Non-orientable Exceptional Points in Twisted Boundary Systems

• URL: http://arxiv.org/abs/2504.11983v1
• Date: Wed, 16 Apr 2025 11:26:05 GMT
• Title: Non-orientable Exceptional Points in Twisted Boundary Systems
• Authors: Jung-Wan Ryu, Jae-Ho Han, Moon Jip Park, Hee Chul Park, Chang-Hwan Yi,
• Abstract summary: We study the adiabatic transport of exceptional points along non-orientable closed loops.<n>We reveal distinct topological responses arising from the lack of global orientation.<n>We numerically implement these ideas in a microdisk cavity with embedded scatterers.
• Score: 1.188383832081829
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-orientable manifolds, such as the M\"obius strip and the Klein bottle, defy conventional geometric intuition through their twisted boundary conditions. As a result, topological defects on non-orientable manifolds give rise to novel physical phenomena. We study the adiabatic transport of exceptional points (EPs) along non-orientable closed loops and uncover distinct topological responses arising from the lack of global orientation. Notably, we demonstrate that the cyclic permutation of eigenstates across an EP depends sensitively on the loop orientation, yielding inequivalent braid representations for clockwise and counterclockwise encirclement; this is a feature unique to non-orientable geometries. Orientation-dependent geometric quantities, such as the winding number, cannot be consistently defined due to the absence of a global orientation. However, when a boundary is introduced, such quantities become well defined within the local interior, even though the global manifold remains non-orientable. We further demonstrate the adiabatic evolution of EPs and the emergence of orientation-sensitive observables in a Klein Brillouin zone, described by an effective non-Hermitian Hamiltonian that preserves momentum-space glide symmetry. Finally, we numerically implement these ideas in a microdisk cavity with embedded scatterers using synthetic momenta.

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