Christian Kern

Experimental Evidence for Sign Reversal of the Hall Coefficient in Three-Dimensional Metamaterials

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.

Maximizing the brilliance of high-order harmonics in a gas jet

We have measured the wave front of high-order harmonics generated in a gas jet with a Hartmann sensor. With this setup we have investigated the influence of typical adjustable parameters such as gas pressure and focal position as well as the spatial laser beam profile on the conversion efficiency and the extreme ultraviolet (XUV) beam profile. Independent of the control parameter we always observed the highest conversion efficiency in connection with the best beam profile, i.e. the highest flux corresponds also to the highest brilliance. Furthermore, we have shown that aberrations of the fundamental laser beam are not simply imprinted onto the XUV beam.

Hall-effect metamaterials and “anti-Hall bars”

In this letter in the July 2017 issue of Physics Today (page 13), Ramesh Mani points to the connection between part of one unit cell of our three-dimensional chainmail-like Hall-effect metamaterial1 (see Physics Today, February 2017, page 21) and his earlier work on planar “anti-Hall bars.”2 We were not aware of his work and thank Mani for pointing it out to us. However, the conclusions he derives in his comment are misleading. He argues that the change in Hall-voltage sign “should be attributed to a change in effective geometry rather than to a change in sign of the Hall coefficient.” That viewpoint completely ignores the idea of metamaterials and composites, as described by homogenization theory.3,4 Indeed, as emphasized by Mani, the Hall coefficient of the host material does not change when one introduces voids into it. However, the geometry or structure inside the metamaterial unit cell determines the effective Hall coefficient of the metamaterial crystal. What does the metamaterial community generally mean by effective material parameters? Suppose, in the sense of a black box, an experimentalist cannot look into the unit cell of an artificial crystal but can perform experiments on the crystal. He or she may change the strength and direction of the applied static magnetic field, the amplitude and direction of the injected electrical current, the pickup of the Hall voltage, and the size of the sample, measured by the number of unit cells in any one direction. For our 3D metamaterial, the experimentalist would conclude that all observations are perfectly consistent with a sign reversal of the Hall coefficient—that is, the effective Hall coefficient—with respect to that of the bulk host material. In sharp contrast, that statement is not true for a single planar anti-Hall bar

Parallel Hall effect from three-dimensional single-component metamaterials

We propose a class of three-dimensional metamaterial architectures composed of a single doped semiconductor (e.g., n-Si) in air or vacuum which lead to an unusual effective behavior of the classical Hall effect. Using an anisotropic structure, we numerically demonstrate a Hall voltage that is parallel—rather than orthogonal—to the external static magnetic-field vector (“parallel Hall effect”). The sign of this parallel Hall voltage can be determined by a structure parameter. Together with the previously demonstrated positive or negative orthogonal Hall voltage, we demonstrate four different sign combinations.

Three-Dimensional Chiral Photonic Crystals in the THz Regime Exhibiting Weyl Points with Topological Charges

Recently, the existence of multiple Weyl points was theoretically shown for chiral woodpile photonic crystals [1]. These Weyl points carry topological charges and thus lead to the emergence of backscattering-immune gapless surface states, making the photonic crystal a topological photonic insulator. The proposed photonic crystal structure consists of chirally stacked rods made of a perfect electric conductor (PEC), forming a hexagonal lattice. The structure parameters are designed to obtain isolated Weyl points in the THz regime. Polymer structures are fabricated using three-dimensional laser lithography and subsequently coated with silver via polymer sensitization and electroless deposition. For a silver film thickness well above the skin depth of the THz radiation, a material optically comparable to a bulk PEC can be realized. Measurements of the angle resolved transmission spectra using photoconductive antennas as THz sources and detectors will be carried out soon. From these spectra one can obtain the band structure and hence show the existence of the Weyl points.

Theory of the Hall effect in three-dimensional metamaterials

We apply homogenization theory to calculate the effective electric conductivity and Hall coefficient tensor of passive three-dimensionally periodic metamaterials subject to a weak external static homogeneous magnetic field. We not 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. We present 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 break previous bounds for the effective mobility.

Hall effect sign-inversion and parallel hall effect in single-constituent 3D metamaterials

A few years ago, Briane and Milton have shown the existence of three-dimensional, isotropic, periodic metamaterials with a Hall coefficient that is negative with respect to that of its constituents using homogenization theory [1]. They also gave an example of such a metamaterial structure. Recently, we simplified their blueprint decisively and numerically demonstrated this sign-inversion which turned out to be controllable by a structure parameter [2].