Related papers: Eigenvalues of strictly regular Hall-plates
Magnetic skyrmions are topologically stable objects that are made with a bunch of spins tightly arranged in a smooth fashion. Their topological nature provides unusual and complex transport properties, such as the skyrmion Hall effect.…
We consider the Schr\"odinger operator $Hy=-y"+(p+q)y$ with a periodic potential $p$ plus a compactly supported potential $q$ on the real line. The spectrum of $H$ consists of an absolutely continuous part plus a finite number of simple…
We prove Lieb-Thirring inequalities for Schr\"odinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength…
We clarify the origin of what is sometimes called the "topological anomalous Hall effect," provide analytical formulas to compute all the contributions to the Hall conductivity in the presence of Kondo-coupled spins and spin orbit coupling.…
We formulate a self-consistent model of the integer quantum Hall effect on an infinite strip, using boundary conditions to investigate the influence of finite-size effects on the Hall conductivity. By exploiting the translation symmetry…
In a large range of physics and space experiments, the direction of the magnetic field needs to be determined with an accuracy on the level of one milli radian or better. We have proposed a new type of magnetic compass - a rotation-based…
Symmetry is a cornerstone of condensed matter physics, fundamentally shaping the behavior of electronic systems and inducing the emergence of novel phenomena. The Hall effect, a key concept in this field, demonstrates how symmetry breaking,…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
Extraordinary Hall effect (EHE) is a spin-dependent phenomenon that generates voltage proportional to magnetization across a current carrying magnetic film. Magnitude of the effect can be artificially increased by stimulating properly…
The Hall effect, ever intriguing since its discovery, has spurred the exploration of its phenomena, intensified by advances in topology and novel materials. Differentiating the ordinary Hall effect from extraordinary properties like the…
In this review we summarise recent results for the complex eigenvalues and singular values of finite products of finite size random matrices, their correlation functions and asymptotic limits. The matrices in the product are taken from…
We compute the local spectrum of the magnetic field near a metallic microstructure at finite temperature. Our main focus is on deviations from a plane-layered geometry for which we review the main properties. Arbitrary geometries are…
The effect of strong magnetic fields parallel to GaAs/AlGaAs interface on the subband structure of a 2D electron layer is ivestigated theoretically. The system with two levels occupied in zero magnetic field is considered and the magnetic…
In the theory of composites, hierarchical laminate microstructures are known to often show optimal behavior. In this paper, their performance in the context of the Hall effect is evaluated. Using numerical calculations, it is shown that -…
We consider a charged spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to the loop plane. We derive the reflection…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
We adopt the concept of the correlation matrix to study correlations among sequences of time-extended events occuring repeatedly at consecutive time-intervals. As an application we analyse the magnetoencephalography recordings obtained from…
We investigate the stability of the Hall-MHD system and determine its importance for neutron stars at their birth, when they still consist of differentially rotating plasma permeated by extremely strong magnetic fields. We solve the…
We produce an explicit parameterization of well-rounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest…
We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose…