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arXiv · 2503.04889

Exceptional topology on nonorientable manifolds

J. Lukas K. König·Kang Yang·André Grossi Fonseca·Sachin Vaidya·Marin Soljačić·Emil J. Bergholtz
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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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J. Lukas K. König, Kang Yang, André Grossi Fonseca, Sachin Vaidya, Marin Soljačić, Emil J. Bergholtz. 2025-03-06. Exceptional topology on nonorientable manifolds. https://doi.org/10.1103/g5cr-dwxz

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