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In 2009, Briane and Milton proved mathematically the existence ofthree-dimensional isotropic metamaterials with a classical Hall coefficientwhich is negative with respect to that of all of the metamaterial constituents.Here, we significantly simplify their blueprint towards an architecturecomposed of only a single constituent material in vacuum/air, which can be seenas a special type of porosity. We show that the sign of the Hall voltage isdetermined by a separation parameter between adjacent tori. This qualitativebehavior is robust even for only a small number of metamaterial unit cells. Thecombination of simplification and robustness brings experimental verificationsof this striking sign-inversion into reach.

Hall-effect sign-inversion in a realizable 3D metamaterial