Related papers: Theory of the Hall effect in three-dimensional met…
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…
Metamaterials can exhibit exotic nonreciprocal properties, yet corresponding fundamental limits and design blueprints achieving them are largely unexplored. Here, we derive comprehensive bounds on the effective nonreciprocal properties of…
We propose a class of three-dimensional metamaterial architectures composed of a single doped semiconductor (e.g., n-Si) in air or vacuum that lead to unusual effective behavior of the classical Hall effect. Using an anisotropic structure,…
We consider the problem of bounding the effective nonreciprocal properties of metamaterials. Recently, significant progress was made by showing that this problem can be reduced to bounding an equivalent reciprocal one and applying a…
It is now well established that the homogenization of a periodic array of parallel dielectric fibers with suitably scaled high permittivity can lead to a (possibly) negative frequency-dependent effective permeability. However this result…
The paper extends and enhances in several ways the recently proposed homogenization theory of metamaterials [J. Opt. Soc. Am. B 28, 577 (2011)]. The theory is based on a direct analysis of fields in the lattice cells rather than on an…
Magnus Hall effect (MHE) is a non-linear Hall effect requiring no external magnetic field, which can be observed when an in-built electric field couples to the Berry curvature of the bandstructure, producing a current in the transverse…
In this paper, we develop a unified theory for describing Hall effect in various electronic systems based on a pure electron picture (without the hole concept). We argue that the Hall effect is the magnetic field induced symmetry breaking…
The magneto-transport properties of planar and layered strongly inhomogeneous two-phase systems are investigated, using the explicit expressions for the effective conductivities and resistivities obtained by the exact dual transformation,…
We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with non-magnetic inclusions in the long wavelength limit, including spatial dispersion up to the second order.…
We study the phase structure and Hall conductance quantization in weakly coupled multi-layer electron systems in the integer quantum Hall regime. We derive an effective field theory and perform a two-loop renormalization group calculation.…
The Hall conductivity in a weak homogeneous magnetic field, $\omega_{c}\tau \ll 1$, is calculated. We have shown that to leading order in $1/\epsilon_{F}\tau$ the Hall coefficient $R_{H}$ is not renormalized by the electron-electron…
The mutual interplay between electron transport and magnetism has attracted considerable attention in recent years, primarily motivated by strategies to manipulate magnetic degrees of freedom electrically, such as spin-orbit torques and…
Reflection and refraction of electromagnetic waves by artificial periodic composites (metamaterials) can be accurately modeled by an effective medium theory only if the boundary of the medium is explicitly taken into account and the two…
The nonlinear Hall effect (NLHE) has been detected in various of condensed matter systems. Unlike linear Hall effect, NLHE may exist in physical systems with broken inversion symmetry in the crystal. On the other hand, real space spin…
A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas of electrons at zero temperature) coupled to the potential vector of an external local magnetic…
The concept of periodic structures has driven the development of advanced materials like photonic and phononic crystals. These metamaterials typically rely on complex repeating units or meta-atoms, limiting their adaptability after…
Two-component conductors -- e.g., semi-metals and narrow band semiconductors -- often exhibit unusually strong magnetoresistance in a wide temperature range. Suppression of the Hall voltage near charge neutrality in such systems gives rise…
We present a theoretical framework to describe the integer quantum Hall effect (IQHE) in three-dimensional (3D) electron systems. This extends our previous single-electron approach, which was successfully applied to two-dimensional (2D)…
I examine a model for the Hall effect in the strongly correlated regime. It emerges from an approach proposed in my previous articles [e.g. J. Phys. Chem. Solids, 65 (2004), 1507-1515; J. Geom. Phys., in press, cf. math-ph/0409023]. The…