The concept of photonic frequency (ω) - momentum (𝑞) dispersion has been extensively studied in artificial dielectric structures such as photonic crystals and metamaterials. However, the ω−𝑞 dispersion of electrodynamic waves hosted in natural materials at the atomistic level is far less explored. Here, we develop an atomistic nonlocal electrodynamic theory of matter by combining the Maxwell Hamiltonian theory of matter with a quantum theory of atomistic polarization. We apply this theory to silicon and discover the existence of atomistic electrodynamic waves. Atomistic electrodynamic waves have sub-nano-meter effective wavelengths in the picoelectrodynamics regime. Further, we show that the atomistic optical conductivity in silicon is highly anisotropic along different momentum directions due to atomistic electronic correlations. Our findings demonstrate that the natural media host variety of yet to be discovered electromagnetic phases of matter and provide a pathway towards the discovery of rich atomic scale light-matter interaction phenomena.
Over the past three decades, graphene has become the prototypical platform for discovering topological phases of matter. Both the Chern C∈Z and quantum spin Hall υ∈Z2 insulators were first predicted in graphene, which led to a veritable explosion of research in topological materials. We introduce a new topological classification of two-dimensional matter – the optical N-phases N∈Z. This topological quantum number is connected to polarization transport and captured solely by the spatiotemporal dispersion of the susceptibility tensor χ. We verify N ≠ 0 in graphene with the underlying physical mechanism being repulsive Hall viscosity. An experimental probe, evanescent magneto-optic Kerr effect (e-MOKE) spectroscopy, is proposed to explore the N-invariant. We also develop topological circulators by exploiting gapless edge plasmons that are immune to back-scattering and navigate sharp defects with impunity. Our work indicates that graphene with repulsive Hall viscosity is the first candidate material for a topological electromagnetic phase of matter.
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