Non-Hermitian spectral flows and Berry-Chern monopoles

Abstract

We propose a non-Hermitian generalization of the correspondence between the spectral flow and the topological charges of band crossing points (Berry-Chern monopoles). A class of non-Hermitian Hamiltonians that display a complex-valued spectral flow is built by deforming an Hermitian model while preserving its analytical index. We relate those spectral flows to a generalized Chern number that we show to be equal to that of the Hermitian case, provided a line gap exists. We demonstrate the homotopic invariance of both the non-Hermitian Chern number and the spectral flow index, making explicit their topological nature. In the absence of a line gap, our system still displays a spectral flow whose topology can be captured by exploiting an emergent pseudo-Hermitian symmetry.

arXiv comment10 pages, 4 figures

References in corpus (38)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Photonics
• Edge states and topological invariants of non-Hermitian systems
• Non-Hermitian Physics
• Topological phases of non-Hermitian systems
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Topological Band Theory for Non-Hermitian Hamiltonians
• Anomalous edge state in a non-Hermitian lattice
• Non-Hermitian Chern bands
• Topological response in Weyl semimetals and the chiral anomaly
• Non-Hermitian Boundary Modes
• Topological mechanics of gyroscopic metamaterials
• Nonlinear topological photonics
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Non-Hermitian Topological Invariants in Real Space
• Chiral anomaly and transport in Weyl metals
• Topological active matter
• Topological Sound
• New topological invariants in non-Hermitian systems
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Topological Origin of Equatorial Waves
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Gain and loss induced topological insulating phase in a non Hermitian electrical circuit
• Symmetry-protected multifold exceptional points and their topological characterization
• Topological Chern indices in molecular spectra
• Designing non-Hermitian real spectra through electrostatics
• Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems
• Non-Hermitian tight-binding network engineering
• Chiral anomaly enhancement and photo-irradiation effects in multi-band touching fermion systems
• Real spectra in non-Hermitian topological insulators
• Topological phase in plasma physics
• Wave topology brought to the coast
• Chiral Maxwell waves in continuous media from Berry monopoles
• Unidirectional modes induced by nontraditional Coriolis force in stratified fluids
• Topological chiral interface states beyond insulators
• Robust propagating in-gap modes due to spin-orbit domain walls in graphene

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• Self acceleration from spectral geometry in dissipative quantum-walk dynamics
• Anomalous Andreev Spectrum and Transport in Non-Hermitian Josephson Junctions
• Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Symmetry-Driven Bulk-Edge Correspondence in Electron Magnetofluids at Finite Temperature
• Non-Hermitian second-order topological insulator with point gap