tunable Möbius insulators and various higher-order topological insulators (HOTIs), enabled by the interplay of quasicrystalline symmetry and magnetic order. By constructing a minimal model based on stacked Ammann-Beenker tilings with magnetic exchange coupling and octagonal warping, we demonstrate that an A-type antiferromagnetic (AFM) configuration yields a topological phase protected by an effective time-reversal symmetry $\mathcal{S}=\mathcal{T}τ_{1/2}$. Breaking $\mathcal{S}$ via an in-plane magnetic field induced canting of the AFM order while preserving a nonsymmorphic glide symmetry $\mathcal{G}_n=τ_{1/2}\mathcal{M}_n$ leads to Möbius-twisted surface states, realizing a Möbius insulator in an aperiodic 3D system. Furthermore, we show that the quasicrystal with a general magnetic configuration supports multiple HOTI phases characterized by distinct hinge mode configurations that can be switched by rotating the magnetic field. A low-energy effective theory reveals that these transitions are driven by mass kinks between adjacent surfaces. Our work establishes a platform for realizing symmetry-protected topological phases unique to quasicrystals and highlights the tunability of hinge and surface states via magnetic control. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_17497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals Chen, Yuxiao Xu, Zhiming Wang, Citian Huang, Huaqing Mesoscale and Nanoscale Physics We propose that three-dimensional layered octagonal quasicrystals can host magnetic-field-tunable Möbius insulators and various higher-order topological insulators (HOTIs), enabled by the interplay of quasicrystalline symmetry and magnetic order. By constructing a minimal model based on stacked Ammann-Beenker tilings with magnetic exchange coupling and octagonal warping, we demonstrate that an A-type antiferromagnetic (AFM) configuration yields a topological phase protected by an effective time-reversal symmetry $\mathcal{S}=\mathcal{T}τ_{1/2}$. Breaking $\mathcal{S}$ via an in-plane magnetic field induced canting of the AFM order while preserving a nonsymmorphic glide symmetry $\mathcal{G}_n=τ_{1/2}\mathcal{M}_n$ leads to Möbius-twisted surface states, realizing a Möbius insulator in an aperiodic 3D system. Furthermore, we show that the quasicrystal with a general magnetic configuration supports multiple HOTI phases characterized by distinct hinge mode configurations that can be switched by rotating the magnetic field. A low-energy effective theory reveals that these transitions are driven by mass kinks between adjacent surfaces. Our work establishes a platform for realizing symmetry-protected topological phases unique to quasicrystals and highlights the tunability of hinge and surface states via magnetic control. |
| title | Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2507.17497 |