PT-symmetric Non-Hermitian Hopf Metal

Abstract

Hopf insulator is a representative class of three-dimensional topological insulators beyond the standard topological classification methods based on K-theory. In this letter, we discover the metallic counterpart of the Hopf insulator in the non-Hermitian systems. While the Hopf invariant is not a stable topological index due to the additional non-Hermitian degree of freedom, we show that the PT-symmetry stabilizes the Hopf invariant even in the presence of the non-Hermiticity. In sharp contrast to the Hopf insulator phase in the Hermitian counterpart, we discover an interesting result that the non-Hermitian Hopf bundle exhibits the topologically protected non-Hermitian degeneracy, characterized by the two-dimensional surface of exceptional points. Despite the non-Hermiticity, the Hopf metal has the quantized Zak phase, which results in bulk-boundary correspondence by showing drumhead-like surface states at the boundary. Finally, we show that, by breaking PT-symmetry, the nodal surface deforms into the knotted exceptional lines. Our discovery of the Hopf metal phase firstly confirms the existence of the non-Hermitian topological phase outside the framework of the standard topological classifications.

arXiv comment6 pages, 3 figures

References in corpus (65)

• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Edge states and topological invariants of non-Hermitian systems
• Periodic table for topological insulators and superconductors
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Edge states and topological phases in non-Hermitian systems
• Non-Hermitian Topological Invariants in Real Space
• Universal non-Hermitian skin effect in two and higher dimensions
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• Fragile Topology and Wannier Obstructions
• New topological invariants in non-Hermitian systems
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Dynamically encircling an exceptional point in anti-PT-symmetric systems: asymmetric mode switching for symmetry-broken states
• Band topology in classical waves: Wilson-loop approach to topological numbers and fragile topology
• Symmetry and Higher-Order Exceptional Points
• Topological surface states in three-dimensional magnetic insulators
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Topological Euler class as a dynamical observable in optical lattices
• Topological Classification of Non-Hermitian Hamiltonians
• Phases of Wave Functions and Level Repulsion
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
• Geometric approach to fragile topology beyond symmetry indicators
• Experimental characterization of fragile topology in an acoustic metamaterial
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Knotted Non-Hermitian Metals
• Measuring the knot of non-Hermitian degeneracies and non-commuting braids
• Exceptional Point Dynamics in Photonic Honeycomb Lattices with PT Symmetry
• PT symmetry and necessary and sufficient conditions for the reality of energy eigenvalues
• The Landau Level of Fragile Topology
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Observation of non-Hermitian topology with non-unitary dynamics of solid-state spins
• Hopf Insulators and Their Topologically Protected Surface States
• Engineering Fragile Topology in Photonic Crystals: Topological Quantum Chemistry of Light
• Topological classification of non-Hermitian bands
• Hopf characterization of two-dimensional Floquet topological insulators
• Probing Complex-energy Topology via Non-Hermitian Absorption Spectroscopy in a Trapped Ion Simulator
• Symmetry Protected Topological Hopf Insulator and its Generalizations
• Realization of a Hopf insulator in circuit systems
• Topology and Observables of the Non-Hermitian Chern Insulator
• Multicellularity of delicate topological insulators
• Floquet Hopf Insulators
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Braid Protected Topological Band Structures with Unpaired Exceptional Points
• Realizing Hopf Insulators in Dipolar Spin Systems
• Observation of topological links associated with Hopf insulators in a solid-state quantum simulator
• $N$-band Hopf insulator
• Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators
• Massless multifold Hopf semimetals
• ${\mathbb{Z}}_2$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump

Cited by in corpus (2)

• Pseudo-Hermitian Topology of Multiband Non-Hermitian Systems
• Non-Hermitian Hopf insulators