Photonic Dirac monopoles and skyrmions: spin-1 quantization

Abstract

We introduce the concept of a photonic Dirac monopole, appropriate for photonic crystals, metamaterials and 2D materials, by utilizing the Dirac-Maxwell correspondence. We start by exploring vacuum where the reciprocal momentum space of both Maxwell's equations and the massless Dirac equation (Weyl equation) possess a magnetic monopole. The critical distinction is the nature of magnetic monopole charges, which are integer valued for photons but half-integer for electrons. This inherent difference is directly tied to the spin and ultimately connects to the bosonic or fermionic behavior. We also show the presence of photonic Dirac strings, which are line singularities in the underlying Berry gauge potential. While the results in vacuum are intuitively expected, our central result is the application of this topological Dirac-Maxwell correspondence to 2D photonic (bosonic) materials, as opposed to conventional electronic (fermionic) materials. Intriguingly, within dispersive matter, the presence of photonic Dirac monopoles is captured by nonlocal quantum Hall conductivity - i.e. a spatiotemporally dispersive gyroelectric constant. For both 2D photonic and electronic media, the nontrivial topological phases emerge in the context of massive particles with broken time-reversal symmetry. However, the bulk dynamics of these bosonic and fermionic Chern insulators are characterized by spin-1 and spin-1/2 skyrmions in momentum space, which have fundamentally different interpretations. This is exemplified by their contrasting spin-1 and spin-1/2 helically quantized edge states. Our work sheds light on the recently proposed quantum gyroelectric phase of matter and the essential role of photon spin quantization in topological bosonic phases.

arXiv comment25 pages, 4 figures. This is the fourth paper in a series of papers on spin and topological bosonic phases of light. The others can be found here: https://doi.org/10.1103/PhysRevA.98.023842, arXiv:1708.08192, and https://doi.org/10.1364/OPTICA.3.000118

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• Roadmap for Photonics with 2D Materials
• Topologically non-trivial photonic surface degeneracy in a photonic metamaterial
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• Universal momentum-to-real-space mapping of topological singularities
• Symmetry-protected photonic chiral spin textures by spin-orbit coupling
• Non-local topological electromagnetic phases of matter
• Light-controlled skyrmions and torons as reconfigurable particles
• Unidirectional Maxwellian Spin Waves
• Theory of paraxial optical Skyrmions
• Quantum sensing of photonic spin density
• Indifferent electromagnetic modes: bound states and topology
• Optically enriched and guided dynamics of active skyrmions
• Optical $N$-invariant of graphene's viscous Hall fluid
• Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter
• Intrinsic triple degeneracy point bounded by nodal surfaces in chiral photonic crystal
• Pico-photonics: Anomalous Atomistic Waves in Silicon
• Nonlinearity and Topology
• Electron g-factor engineering for non-reciprocal spin photonics
• Dirac Wire
• Optical N-plasmon: Topological hydrodynamic excitations in Graphene from repulsive Hall viscosity
• Tutorial: Topology, waves, and the refractive index
• Stokes and skyrmion tensors and their application to structured light
• Theory of classical electrodynamics with topologically quantized singularities as electric charges