Anomalous Collision of Exceptional Points on Nonorientable Manifolds

TL;DR

This paper demonstrates that in a simple two-band non-Hermitian system on a nonorientable manifold, anomalous collision of exceptional points can occur, leading to novel topological phase transitions and enriching the understanding of degeneracy interactions.

Contribution

It reveals and experimentally demonstrates anomalous EP collisions in a two-band system on a nonorientable Klein bottle, previously thought to require non-Abelian multiband systems.

Findings

Anomalous EP collision occurs in a two-band non-Hermitian lattice.

Hybrid point is a defective degeneracy with no eigenenergy braiding.

Phase transition from gapped to gapless phase observed experimentally.

Abstract

Band degeneracies, ranging from Hermitian Dirac points to non-Hermitian exceptional points (EPs), play a central role in topological phase transitions. Beyond the topology of individual degeneracies, their mutual interactions yield richer phenomena. A representative example is the anomalous non-annihilating collision of pairwise-created degeneracies, previously believed to occur only in non-Abelian multiband systems. Here, we theoretically reveal and experimentally demonstrate that such an anomalous collision can emerge even in a simple two-band system without non-Abelian nature. In a two-dimensional non-Hermitian lattice whose Brillouin zone forms a nonorientable Klein bottle, two EPs with opposite topological charges, pairwise created from a hybrid point, merge into a new vortex point upon re-encounter, instead of annihilating. Remarkably, the hybrid point is a defective degeneracy featuring no eigenenergy braiding, whereas the vortex point is a non-defective degeneracy yet exhibits nontrivial eigenenergy braiding. This process manifests a non-Hermitian phase transition from a gapped phase to a gapless phase, a scenario that we directly observe in a hybrid-dimensional acoustic lattice via momentum-resolved band braid and Berry phase measurements. Our findings identify nonorientability as a new arena for engineering band degeneracies and topological phases, and pave the way for experimentally exploring the interplay between exceptional and nonorientable topology.