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

TL;DR

This paper presents a simplified 3D metamaterial design that achieves Hall-effect sign inversion using a single material, with robust behavior suitable for experimental validation.

Contribution

It simplifies previous complex designs to a single-material architecture, enabling practical realization of Hall-effect sign inversion in 3D metamaterials.

Findings

Sign of Hall voltage determined by separation parameter between tori

Sign-inversion behavior is robust with few unit cells

Design is feasible for experimental verification

Abstract

In 2009, Briane and Milton proved mathematically the existence of three-dimensional isotropic metamaterials with a classical Hall coefficient which is negative with respect to that of all of the metamaterial constituents. Here, we significantly simplify their blueprint towards an architecture composed of only a single constituent material in vacuum/air, which can be seen as a special type of porosity. We show that the sign of the Hall voltage is determined by a separation parameter between adjacent tori. This qualitative behavior is robust even for only a small number of metamaterial unit cells. The combination of simplification and robustness brings experimental verifications of this striking sign-inversion into reach.