Topological classification of non-Hermitian bands

Abstract

We proposed a framework for the topological classification of non-Hermitian systems. Different from previous $K$-theoretical approaches, our approach is a homotopy classification, which enables us to see more topological invariants. Specifically, we considered the classification of non-Hermitian systems with separable band structures. We found that the whole classification set is decomposed into several sectors based on the braiding of energy levels and characterized by some braid group data. Each sector can be further classified based on the topology of eigenstates (wave functions). Due to the interplay between energy levels braiding and eigenstates topology, we found some torsion invariants, which only appear in the non-Hermitian world via homotopical approach. We further proved that these new topological invariants are unstable (fragile), in the sense that adding more bands will trivialize these invariants.

contains some updates for presentational purpose

References in corpus (14)

• Classification of topological insulators and superconductors in three spatial dimensions
• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Visualization of Branch Points in PT-Symmetric Waveguides
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• New topological invariants in non-Hermitian systems
• On the $Z_2$ classification of Quantum Spin Hall Models
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Topological surface states in three-dimensional magnetic insulators
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Topological Classification of Non-Hermitian Hamiltonians
• Perspective on topological states of non-Hermitian lattices

Cited by in corpus (45)

• Non-Hermitian Topology and Exceptional-Point Geometries
• Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
• Knot topology of exceptional point and non-Hermitian no-go theorem
• Fate of the non-Hermitian skin effect in many-body fermionic systems
• Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems
• Probing Complex-energy Topology via Non-Hermitian Absorption Spectroscopy in a Trapped Ion Simulator
• Dimensional transmutation from non-Hermiticity
• Eigenvalue topology of non-Hermitian band structures in two and three dimensions
• Unsupervised Learning of Non-Hermitian Topological Phases
• Realization and Topological Properties of Third-Order Exceptional Lines Embedded in Exceptional Surfaces
• Symmetry and topological classification of Floquet non-Hermitian systems
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Braid Protected Topological Band Structures with Unpaired Exceptional Points
• Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• Manipulating non-Hermitian skin effect via electric fields
• Non-Hermitian eigenvalue knots and their isotopic equivalence
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
• Hermitian Topologies originating from non-Hermitian braidings
• Unravelling the edge spectra of non-Hermitian Chern insulators
• Versatile Braiding of Non-Hermitian Topological Edge States
• Braiding topology of symmetry-protected degeneracy points in non-Hermitian systems
• Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States
• One-dimensional non-Hermitian band structures as Riemann surfaces
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Realization of geometric phase topology induced by multiple exceptional points
• Observation of Braid-Protected Unpaired Exceptional Points
• Topological eigenvalues braiding and quantum state transfer near a third-order exceptional point
• Pseudo-Hermitian Topology of Multiband Non-Hermitian Systems
• Exceptional deficiency of non-Hermitian systems
• PT-symmetric Non-Hermitian Hopf Metal
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Non-Hermitian Hopf insulators
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Machine learning topological energy braiding of non-Bloch bands
• Nodal Spectral Functions Stabilized by Non-Hermitian Topology of Quasiparticles
• Topology of the generalized Brillouin zone of one-dimensional models
• Exceptional topology on nonorientable manifolds
• Braiding of dynamical eigenvalues of Hermitian bosonic Kitaev chains
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars
• Emergence of Hermitian topology from non-Hermitian knots
• Non-orientable Exceptional Points in Twisted Boundary Systems