Topological theory of non-Hermitian photonic systems

Abstract

Here, we develop a gauge-independent Green function approach to characterize the Chern invariants of generic non-Hermitian systems. It is shown that analogous to the Hermitian case, the Chern number can be expressed as an integral of the system Green function over a line parallel to the imaginary-frequency axis. The approach introduces in a natural way the "band-gaps" of non-Hermitian systems as the strips of the complex-frequency plane wherein the system Green function is analytical. We apply the developed theory to nonreciprocal electromagnetic continua, showing that the topological properties of gyrotropic materials are strongly robust to the effect of material loss. Furthermore, it is proven that the spectrum of a topological material cavity terminated with opaque-type walls must be gapless. This result suggests that the bulk-edge correspondence remains valid for a class of non-Hermitian systems.

arXiv comment44 pages, accepted for publication in Phys. Rev. B

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• Non-Hermitian skin effect and chiral damping in open quantum systems
• Non-Hermitian Topological Invariants in Real Space
• Simple formulas of directional amplification from non-Bloch band theory
• Floquet Topological Phases of Non-Hermitian Systems
• Photonic corner skin modes
• Inversion symmetric non-Hermitian Chern insulator
• Non-Hermitian anomalous skin effect
• Topological energy braiding of the non-Bloch bands
• Topological Microlaser with A non-Hermitian Topological Bulk
• Chiral Maxwell waves in continuous media from Berry monopoles
• Non-Bloch band theory for non-Hermitian continuum systems
• Exact formulas of the end-to-end Green's functions in non-Hermitian systems
• Ill-defined Topological Phases in Dispersive Photonic Crystals
• Rotating Spacetime Modulation: Topological Phases and Spacetime Haldane Model
• A renormalization group approach to non-Hermitian topological quantum criticality
• Anomalous features of non-Hermitian topological states
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• Direct visualization of topological transitions and higher-order topological states in photonic metasurfaces