Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911871924174848 |
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| author | Mao, Yu-Feng Tao, Yu-Liang Wang, Jiong-Hao Zeng, Qi-Bo Xu, Yong |
| author_facet | Mao, Yu-Feng Tao, Yu-Liang Wang, Jiong-Hao Zeng, Qi-Bo Xu, Yong |
| contents | Quasicrystals allow for symmetries that are impossible in crystalline materials, such as eight-fold rotational symmetry, enabling the existence of novel higher-order topological insulators in two dimensions without crystalline counterparts. However, it remains an open question whether three-dimensional higher-order topological insulators and Weyl-like semimetals without crystalline counterparts can exist. Here, we demonstrate the existence of a second-order topological insulator by constructing and exploring a three-dimensional model Hamiltonian in a stack of Ammann-Beenker tiling quasicrystalline lattices. The topological phase has eight chiral hinge modes that lead to quantized longitudinal conductances of $4 e^2/h$. We show that the topological phase is characterized by the winding number of the quadrupole moment. We further establish the existence of a second-order topological insulator with time-reversal symmetry, characterized by a $\mathbb{Z}_2$ topological invariant. Finally, we propose a model that exhibits a higher-order Weyl-like semimetal phase, demonstrating both hinge and surface Fermi arcs. Our findings highlight that quasicrystals in three dimensions can give rise to higher-order topological insulators and semimetal phases that are unattainable in crystals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_14974 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts Mao, Yu-Feng Tao, Yu-Liang Wang, Jiong-Hao Zeng, Qi-Bo Xu, Yong Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Quantum Gases Quasicrystals allow for symmetries that are impossible in crystalline materials, such as eight-fold rotational symmetry, enabling the existence of novel higher-order topological insulators in two dimensions without crystalline counterparts. However, it remains an open question whether three-dimensional higher-order topological insulators and Weyl-like semimetals without crystalline counterparts can exist. Here, we demonstrate the existence of a second-order topological insulator by constructing and exploring a three-dimensional model Hamiltonian in a stack of Ammann-Beenker tiling quasicrystalline lattices. The topological phase has eight chiral hinge modes that lead to quantized longitudinal conductances of $4 e^2/h$. We show that the topological phase is characterized by the winding number of the quadrupole moment. We further establish the existence of a second-order topological insulator with time-reversal symmetry, characterized by a $\mathbb{Z}_2$ topological invariant. Finally, we propose a model that exhibits a higher-order Weyl-like semimetal phase, demonstrating both hinge and surface Fermi arcs. Our findings highlight that quasicrystals in three dimensions can give rise to higher-order topological insulators and semimetal phases that are unattainable in crystals. |
| title | Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts |
| topic | Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Quantum Gases |
| url | https://arxiv.org/abs/2307.14974 |