Hyperbolic non-Abelian semimetal
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914871695638528 |
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| author | Tummuru, Tarun Chen, Anffany Lenggenhager, Patrick M. Neupert, Titus Maciejko, Joseph Bzdušek, Tomáš |
| author_facet | Tummuru, Tarun Chen, Anffany Lenggenhager, Patrick M. Neupert, Titus Maciejko, Joseph Bzdušek, Tomáš |
| contents | We extend the notion of topologically protected semi-metallic band crossings to hyperbolic lattices in a negatively curved plane. Because of their distinct translation group structure, such lattices are associated with a high-dimensional reciprocal space. In addition, they support non-Abelian Bloch states which, unlike conventional Bloch states, acquire a matrix-valued Bloch factor under lattice translations. Combining diverse numerical and analytical approaches, we uncover an unconventional scaling in the density of states at low energies, and illuminate a nodal manifold of codimension five in the reciprocal space. The nodal manifold is topologically protected by a nonzero second Chern number, reminiscent of the characterization of Weyl nodes by the first Chern number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09876 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hyperbolic non-Abelian semimetal Tummuru, Tarun Chen, Anffany Lenggenhager, Patrick M. Neupert, Titus Maciejko, Joseph Bzdušek, Tomáš Mesoscale and Nanoscale Physics Other Condensed Matter Quantum Physics We extend the notion of topologically protected semi-metallic band crossings to hyperbolic lattices in a negatively curved plane. Because of their distinct translation group structure, such lattices are associated with a high-dimensional reciprocal space. In addition, they support non-Abelian Bloch states which, unlike conventional Bloch states, acquire a matrix-valued Bloch factor under lattice translations. Combining diverse numerical and analytical approaches, we uncover an unconventional scaling in the density of states at low energies, and illuminate a nodal manifold of codimension five in the reciprocal space. The nodal manifold is topologically protected by a nonzero second Chern number, reminiscent of the characterization of Weyl nodes by the first Chern number. |
| title | Hyperbolic non-Abelian semimetal |
| topic | Mesoscale and Nanoscale Physics Other Condensed Matter Quantum Physics |
| url | https://arxiv.org/abs/2307.09876 |