Experimental Evidence for Sign Reversal of the Hall Coefficient in Three-Dimensional Metamaterials Christian Kern, 1,2 Muamer Kadic, 1,2 and Martin Wegener 1,2 1 Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany 2 Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76021 Karlsruhe, Germany (Received 18 July 2016; published 4 January 2017) Effectively inverting the sign of material parameters is a striking possibility arising from the concept of metamaterials. Here, we show that the electrical properties of a p-type semiconductor can be mimicked by a metamaterial solely made of an n-type semiconductor. By fabricating and characterizing three- dimensional simple-cubic microlattices composed of interlocked hollow semiconducting tori, we demonstrate that sign and magnitude of the effective metamaterial Hall coefficient can be adjusted via a tori separation parameter—in agreement with previous theoretical and numerical predictions. DOI: 10.1103/PhysRevLett.118.016601 The properties of composites or rationally designed artificial materials called metamaterials are generally not in between those of their constituents; i.e., “one gets out more than one puts in” [1,2]. Unbounded behavior is possible, too. Sign reversal of an effective material param- eter with respect to the constituents is a particularly striking case. The availability of positive and negative parameter values largely enhances our ability to mold waves and fluxes. Thus, sign reversals have contributed much to the excitement in the field of metamaterials. In the dynamic case, they are well known by now. Examples are the magnetic permeability [3–5], the refractive index [4,6,7], the mechanical compressibility [8,9], the mass density [10–12], or both of the latter [13–16]. In all of these examples, the sign inversion arises from some sort of internal resonance. For frequencies above the correspond- ing eigenfrequency, the response exhibits a 180-degree phase shift, i.e., a reversal of sign. Clearly, this mechanism does not work in the stationary limit. Moreover, for passive media in the stationary limit, due to the second law of thermodynamics, reversing the sign of transport coefficients like the electric conductivity, the heat conductivity, or the diffusivity is even fundamentally impossible. The Hall coefficient is a notable exception. It is directly connected to the off-diagonal elements of the electric conductivity tensor in the presence of a static magnetic field. In the simplest case, the Hall coefficient A H is equal to the inverse of the charge density, i.e., A H ¼ ρ −1 . A few years ago, building upon earlier work [17–19], Marc Briane and Graeme W. Milton predicted theoretically that the sign of the isotropic Hall coefficient can be reversed in chainmail-like three-dimensional metamaterials [20]. Notably, art inspired science: Chainmail artist Dylon Whyte suggested to them the three-dimensional structure [21]. Sign reversal of the Hall coefficient in metamaterials is interesting because one can, for example, effectively mimic p-doped silicon when having only n-doped silicon available as a constituent. However, an experimental validation of this mind-boggling prediction has not been published so far. In this Letter, we present experimental evidence for the predicted sign inversion of the effective Hall coefficient in chainmail-like metamaterials. We show that the sign as well as the magnitude of the Hall coefficient can be determined by a geometrical separation parameter while fixing the FIG. 1. Blueprint for the three-dimensional chainmail-like metamaterial discussed in this Letter. It is composed of a simple-cubic lattice of hollow tori. a is the lattice constant, R the torus radius, r the wire radius, t the film thickness, and d the separation parameter. The latter can be positive or negative; the depicted configuration corresponds to d< 0. PRL 118, 016601 (2017) PHYSICAL REVIEW LETTERS week ending 6 JANUARY 2017 0031-9007=17=118(1)=016601(5) 016601-1 © 2017 American Physical Society