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Speaker: Christian Kern, University of Utah
Title: On the Hall effect in three-dimensional metamaterials
Abstract: The Hall effect describes the appearance of a transversal voltage, the so-called Hall voltage,in a current-carrying slab of material that is subject to an external magnetic field. Mathematically, the effect is described by an antisymmetric contribution to the conductivity tensor that is proportional to the magnetic field. This antisymmetric contribution is linked to the nonreciprocity of the effect, which is a result of the external magnetic field breaking time-reversal symmetry. In the isotropic case, the relevant material properties are given by a scalar parameter, the so-called Hall coefficient. In metamaterials, very unusual values of the effective Hall coefficient can be realized by tailoring their microscopic structure. In this talk, based on the work of Marc Briane and Graeme Milton, I will show that the effective Hall coefficient of a single-constituent porous metamaterial can be sign-inverted with respect to the Hall coefficient of the constituent material and how we were able to demonstrate this effect experimentally. Furthermore, I will discuss structures with lower symmetry, which are described by a rank-two tensor instead of a scalar Hall coefficient. In the last part of my talk, I will elaborate on bounds on the effective Hall coeffcient and related effective material parameters. Such bounds can be obtained using results from perturbation theory or via the variational principles of Cherkaev, Gibiansky, and Milton.
Bio: Christian Kern is a Research Assistant Professor in the Department of Mathematics at the University of Utah, Salt Lake City. His research focuses on the theoretical description and experimental realization of three-dimensional composites and metamaterials with highly non-trivial geometries. C. Kern received his Ph.D. in Physics from Karlsruhe Institute of Technology in 2019, where he was advised by Martin Wegener. He holds a B.Sc. and a M.Sc. in Physics from ETH Zurich.