@article{Tummuru:2023,
  title               = {Hyperbolic non-Abelian semimetal}, 
  author              = {Tarun Tummuru and Anffany Chen and Patrick M. Lenggenhager and Titus Neupert and Joseph Maciejko and Tom\'{a}\v{s} Bzdu\v{s}ek},
  journal             = {arXiv preprint},
  year                = {2023},
  doi                 = {10.48550/arXiv.2307.09876},
  url                 = {https://arxiv.org/abs/2307.09876}
  eprint              = {2307.09876},
  eprintType          = {arXiv},
  archivePrefix       = {arXiv}
}

T. Tummuru, A. Chen, P. M. Lenggenhager, T. Neupert, J. Maciejko, and T. Bzdušek

arXiv:2307.09876 (2023) – Published 19 Jul 2023

We extend the notion of topologically protected semi-metallic band crossings to hyperbolic lattices in negatively curved space. Due to their distinct translation group structure, such lattices 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 a quartic 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 non-zero second Chern number, reminiscent of the characterization of Weyl nodes by the first Chern number.