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.

44 pages, accepted for publication in Phys. Rev. B

References in corpus (7)

• Topological Photonics
• The physics of exceptional points
• Analogs of quantum Hall effect edge states in photonic crystals
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Simplified topological invariants for interacting insulators
• Bulk-edge correspondence for topological photonic continua
• Topological Angular Momentum and Radiative Heat Transport in Closed Orbits

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• Non-Bloch band theory for non-Hermitian continuum systems
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• Ill-defined Topological Phases in Dispersive Photonic Crystals
• Exact formulas of the end-to-end Green's functions in non-Hermitian systems
• 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