Berry bands and pseudo-spin of topological photonic phases

Abstract

Realising photonic analogues of the robust, unidirectional edge states of electronic topological insulators would improve our control of light on the nanoscale and revolutionise the performance of photonic devices. Here we show that new symmetry protected topological phases can be detected by reformulating energy eigenproblems as Berry curvature eigenproblems. The "Berry bands" span the same eigenspace as the original valence energy bands, but separate into pseudo-spinful and pseudo-spinless subspaces in ${\mathrm{C}}_2\mathcal{T}$-symmetric crystals. We demonstrate the method on the well-known case of Wu & Hu [Phys. Rev. Lett. 114, 223901 (2015)] and a recently discovered fragilely topological crystal, and show that both crystals belong to the same ${\mathrm{C}}_2\mathcal{T}$-protected ${\mathbb{Z}}_2$ topological phase. This work helps unite theory and numerics, and is useful in defining and identifying new symmetry-protected phases in photonics and electronics.

4 pages, 4 figures

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Cited by in corpus (9)

• Topological Phases of Photonic Crystals under Crystalline Symmetries
• Photonic topological phase transition induced by material phase transition
• Absence of topological protection of the interface states in ${\mathbb{Z}}_2$ photonic crystals
• Double Dirac cones in band structures of periodic Schrödinger operators
• Topological Insights from State Manipulation in a Classical Elastic System
• Higher-order topology in honeycomb lattice with Y-Kekulé distortions
• Harnessing Nonlinear Dynamics for Time-Driven Berry Phase in Classical Systems
• Beyond Decoherence: Control the Collective Quantum Dynamics of Quasi Particles in Topological Interface
• Periodic Behavior of Topology in Graphene with Nanohole Array