Classical Hall Effect Research Articles

The Hall effect in Lobachevsky space

In this paper, we consider the problem of the classical and quantum movement of a charged particle in a two-dimensional Lobachevsky space in the presence of analogues of uniform magnetic and electric fields. Based on this consideration, equations for the conductivity for the classical and quantum Hall effect are obtained. It is shown that in Lobachevsky space the presence of a small electrical field leads to a shift of the stair structure of the quantum Hall conductivity.

Dziedzictwo Edwina Halla

Undoubtedly, all students of physical sciences become acquainted with the classical Hall effect at the very beginning of their scientific path. Moreover, each of us uses the technology based on this phenomenon to a greater or lesser extent without even being aware of it. Although more than one hundred years passed since the experiment of Edwin Hall, the problem of the Hall effect is not a closed chapter in the history of physics. Instead, Hall effects have become an extremely fertile idea yielding discoveries of new phenomena. One can say that the discoveries of new Hall effects have been over the years a kind of metric of scientific progress in solid-state physics.The fast development of quantum mechanics, as well as the technological progress, allowed for the fabrication of semiconducting thin films and, among others, the discovery of the quantum Hall effect. Advancement in the physics of magnetism, and spin physics, allowed to explain the microscopic mechanisms responsible for the anomalous Hall effect [12, 15] and the discovery of the spin Hall effect [17, 18]. It is also not surprising that in contemporary solid-state physics, strongly focusing on topological properties of solids, one can find the new members of the Hall effect family, i.e., the topological and non-linear Hall effect. Hence, it is worth to briefly review one of the most fruitful concepts in solid-state physics. This article aims to introduce the Hall eòects while maintaining the chronology of their discovery. I mainly used a semiclassical picture, where carriers (electrons) are treated as particles governed by the laws of classical mechanics. I also introduced the necessary concepts of quantum physics and topology, which are crucial for explaining the Hall effects described in recent years.

Faraday Rotation Due to Quantum Anomalous Hall Effect in Cr-Doped (Bi,Sb)2Te3

Quantum anomalous Hall effect (QAHE) represents a quantized version of the classical anomalous Hall effect. In the latter case the magnetization takes over the role of magnetic field and induces nonzero off-diagonal elements in the conductivity matrix. In magnetic topological insulators with the band inversion the QAHE can be reached due to quantized conduction channel at the sample edge if the Fermi energy is tuned into the surface magnetic gap. In the static regime the QAHE is seen as a zero-field step in the Hall resistivity. At optical frequencies this step is transformed into a quantized value of the polarization rotation approaching the fine structure constant α=e2/2ε0hc≈1/137. However, due to material issues the steps reach the predicted values at millikelvin temperatures only. In this work we investigate the Faraday polarization rotation in thin films of Cr-doped topological insulator and in the sub-terahertz frequency range. Well defined polarization rotation steps can be observed in transmittance in Faraday geometry. At temperatures down to T=1.85 K the value of the rotation reached about 20% of the fine structure constant and disappeared completely for T>20 K.

The effect of passivation layer, doping and spacer layer on electron- longitudinal optical phonon momentum relaxation time in Al0.3Ga0.7N/AlN/GaN heterostructures

The Raman and classical Hall effect measurements have been used to determine the longitudinal optical phonon energy, effective mass, and optical phonon relaxation times in Al0.3Ga0.7N/AlN/GaN heterostructures grown by the Molecular Beam Epitaxy (MBE) technique. The classical Hall effect measurements were performed at temperatures between 1.8 and 262 K at a fixed magnetic field, while Raman measurements were performed at room temperature. The longitudinal optical (LO) phonon energy has been found at higher temperatures where Hall mobility data is rapidly decreasing. The effective mass is obtained by comparing the A1(LO) peak obtained from Raman measurements to theoretical calculations. The effect of passivation, spacer layer, and doping on the LO phonon relaxation times were determined. The LO phonon relaxation times, which are important for the device's performance, were found between 8.97 and 9.20 fs.

Lorentz forces induce inhomogeneity and flux in active systems

We consider the nonequilibrium dynamics of a charged active Brownian particle in the presence of a space dependent magnetic field. It has recently been shown that the Lorentz force induces a particle flux perpendicular to density gradients, thus preventing a diffusive description of the dynamics. Whereas a passive system will eventually relax to an equilibrium state, unaffected by the magnetic field, an active system subject to a spatially varying Lorentz force settles into a nonequilibrium steady state characterized by an inhomogeneous density and divergence-free bulk fluxes. A macroscopic flux of charged active particles is induced by the gradient of the magnetic field only and does not require additional symmetric breaking such as density or potential gradients. This stands in marked contrast to similar phenomena in condensed matter such as the classical Hall effect. In a confined geometry we observe circulating fluxes, which can be reversed by inverting the direction of the magnetic field. Our theoretical approach, based on coarse-graining of the Fokker-Planck equation, yields analytical results for the density, fluxes, and polarization in the steady state, all of which are validated by direct computer simulation. We demonstrate that passive tracer particles can be used to measure the essential effects of the Lorentz force on the active particle bath, and we discuss under which conditions the effects of the flux could be observed experimentally.

Distinguishing the inverse spin Hall effect photocurrent of electrons and holes by comparing to the classical Hall effect.

The photo-excited electrons and holes move in the same direction in the diffusion and in the opposite direction in the drift under an electric field. Therefore, the contribution to the inverse spin Hall current of photo-excited electrons and holes in the diffusion regime is different to that in the drift regime under electric field. By comparing the classical Hall effect with the inverse spin Hall effect in both diffusion and drift regime, we develop an optical method to distinguish the contributions of electrons and holes in the inverse spin Hall effect. It is found that the contribution of the inverse spin Hall effect of electrons and holes in an InGaAs/AlGaAs un-doped multiple quantum well is approximately equal at room temperature.

Ferroelectric nonlinear anomalous Hall effect in few-layer WTe2

Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials – an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a remarkable ferroelectric nonlinear anomalous Hall effect in time-reversal invariant few-layer WTe2 where nonlinear anomalous Hall current switches in odd-layer WTe2 except 1T′ monolayer while remaining invariant in even-layer WTe2 upon ferroelectric transition. This even-odd oscillation of ferroelectric nonlinear anomalous Hall effect was found to originate from the absence and presence of Berry curvature dipole reversal and shift dipole reversal due to distinct ferroelectric transformation in even and odd-layer WTe2. Our work not only treats Berry curvature dipole and shift dipole on an equal footing to account for intraband and interband contributions to nonlinear anomalous Hall effect, but also establishes Berry curvature dipole and shift dipole as new order parameters for noncentrosymmetric materials. The present findings suggest that ferroelectric metals and Weyl semimetals may offer unprecedented opportunities for the development of nonlinear quantum electronics.

A nonlinear, geometric Hall effect without magnetic field

The classical Hall effect, the traditional means of determining charge-carrier sign and density in a conductor, requires a magnetic field to produce transverse voltages across a current-carrying wire. We demonstrate a use of geometry to create transverse potentials along curved paths without any magnetic field. These potentials also reflect the charge-carrier sign and density. We demonstrate this effect experimentally in curved wires where the transverse potentials are consistent with the doping and change polarity as we switch the carrier sign. In straight wires, we measure transverse potential fluctuations with random polarity demonstrating that the current follows a complex, tortuous path. This geometrically induced potential offers a sensitive characterization of inhomogeneous current flow in thin films.

On the Thermal Activation of Conductivity Electrons in a p-Type HgTe/CdHgTe Double Quantum Well with HgTe Layers of Critical Width

The temperature dependences of the Hall coefficient and magnetoresistivity of a p-type HgTe/CdHgTe double quantum well with HgTe layers of critical thickness in the temperature range T = 35–300 K under magnetic fields up to 9 T are investigated. The position of the earlier observed reentrant quantum Hall transition from plateau i = 1 to plateau i = 2 is found to be close to the transition field from light to heavy holes with an increase in the magnetic field in the classical Hall effect. It is found that thermally activated light electrons contribute to the Hall effect along with light and heavy holes at T ≥ 35 K. The activation energy of electrons is estimated from the temperature dependence of the electron concentration as 28 meV, which exceeds the calculated value from the lateral maximum of the valence subband to the edge of the lowest conduction subband, probably because of heterostructure asymmetry.

The Classical Hall Effect in Multiply-Connected Plane Regions Part I: Topologies with Stream Function

Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. They are commonly called offset and Hall voltage. Contemporary smart Hall sensor circuits extract the Hall voltage via spinning current Hall probe schemes, thereby cancelling out the offset very efficiently. The magnetic field response of such Hall plates can be computed via the electric potential or via the stream function. Conversely, Hall plates with holes show new phenomena: 1) the stream function exists only for a limited class of multiply-connected domains, and 2) a sub-class of 1) behaves like a Hall/Anti-Hall bar configuration, i.e., no Hall voltage appears between any two points on the hole boundary if current contacts are on their outer boundary. The paper studies the requirements under which these effects occur. Canonical cases of simply and doubly connected domains are computed analytically. The focus is on 2D multiply-connected Hall plates where all boundaries are insulating and where all current contacts are point sized.

The Classical Hall Effect in Multiply-Connected Plane Regions Part II: Spiral Current Streamlines

Multiply-connected Hall plates show different phenomena than singly connected Hall plates. In part I (published in Journal of Applied Physics and Mathematics), we discussed topologies where a stream function can be defined, with special reference to Hall/Anti-Hall bar configurations. In part II, we focus on topologies where no conventional stream function can be defined, like Corbino disks. If current is injected and extracted at different boundaries of a multiply-connected conductive region, the current density shows spiral streamlines at strong magnetic field. Spiral streamlines also appear in simply-connected Hall plates when current contacts are located in their interior instead of their boundary, particularly if the contacts are very small. Spiral streamlines and circulating current are studied for two complementary planar device geometries: either all boundaries are conducting or all boundaries are insulating. The latter case means point current contacts and it can be treated similarly to singly connected Hall plates with peripheral contacts through the definition of a so-called loop stream function. This function also establishes a relation between Hall plates with complementary boundary conditions. The theory is explained by examples.

Температурная активация электронов проводимости в двойной квантовой яме HgTe/CdHgTe p-типа проводимости со слоями HgTe критической толщины

AbstractThe temperature dependences of the Hall coefficient and magnetoresistivity of a p -type HgTe/CdHgTe double quantum well with HgTe layers of critical thickness in the temperature range T = 35–300 K under magnetic fields up to 9 T are investigated. The position of the earlier observed reentrant quantum Hall transition from plateau i = 1 to plateau i = 2 is found to be close to the transition field from light to heavy holes with an increase in the magnetic field in the classical Hall effect. It is found that thermally activated light electrons contribute to the Hall effect along with light and heavy holes at T ≥ 35 K. The activation energy of electrons is estimated from the temperature dependence of the electron concentration as 28 meV, which exceeds the calculated value from the lateral maximum of the valence subband to the edge of the lowest conduction subband, probably because of heterostructure asymmetry.

Non-Markovian feature of the classical Hall effect

The classical Hall effect resulting from the impact of external magnetic and electric fields on the non-Markovian dynamics of charge carriers is studied. The dependence of the tangent of the Hall angle on the magnetic field is derived and compared with the experimental data for Zn. The method is proposed to determine experimentally the memory time in a system.

Size-dependent electrical transport properties in Co nanocluster-assembled granular films

A series of Co nanocluster-assembled films with cluster sizes ranging from 4.5 nm to 14.7 nm were prepared by the plasma-gas-condensation method. The size-dependent electrical transport properties were systematically investigated. Both of the longitudinal resistivity ({rho }_{xx}) and saturated anomalous Hall resistivity ({rho }_{xy}^{A}) continuously increased with the decrease of the cluster sizes (d). The {rho }_{xx} firstly increased and then decreased with increasing the temperature for all samples, which could be well described by involving the thermally fluctuation-induced tunneling (FIT) process and scattering. The tunneling effect was verified to result in the invalidation of classical anomalous Hall effect (AHE) scaling relation. After deducting the contribution from tunneling effect to {rho }_{xx}, the AHE scaling relation between {rho }_{xy}^{A} and the scattering resistivity ({rho }_{S}) by varying the temperature was reconstructed. The value of scaling exponent γ increased with increasing Co cluster sizes. The size dependence of γ might be qualitatively interpreted by the interface and surface-induced spin flip scattering. We also determined the scaling relation between {rho }_{xy}^{A} and {rho }_{S} at 5 K by changing the Co cluster sizes, and a large value of γ = 3.6 was obtained which might be ascribed to the surface and interfacial scattering.

Valley Hall effect and nonlocal transport in strained graphene

Graphene subject to high levels of shear strain leads to strong pseudo-magnetic fields resulting in the emergence of pseudo-Landau levels. Here we show that, with modest levels of strain, graphene can also sustain a classical valley Hall effect (VHE) that can be detected in nonlocal transport measurements. We provide a theory of the strain-induced VHE starting from the quantum Boltzmann equation. This allows us to show that, averaging over short-range impurity configurations destroys quantum coherence between valleys, leaving the elastic scattering time and inter-valley scattering rate as the only parameters characterizing the transport theory. Using the theory, we compute the nonlocal resistance of a Hall bar device in the diffusive regime. Our theory is also relevant for the study of moderate strain effects in the (nonlocal) transport properties of other two-dimensional materials and van der Walls heterostructures.

Topological order of mixed states in correlated quantum many-body systems

Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical ensembles. For a large class of quasi-thermal states, which can be realized as thermal states of some quasi-local Hamiltonian, we generalize earlier definitions of density matrix topology to generic many-body systems with strong correlations. We point out that the robustness of topological order, defined as a pattern of long-range entanglement, depends crucially on the perturbations under consideration. While it is intrinsically protected against local perturbations of arbitrary strength in an infinite closed quantum system, purely local perturbations can destroy topological order in open systems coupled to baths if the coupling is sufficiently strong. We discuss our classification scheme using the finite-temperature quantum Hall states and point out that the classical Hall effect can be understood as a finite temperature topological phase.

Temperature dependence of electron density and electron–electron interactions in monolayer epitaxial graphene grown on SiC

We report carrier density measurements and electron–electron (e–e) interactions in monolayer epitaxial graphene grown on SiC. The temperature (T)-independent carrier density determined from the Shubnikov–de Haas (SdH) oscillations clearly demonstrates that the observed logarithmic temperature dependence of the Hall slope in our system must be due to e–e interactions. Since the electron density determined from conventional SdH measurements does not depend on e–e interactions based on Kohn’s theorem, SdH experiments appear to be more reliable compared with the classical Hall effect when one studies the T dependence of the carrier density in the low T regime. On the other hand, the logarithmic T dependence of the Hall slope δRxy/δB can be used to probe e–e interactions even when the conventional conductivity method is not applicable due to strong electron–phonon scattering.

Skyrmion Hall effect

Two independent teams have demonstrated that the current-driven motion of a topological charge experiences a transverse deflection analogous to charged particles in the classical Hall effect.

Transverse optical forces for manipulating nanoparticles

We study optical forces acting on a subwavelength particle with anisotropic polarizability and discover an optomechanical effect that resembles the Hall effect for electrons. While in the classical Hall effect the transverse Lorentz force and the transverse voltage appear due to the static magnetic field which induces the nondiagonal components of the electric conductivity tensor; in our case the imaginary parts of the nondiagonal elements of the polarizability tensor are responsible for the transverse scattering force. We calculate this force for the examples of the ellipsoidal plasmonic nanoparticles and the spherical particle with gyromagnetic properties, and show that the transverse force depends on the physical origin of the anisotropy of the polarizability, and on the electromagnetic wave structure around the particle. Moreover, this force primarily occurs in the inhomogeneous field only.

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.