Nodal phases in non-Hermitian wallpaper crystals

Abstract

Symmetry and non-Hermiticity play pivotal roles in photonic lattices. While symmetries such as parity-time ($\mathcal{P}\mathcal{T}$) symmetry have attracted ample attention, more intricate crystalline symmetries have been neglected in comparison. Here, we investigate the impact of the 17 wallpaper space groups of two-dimensional crystals on non-Hermitian band structures. We show that the non-trivial space group representations enforce degeneracies at high symmetry points and dictate their dispersion away from these points. In combination with either $\mathcal{T}$ or $\mathcal{P}\mathcal{T}$, the symmorphic p4mm symmetry, as well as the non-symmorphic p2mg, p2gg, and p4gm symmetries, protect novel exceptional chains intersecting at the pertinent high symmetry points.

6 pages, 2 figures

References in corpus (13)

• Topological Crystalline Insulators
• The physics of exceptional points
• Topological Origin of Non-Hermitian Skin Effects
• Non-Hermitian Topology and Exceptional-Point Geometries
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Non-Hermitian topological phenomena: A review
• Topological Non-Hermitian skin effect
• Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point
• Experimental Simulation of Symmetry-Protected Higher-Order Exceptional Points with Single Photons
• Fourth-Order Exceptional Points in Correlated Quantum Many-Body Systems
• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• Experimental realization of stable exceptional chains protected by non-Hermitian latent symmetries unique to mechanical systems

Cited by in corpus (4)

• Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Fragmented exceptional points and their bulk and edge realizations in lattice models
• Exceptional topology on nonorientable manifolds