Hall-drift induced magnetic field instability in neutron stars

In the presence of a strong magnetic field and under conditions as realized in the crust and the superfluid core of neutron stars, the Hall drift dominates the field evolution. We show by a linear analysis that, for a sufficiently strong large-scale background field depending at least quadratically on position in a plane conducting slab, an instability occurs which rapidly generates small-scale fields. Their growth rates depend on the choice of the boundary conditions, increase with the background field strength, and may reach 10(3) times the Ohmic decay rate. The effect of that instability on the rotational and thermal evolution of neutron stars is discussed.     

Analysis of the Zeeman effect on the energy spectrum in graphenes

An analysis of the Zeeman effect with a strong external magnetic field on the energy spectrum in graphene is presented. In general, the Hamiltonian of graphene in applied electric and magnetic fields is not of SO(1, 2) invariance even in the nearest-neighbor approximation because of the Zeeman coupling. But an approximate SO(1, 2) invariance can be obtained when the applied magnetic field is very strong. This approximate invariance can be used to relate the energy structure of graphene in the presence of both electric and magnetic fields to that when there is only magnetic field. Therefore, it can help explain the recently found quantum Hall conductance (4q ²/h)L for L = 0.1.     

Motion of Charged Particle in Electric and Magnetic Fields in 3D Noncommutative Spaces and Related Problems

In three-dimensional noncommutative phase space, the energy spectrum and wave functions for the motion of a charged particle in a magnetic field are derived. Due to the momentum–momentum noncommutativity, the particle feels an effective magnetic field in a new direction. When an external electric field perpendicular to this effective magnetic field is applied, the Hall conductivity can be calculated. To get the Hall conductivity, one should define the electric currents from the probability currents in quantum mechanics rather than extending the classical electric currents to quantum mechanics directly. When the electric field is not perpendicular to the effective magnetic field, it is difficult to define the Hall conductivity.     

Galvanomagnetic phenomena in layered conductors

The dependence of the resistance and the Hall field in a layered conductor with a quasi-two-dimensional electron energy spectrum of arbitrary shape on the magnitude and orientation of the magnetic field in relation to the layers is analyzed. It is found that when current flows perpendicular to the layers, the resistance of the specimen strongly depends on the angle ϑ between the normal and the vector of a strong magnetic field. The Kapitza law is shown to hold within a fairly broad range of magnetic fields in the plane of the layers, i.e., the resistance increases linearly with the magnetic field strength. The Hall field proves to be insensitive to the emergence of open sections of the Fermi surface, and the Hall constant in strong magnetic fields is the same for any orientation of the magnetic field and the current. Zh. éksp. Teor. Fiz. 112, 618–627 (August 1997)     

Hall resistance and the diamagnetic moment of periodically modulated two-dimensional systems

It is argued that the Hall resistance of macroscopic samples can be directly obtained by ensemble averaged transport properties of mesoscopic systems. The resulting formula relates the Hall current to the part of the magnetic moment of Fermi electrons, which originates in macroscopic currents only. As one of the possible application the Hall resistance of the periodically modulated two-dimensional electron system in the strong magnetic field is briefly discussed.     

Zur anschaulichen Diskussion der qualitativen Eigenschaften der galvanomagnetischen Koeffizienten

The dependence of the different components of the conductivity resp. the resistivity tensor upon the strength and direction of an external magnetic field is discussed qualitatively. — In metals, in which the Fermi surface is simply closed, the changes in longitudinal and transversal resistance and the Hall coefficients are large if the anisotropies of the Fermi surface resp. of the scattering mechanism in the planes perpendicular to magnetic field direction are large, and vice versa. In fields, in which this effect already clearly is marked, the changes in transversal resistance in addition increase with increasing anisotropies ink-space perpendicular to Hall field direction, whereas by equal set in of current and Hall field direction the Hall coefficients now show a tendency to decrease with increasing anisotropies perpendicular to magnetic field direction. The order of Hall coefficients may change in high magnetic fields. In contrast to the changes in resistance the Hall coefficients decrease with increasing strength of magnetic field. — In the presence of open Fermi surfaces the transversal resistance doesn't saturate in the direction of the open orbits. If open orbits exist in more than one direction, saturation returns and the Hall coefficients now vanish proportional to 1/B ². In considering open Fermi surfaces it is not allowed to neglect scattering in strong magnetic fields.     

Scattering mechanism of integer quantum Hall conductance in a model system

We consider a large class of two-dimensional systems of charged particles in crossed electric and strong magnetic fields in the presence of a static substrate potentialV(x,y), which contains disorder. The time dependence of the single-particle Schroedinger functions are investigated. It is found on general grounds, that adiabatic states are dc-insulating and, that the macroscopic Hall current is carried by the non-adiabatic states. Hall conductance plateaus correspond to spectral domains, which contain only adiabatic states. The plateaus disappear, when these states become non-adiabatic at sufficiently high electric fields, i.e., at sufficiently large Hall currents. An explicit model system is investigated with a substrate potential composed of disorder and of a sequence of smooth barriers and wells. Here the non-adiabatic states can be calculated in a weak-disorder approximation, whenever the electric field (and hence the Hall current) is sufficiently low. In this case the quantum mechanical scattering process leading, to the quantisation of the Hall conductance can be understood in detail. Non-classical particle propagation plays a crucial role in this process. Our analysis opens new perspectives for the theory of the integer quantum Hall effect.     

Quantum Hall effect in intentionally disordered two‐dimensional electron systems

In this work intentionally disordered two‐dimensional electron systems in modulation doped GaAs/GaAlAs heterostructures are studied by magnetotransport experiments. The disorder is provided by a δ‐doped layer of negatively charged beryllium acceptors. In low magnetic fields a strong negative magnetoresistance is observed that can be ascribed to magnetic‐field‐induced delocalization. At increased magnetic fields the quantum Hall effect exhibits broad Hall plateaus whose centers are shifted to higher magnetic fields, i.e. lower filling factors. This shift can be explained by an asymmetric density of states. Consistently, the transition into the insulating state of quantum Hall droplets in high magnetic fields occurs at critical filling factors around ν_c=0.4, i.e. well below the value 1/2 that is expected for symmetric disorder potentials. The insulator transition is characterized by the divergence of both the longitudinal resistance as well as the Hall resistance. This is contrary to other experiments which observe a finite Hall resistance in the insulating regime and has not been observed previously. According to recent theoretical studies the divergence of the Hall resistance points to quantum coherent transport via tunneling between quantum Hall droplets. The magnetotransport experiments are supplemented by simulations of potential landscapes for random and correlated distributions of repulsive scatterers, which enable the determination of percolation thresholds, densities of states, and oscillator strengths for far‐infrared excitations. These simulations reveal that the strong shift of the Hall plateaus and the observed critical filling factor for the insulator transition in high magnetic fields require an asymmetric density of states that can only be generated by a strongly correlated beryllium distribution. Cyclotron resonance on the same samples also indicates the possibility of correlations between the beryllium acceptors.     

Electrical properties of bilayer heterojunctions in a strong magnetic field

The electrical properties of bilayer heterojunctions in a strong magnetic field at low temperatures have been considered. It has been shown that both the ohmic and Hall conductivities decrease exponentially due to the formation of neutral pairs if the electric fields in the two layers are parallel. In the antiparallel fields, the Hall conductivity is still determined by the activation energy of the excited electrons and decreases exponentially, but the ohmic conductivity decreases much slower, proportional to the temperature square.     

Magnetotransport in a semconductor superlattice with transverse magnetic field

Magnetotransport in a semiconductor superlattice (SL) under transverse magnetic field has been investigated. It is shown that in weak magnetic and electric fields there is negative magnetoresistivity along the SL layers and positive magnetoresistivity along the SL axis. The Hall resistivity is much less than the usual semiconductor value. With an increase of electric field, there appears a negative differential conductivity (NDC) along the SL layers, and the Hall voltage depends nonlinearly on current density. In higher electric field, destroying the miniband structure, the magnetoresistivity along the SL axis is negative. The magnetoresistivity along the SL axis in strong magnetic field is positive for any current density. The Hall resistivity in strong magnetic (electric) field equals the classical value.     

Electron polarizability of crystalline solids in quantizing magnetic fields and topological gap numbers

A theory of the static electron polarizability of crystals whose energy spectrum is modified by quantizing magnetic fields is presented. The polarizability is strongly affected by nondissipative Hall currents induced by the presence of crossed electric and magnetic fields: these can even change its sign. Results are illustrated in detail for a two-dimensional square lattice. The polarizability and the Hall conductivity are, respectively, linked to the two topological quantum numbers entering the so-called Diophantine equation. These numbers could in principle be detected in actual experiments.     

Linear and Nonlinear Magnetic Electron Drift Waves in a Nonuniform Strong Magnetic Field

Linear and nonlinear propagation of magnetic electron drift vortex waves in a nonuniform magnetic field is investigated by means of a generalized adiabatic law which takes into account the effect of strong fields and reduces in the appropriate limits to several well known energy conservation equations in a collisionless plasma. In the linear limit, an instability is shown to exist, whereas in the nonlinear regime, steady-state dipole vortices associated with the electron drift vortex waves may appear. The anomalous electron energy transport associated with the unstable magnetic electron drift vortex waves is investigated by means of a quasilinear theory.     

Quantum Hall states near the charge-neutral Dirac point in graphene

We investigate the quantum Hall (QH) states near the charge-neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling factors nu=+/-1 depend only on the perpendicular component of the field with respect to the graphene plane, indicating that they are not spin related. A nonlinear magnetic field dependence of the activation energy gap at filling factor nu=1 suggests a many-body origin. We therefore propose that the nu=0 and +/-1 states arise from the lifting of the spin and sublattice degeneracy of the n=0 Landau level, respectively.     

Interaction between Vacuum Arcs and Transverse Magnetic Fields with Application to Current Limitation

The interaction between diffuse vacuum arcs and magnetic fields applied transverse to the electrode axis has been investigated both theoretically and experimentally. For arc currents < 6 kA, Hall electric fields, generated by the interaction, bow the plasma out of contact with the anode and raise the arc voltage. In the presence of a parallel capacitor, the arc current falls to zero and the arc is extinguished. For arc currents of 6 to 15 kA, arc extinction can be achieved with an oscillatory magnetic field; during such extinctions the arc voltage remains in phase with the magnitude of the field. Arc extinction via magnetic field/vacuum arc interaction could have applications to ac-current limiters and dc breakers. The fault current limiter application is discussed in this paper.     

Effects of Hall Currents on the Self-Gravitational Instability of a Finitely Conducting Plasma of Variable Density

The effects of Hall currents have been studied on the hydromagnetic stability of a self-gravitating, incompressible, viscous and finitely conducting plasma of variable density. For a uniform and horizontal magnetic field which is present, it is shown that the problem is characterized by a variational principle. Making use of this, proper solutions have been obtained for a semi-infinite plasma in which the density varies one-dimensionally (exponentially) along the vertical. The dispersion relation has been solved numerically for the different values of the parameters involved. It is found that the growth rate increases with both the Hall currents and resistivity, showing thereby the destabilizing character of these effects. However, the influence of viscosity is found to be stabilizing as the growth rate decreases with viscosity.     

Some peculiarities of magnetoresistance and Hall resistance of Sb<Subscript>2</Subscript>Te<Subscript>3</Subscript> nanoplates

Antimony telluride (Sb₂Te₃) nanoplates of various thickness were grown by the vapor phase deposition method. The Hall resistance and magnetoresistance of the samples were measured in magnetic fields up to 9 T at temperatures from 2 to 300 K. Temperature dependence of the magnetoresistance and Hall resistance of the nanoplates shows a strong dependence on the thickness of the samples. Relatively thick samples show a nonlinear dependence of the Hall resistance on magnetic field. The measurement data are analyzed within the model of multi-channel transport. The difference in behavior is attributed to the existence of two channels of charge transfer with high and low mobility.     

Numerical Simulation of Plasma Edge Turbulence Due to E×B Flow Velocity Shear

A numerical code is used to study the nonlinear evolution of the Kelvin-Helmholtz instability, and the existence and time evolution of a charge separation with the self-consistent electric field at a plasma edge. Both ions and electrons are described by gyrokinetic equations that include the ions finite Larmor radius correction and the polarization drift. We present results for the case where the plasma layer is two-dimensional, and the magnetic field makes an angle very close to the normal to the plane of the plasma. At = 88.5°, the nonlinear evolution of the Kelvin-Helmholtz instability shows a spectrum which is turbulent and is dominated by higher harmonics, saturates at low level and has little effect on the electrons and ions initial equilibrium density profiles. At an angle of the magnetic field closer to 90°, when the component of the motion of the electrons along the magnetic field decreases, the behavior is in accordance with some basic physics associated with the set of equations describing the behavior of a guiding center plasma in a strong magnetic field, namely the energy condensing in the lowest k modes (inverse cascades). The results show the sensitivity of the turbulent spectrum to the motion of the electrons along magnetic field lines. In particular, we study the effect of different algorithms to compute this sensitive electrons motion, and their effect on the turbulent spectrum. We show that Eulerian Vlasov codes associated with cubic spline interpolations perform favorably when compared to other methods.     

Nonlinear simulation of a high-power, collective free-electronlaser

Results obtained with the three-dimensional nonlinear analysis and simulation code, ARACHNE, and a recent 33.4-GHz, collective, free-electron laser (FEL) amplifier experiment are compared. The experiment has demonstrated power levels of 61 MW (≈27% efficiency) without recourse to tapered magnetic fields, using a 750-keV/300-A electron beam with a nominal axial energy spread of 1.5% propagating through a cylindrical drift tube in the presence of a helical wiggler and an axial guide magnetic field. Significant differences in the character of the emission were found, depending on the direction of the guide magnetic field. When the wiggler and guide fields were parallel, observed power levels reached approximately 4 MW for both the strong and weak guide field regimes, but vanished in the neighborhood of the magnetic resonance. However, the maximum power was observed in the reversed field case when the wiggler and guide fields were antiparallel. In this case, no resonant enhancement in the transverse velocity is expected to occur; however, a significant reduction in the output power occurred in the neighborhood of the antiresonance. The ARACHNE simulation is in substantial agreement with the experiment     

Are cluster magnetic fields primordial?

We present results of a detailed and fully nonlinear numerical and analytical investigation of magnetic field evolution from the very earliest cosmic epochs to the present. We find that, under reasonable assumptions concerning the efficiency of a putative magnetogenesis era during cosmic phase transitions, surprisingly strong magnetic fields 10(-13)-10(-11) G on comparatively small scales 100 pc-10 kpc may survive to the present. Building on prior numerical work on the evolution of magnetic fields during the course of gravitational collapse of a cluster, which indicates that precollapse fields of approximately 4 x 10(-12) G extant on small scales may suffice to produce clusters with acceptable Faraday rotation measures, we argue that it seems possible for cluster magnetic fields to be entirely of primordial origin.