Topological Bands and Triply Degenerate Points in Non-Hermitian Hyperbolic Metamaterials

Abstract

Hyperbolic metamaterials (HMMs), an unusual class of electromagnetic metamaterials, have found important applications in various fields due to their distinctive properties. A surprising feature of HHMs found recently is that even continuous HMMs can possess topological edge modes. However, previous studies based on equal-frequency surface (analogy of Fermi surface) may not correctly capture the topology of entire bands. Here we develop a topological band description for continuous HMMs that can be described by a non-Hermitian Hamiltonian formulated from Maxwell's equations. We find two types of three dimensional photonic triply-degenerate points with topological charges ±2 and 0 induced by chiral and gyromagnetic effects that break spatial inversion and time-reversal symmetries, respectively. Because of the photonic nature, the vacuum band plays an important role for topological edge states and bulk-edge correspondence in HMMs. The topological band results are numerically confirmed by direct simulation of Maxwell's equations. Our work presents a general non-Hermitian topological band treatment of continuous HMMs, paving the way for exploring interesting topological phases in photonic continua. arXiv:1808.06972v1 [cond-mat.mes-hall]

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Designing non-Hermitian real spectra through electrostatics

“…The working principle behind this analogy is the intimate relation between the conformal structure of electrostatics and the complex spectral flow in non-Hermitian systems. Our work opens up a new paradigm for engineering non-Hermitian spectra, particularly real spectra, in various settings, such as cold atoms [44,45], photonics [19,22], metamaterials [50,51], mechanical and acoustic systems [47]. While real spectra are important for state stability in the majority of experiments, we point out that non-real spectra present further possibilities in terms of topological sophistication [34], and are just as physically relevant in the form of the Laplacian spectra of steady-state networks such as electrical circuits [28,48,52,53].…”

Designing non-Hermitian real spectra through electrostatics

“…The working principle behind this analogy is the intimate relation between the conformal structure of electrostatics and the complex spectral flow in non-Hermitian systems. Our work opens up a new paradigm for engineering non-Hermitian spectra, particularly real spectra, in various settings, such as cold atoms [44,45], photonics [19,22], metamaterials [50,51], mechanical and acoustic systems [47]. While real spectra are important for state stability in the majority of experiments, we point out that non-real spectra present further possibilities in terms of topological sophistication [34], and are just as physically relevant in the form of the Laplacian spectra of steady-state networks such as electrical circuits [28,48,52,53].…”