On Dec. 11, 2019, a general framework for incorporating and correcting for nonclassical electromagnetic phenomena in nanoscale systems will be presented in the journal Nature.
More than 150 years have passed since the publication of James Clerk Maxwell's "A Dynamical Theory of the Electromagnetic Field" (1865). His treatise revolutionized the fundamental understanding of electric fields, magnetic fields and light. The 20 original equations (elegantly reduced to four today), their boundary conditions at interfaces, and the bulk electronic response functions (dielectric permitivity and magnetic permeability) are at the root of the ability to manipulate electromagnetic fields and light.
Life without Maxwell's equations would lack most current science, communications and technology.
On large (macro) scales, bulk response functions and the classical boundary conditions are sufficient for describing the electromagnetic response of materials, but as we consider phenomena on smaller scales, nonclassical effects become important. A conventional treatment of classical electromagnetism fails to account for the mere existence of effects such as nonlocality, spill-out, and surface-enabled Landau damping. Why does this powerful framework break down at nanoscales? The problem is that electronic length scales are at the heart of nonclassical phenomena, and they are not part of the classical model. Electronic length scales can be thought of as the Bohr radius or the lattice spacing in solids: small scales that are relevant for the quantum effects at hand.
Today, the path to understanding and modeling nanoscale electromagnetic phenomena is finally open. In the breakthrough Nature paper "A General Theoretical and Experimental Framework for Nanoscale Electromagnetism," Yang et al. present a model that extends the validity of the macroscopic electromagnetism into the nano regime, bridging the scale gap. On the theoretical side, their framework generalizes the boundary conditions by incorporating the electronic length scales in the form of so-called Feibelman d-parameters.
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