${\mathbb{Z}}_2$ Topological Index for Continuous Photonic Materials

Abstract

Electronic topological insulators are one of the breakthroughs of the 21st century condensed matter physics. So far, the search for a light counterpart of an electronic topological insulator has remained elusive. This is due to the fundamentally different natures of light and matter and the different spins of photons and electrons. Here, it is shown that the theory of electronic topological insulators has a genuine analogue in the context of light wave propagation in time-reversal invariant continuous materials. We introduce a Gauge invariant $Z_2$ index that depends on the global properties of the photonic band structure and is robust to any continuous weak variation of the material parameters that preserves the time-reversal invariance. A nontrivial $Z_2$ index has two possible causes: (i) the lack of smoothness of the pseudo-Hamiltonian in the $\mathbf{k}\to \infty$ limit, and (ii) the entanglement between positive and negative frequency eigenmode branches. In particular, it is proven that electric-type plasmas and magnetic-type plasmas are topologically inequivalent for a fixed wave polarization. We propose a bulk-edge correspondence that links the number of edge modes with the topological invariants of two continuous bulk materials, and present detailed numerical examples that illustrate the application of the theory.

published in PHYSICAL REVIEW B 93, 075110 (2016)

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• PTD Symmetry Protected Scattering Anomaly in Optics
• Twisted quadrupole topological photonic crystals
• Photonic Spin Hall Effect in Waveguides Composed of Two Types of Single-Negative Metamaterials
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• The effects of three-dimensional defects on one-way surface plasmon propagation for photonic topological insulators comprised of continuous media
• Topological Angular Momentum and Radiative Heat Transport in Closed Orbits
• Exact Solution for the Protected TEM edge mode in a PTD-Symmetric Parallel-Plate Waveguide
• Topological origin of electromagnetic energy sinks
• Spin-wave chirality and its manifestations in antiferromagnets
• Quantized Angular Momentum in Topological Optical Systems
• The Schrödinger Formalism of Electromagnetism and Other Classical Waves --- How to Make Quantum-Wave Analogies Rigorous
• Notes on photonic topological insulators and scattering-protected edge states - a brief introduction
• The effects of dissipation on topological mechanical systems
• Current-induced nonreciprocity and refraction-free propagation in a one-dimensional graphene-based photonic crystal
• Effective Medium Perspective on Topological Transitions in Metamaterials
• Electromagnetism at finite temperature: a density operator approach