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

Kern, Christian; Kadic, Muamer; Wegener, Martin

doi:10.1103/physrevlett.118.016601

Cited by 46 publications

(37 citation statements)

References 52 publications

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“…These are mainly the regions where the cylinders and tori intersect. This finding is in good agreement with our previous intuitive explanation [19]. Consider a torus in the xy-plane, a magnetic field alongẑ, and a current flowing in the x-direction.…”

Section: Isotropic Structures and Sign-inversion Of The Hall Coefficientsupporting

confidence: 92%

“…An effective material exhibiting a sign-inversion of the Hall coefficient can be obtained by placing a material with nonzero Hall coefficient there and choosing the Hall coefficient to be zero everywhere else [17,39]. Parameters are defined as in [19], R=36 μm, d=−18 μm, 1 , where s 0 Tori is the conductivity of the tori and s 0 Surr. is the conductivity of the surrounding material.…”

Section: Isotropic Structures and Sign-inversion Of The Hall Coefficientmentioning

confidence: 99%

“…is the conductivity of the surrounding material. (c) A single unit cell of such an effective material [19,39]. The only parts with a nonzero Hall coefficient are the small black spheres placed in between the intertwined tori.…”

Section: Isotropic Structures and Sign-inversion Of The Hall Coefficientmentioning

confidence: 99%

“…Early mathematical work based on homogenization theory has shown that the effective Hall coefficient, which is directly linked to the off-diagonal elements of the effective conductivity tensor, can exhibit a sign reversal with respect to the constituent materials in three-dimensional (3D) structures [17], but not in 2D structures for perpendicular magnetic fields [18]. Recent experiments based on 3D singlesemiconductor-constituent structures [19] have brought these predictions to life. The parallel Hall effect [20,21], for which the Hall voltage drop is parallel to the magnetic field axis, has been observed in anisotropic 3D structures [22].…”

Section: Introductionmentioning

confidence: 99%

“…Yet another approach is to calculate the behavior of a finitesize microstructure numerically, then consider it a black box, and map the result onto effective material parameters. While all of these viewpoints and approaches are valid in their own right, it is unsatisfactory that the early mathematical work [17] considered idealized microstructures that were actually quite different from the ones realized in experiments more recently [19]. This left it unclear, whether the physical mechanisms at work are the same.…”

Section: Introductionmentioning

confidence: 99%

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Theory of the Hall effect in three-dimensional metamaterials

Kern¹,

Milton²,

Kadic³

et al. 2018

New J. Phys.

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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.

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Section: Isotropic Structures and Sign-inversion Of The Hall Coefficientsupporting

confidence: 92%

Section: Isotropic Structures and Sign-inversion Of The Hall Coefficientmentioning

confidence: 99%

Section: Isotropic Structures and Sign-inversion Of The Hall Coefficientmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Theory of the Hall effect in three-dimensional metamaterials

Kern¹,

Milton²,

Kadic³

et al. 2018

New J. Phys.

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New Twists of 3D Chiral Metamaterials

et al. 2019

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Rationally designed artificial materials, called metamaterials, allow for tailoring effective material properties beyond (“meta”) the properties of their bulk ingredient materials. This statement is especially true for chiral metamaterials, as unlocking certain degrees of freedom necessarily requires broken centrosymmetry. While the field of chiral electromagnetic/optical metamaterials has become rather mature, the field of elastic/mechanical metamaterials is just emerging and wide open. This research news reviews recent theoretical and experimental progress concerning 3D chiral mechanical and optical metamaterials, with special emphasis on work performed at KIT.

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Photonic and Plasmonic Metasensors

Ahmadivand

Gerislioglu

2021

Laser & Photonics Reviews

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Biosensors have been designed and developed for detecting biomarkers, biomolecules, proteins, enzymes, organisms, and various types of bacterial and viral diseases since the turn of the century. Initially marred by poor sensitivity, specificity, and selectivity, the advent of the notion of photonic biosensors has successfully addressed such drawbacks. One of the hallmarks of modern pharmaceutical industries is the miniaturization of photonic platforms via continuous scaling down of their sizes, which was accomplished by leveraging the concept of artificial media. Numerous forms of photonic and plasmonic devices have been configured for next-generation technologies since the emergence of metamaterials. Among diverse applications, the development of cost-effective, label-free, selective, precise, and on-chip immunobiosensors with rapid sample-to-result feature has received copious interest, recently. This focused Review brings clarity to the rapidly growing body of available and in-development metamaterials-enabled diagnostic instruments based on inventive and promising approaches. Through centering on the operating principles of plasmonic, photonic, and hybrid metasensors, we mechanistically characterize and describe the properties of such tools and summarize the most recent achievements in devising metasensors and bioimaging tools with high precision. This insightful understanding serves as a comprehensive source for scientists, physicians, and students to construct ultradense and high-throughput clinical screening metadevices.

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

Cited by 46 publications

References 52 publications

Theory of the Hall effect in three-dimensional metamaterials

Theory of the Hall effect in three-dimensional metamaterials

New Twists of 3D Chiral Metamaterials

Photonic and Plasmonic Metasensors

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