@article{Tummuru:2024,
  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},
  journal             = {Phys. Rev. Lett.},
  volume              = {132},
  issue               = {20},
  pages               = {206601},
  numpages            = {7},
  year                = {2024},
  month               = {May},
  publisher           = {American Physical Society},
  doi                 = {10.1103/PhysRevLett.132.206601},
}

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

Phys. Rev. Lett. 132, 206601 (2024) – Published 14 May 2024

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.