Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
arXiv:2503.06933 · doi:10.1103/h9c2-h3t7
Abstract
Exceptional points (EPs) are prominent non-Hermitian band degeneracies that give rise to a variety of intriguing and unconventional phenomena. Similar to Weyl and Dirac points, EPs carry topological charges and comply with the celebrated fermion doubling theorems in lattices. Beyond these characteristics, EPs exhibit more exotic topological properties, particularly non-Abelian braiding topologies not seen in conventional degeneracies. Here, we investigate these foundational concepts of EPs in two-dimensional non-Hermitian lattices where the fundamental domain of the Brillouin zone is a Klein bottle, rather than a torus assumed in previous studies. We find that EPs do not necessarily appear in pairs with opposite topological charges in the Brillouin Klein bottle, thus violating the fermion doubling theorem. The violation occurs because, without crossing the boundary, the sum of the topological charges of EPs is in fact an even number rather than zero. Moreover, we uncover unique braiding topologies of EPs that cannot be captured by existing theories. Specifically, the composite braidings around all EPs equals the braiding along the boundary of the Brillouin Klein bottle. This novel braiding topology further confirms the failure of the fermion doubling theorem, and allows us to explore the non-Abelian braidings of EPs beyond the scope of topological charges. Our work highlights the fundamental role of Brillouin-zone topology in non-Hermitian systems.
7 pages, 3 figures
References in corpus (30)
- Non-Hermitian Physics
- The physics of exceptional points
- Topological Origin of Non-Hermitian Skin Effects
- Loss-induced suppression and revival of lasing
- Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
- Non-Hermitian Topology and Exceptional-Point Geometries
- Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
- Symmetry and Higher-Order Exceptional Points
- Knots and Non-Hermitian Bloch Bands
- Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
- Measuring the knot of non-Hermitian degeneracies and non-commuting braids
- Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
- Knot topology of exceptional point and non-Hermitian no-go theorem
- Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems
- Brillouin Klein Bottle From Artificial Gauge Fields
- Eigenvalue topology of non-Hermitian band structures in two and three dimensions
- Topology and exceptional points of massive Dirac models with generic non-Hermitian perturbations
- Realization and Topological Properties of Third-Order Exceptional Lines Embedded in Exceptional Surfaces
- Classification of time-reversal-invariant crystals with gauge structures
- Bulk-boundary correspondence in point-gap topological phases
- Braid Protected Topological Band Structures with Unpaired Exceptional Points
- General Theory of Momentum-Space Nonsymmorphic Symmetry
- Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals
- Klein-bottle quadrupole insulators and Dirac semimetals
- Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
- Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
- Making topologically trivial non-Hermitian systems nontrivial via gauge fields
- Weyl points on non-orientable manifolds
- Hermitian Topologies originating from non-Hermitian braidings
- Instanton-Induced Supersymmetry Breaking in Topological Semimetals