Theory of the Hall effect in three-dimensional metamaterials - Franche-Comté Electronique, Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
Article Dans Une Revue New Journal of Physics Année : 2018

Theory of the Hall effect in three-dimensional metamaterials

Résumé

Weapply homogenization theory to calculate the effective electric conductivity and Hall coefficienttensor of passive three-dimensionally periodic metamaterials subject to a weak external static homogeneous magnetic field.Wenot only allow for variations of the conductivity and the Hall coefficient of the constituent material(s) within the metamaterial unit cells, but also for spatial variations of the magnetic permeability.Wepresent four results. First, our findings are consistent with previous numerical calculations for finite-size structures as well as with recent experiments. This provides a sound theoretical justification for describing such metamaterials in terms of effective material parameters. Second, we visualize the cofactor fields appearing in the homogenization integrals. Thereby, we identify those parts of the metamaterial structures which are critical for the observed effective metamaterial parameters, providing a unified view onto various previously introduced single-constituent/multiple-constituent and isotropic/anisotropic architectures, respectively. Third, we suggest a novel three-dimensional non-magnetic metamaterial architecture exhibiting a sign reversal of the effective isotropic Hall coefficient. It is conceptually distinct from the original chainmail-like geometry, for which the sign reversal is based on interlinked rings. Fourth, we discuss two examples for metamaterial architectures comprising magnetic materials: yet another possibility to reverse the sign of the isotropic Hall coefficient and an approach to conceptually breakprevious bounds for the effective mobility.
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hal-02380793 , version 1 (27-10-2024)

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Christian Kern, Graeme W. Milton, Muamer Kadic, Martin Wegener. Theory of the Hall effect in three-dimensional metamaterials. New Journal of Physics, 2018, 20 (22), pp.083034. ⟨10.1088/1367-2630/aad92b⟩. ⟨hal-02380793⟩
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