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arXiv · 2307.09876

Hyperbolic non-Abelian semimetal

Tarun Tummuru·Anffany Chen·Patrick M. Lenggenhager·Titus Neupert·Joseph Maciejko·Tomáš Bzdušek
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Abstract

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.

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Tarun Tummuru, Anffany Chen, Patrick M. Lenggenhager, Titus Neupert, Joseph Maciejko, Tomáš Bzdušek. 2023-07-19. Hyperbolic non-Abelian semimetal. https://doi.org/10.1103/physrevlett.132.206601

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