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Exceptional topology on nonorientable manifolds

J. Lukas K. König1,*, Kang Yang2,*, André Grossi Fonseca3, Sachin Vaidya3, Marin Soljačić3, and Emil J. Bergholtz1,†

  • *These authors contributed equally to this work.
  • †Contact author: emil.bergholtz@fysik.su.se
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Phys. Rev. Research 8, 013233 – Published 3 March, 2026

DOI: https://doi.org/10.1103/g5cr-dwxz

Abstract

We classify gapped phases and characteristic nodal points of non-Hermitian band structures on two-dimensional nonorientable parameter spaces. Such spaces arise in a wide range of physical systems in the presence of nonsymmorphic parameter space symmetries. For gapped phases, we find that nonorientable spaces provide a natural setting for exploring fundamental structural problems in braid group theory, such as torsion and conjugacy. Gapless systems, which host exceptional points (EPs), explicitly violate fermion doubling, even in two-band models. We demonstrate that EPs traversing the nonorientable parameter space exhibit non-Abelian charge inversion. These braided phases and their transitions leave distinct signatures in the form of bulk Fermi arc degeneracies, offering a concrete route toward experimental realization and verification.

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Phys. Rev. Research 8, 013233– Published 3 March, 2026
  • Received 11 March 2025
  • Accepted 6 February 2026
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