Three-dimensional quantum Hall effect in Weyl and double-Weyl semimetals

The well-known quantum Hall effect (QHE) was usually studied in 2D systems. In this work, we investigate the integer QHE in 3D Weyl and double-Weyl semimetals. Based on the lattice models of Weyl and double-Weyl semimetals subjected to a uniform magnetic field, we derive the generalized 3D spinfull Hofstadter Hamiltonians and Harper equations for the two systems, and obtain their corresponding energy spectra. Furthermore, we show that for proper hopping parameters and rational magnetic fluxes, both systems exhibit the 3D QHE when the Fermi level lies in some band gaps. The 3D QHE is topologically characterized by three Chern numbers with one or two nonzero Chern values which are respectively defined for three crystal planes. The possible experimental realization and detection of the 3D QHE are also discussed.     

Plasmons and polaritons in a semi-infinite plasma and a plasma slab

Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions. Known results are re-obtained in much a more direct manner and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The dielectric response and the electron energy loss are computed. The surface contribution to the energy loss exhibits an oscillatory behaviour in the transient regime near the surfaces. The propagation of an electromagnetic wave in these plasmas is treated by using the retarded electromagnetic potentials. The resulting integral equations are solved and the reflected and refracted waves are computed, as well as the reflection coefficient. For the slab we compute also the transmitted wave and the transmission coefficient. Generalized Fresnel's relations are thereby obtained for any incidence angle and polarization. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient for a semi-infinite plasma exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection). Similarly, apart from characteristic oscillations, the reflection and transmission coefficients for a plasma slab exhibit an appreciable enhancement in the damped regime.     

Reflection and refraction of the electromagnetic field in a semi-infinite plasma

We compute the reflected and refracted electromagnetic fields for an ideal semi-infinite (half-space) plasma, as well as the reflection coefficient, by using a general procedure based on equations of motion and electromagnetic potentials. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The propagation of an electromagnetic wave in plasma is treated by means of the retarded electromagnetic potentials, and the resulting integral equations are solved. Generalized Fresnel’s relations are thereby obtained for any incidence angle and polarization and the angles of total polarization and total reflection are derived. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).     

关于真空中的位移电流、Maxwell方程组、电磁场的源及Jefimenko公式的几点注记

通过分析指出：电磁场是一个不可分割的整体，Maxwell方程组是电磁场的运动方程，电磁场的源是电荷与电流的分布，Jefimenko公式是真空中Maxwell方程组的解。     

Reflected and refracted electromagnetic fields in a semi-infinite body

We compute the reflected and refracted electromagnetic fields for an ideal semi-infinite body (either a plasma or a dielectric), as well as the reflection coefficient, by using a general approach based on the polarization equation of motion and electromagnetic potentials. The method consists of representing the charge disturbances by a displacement field in the positions of the moving charges. The propagation of an electromagnetic wave in matter is treated by means of the retarded electromagnetic potentials, and the resulting integral equations are solved. Generalized Fresnel’s relations are thereby obtained for any incidence angle and polarization and the angles of total polarization and total reflection are derived (the latter for the plasma). Bulk and surface plasmon–polariton modes are also identified for the plasma. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).     

Effects of geometry and linearly polarized cavity photons on charge and spin currents in a quantum ring with spin-orbit interactions

We calculate the persistent charge and spin polarization current inside a finite-width quantum ring of realistic geometry as a function of the strength of the Rashba or Dresselhaus spin-orbit interaction. The time evolution in the transient regime of the two-dimensional (2D) quantum ring connected to electrically biased semi-infinite leads is governed by a time-convolutionless non-Markovian generalized master equation. The electrons are correlated via Coulomb interaction. In addition, the ring is embedded in a photon cavity with a single mode of linearly polarized photon field, which is polarized either perpendicular or parallel to the charge transport direction. To analyze carefully the physical effects, we compare to the analytical results of the toy model of a one-dimensional (1D) ring of non-interacting electrons with spin-orbit coupling. We find a pronounced charge current dip associated with many-electron level crossings at the Aharonov-Casher phase ΔΦ = π, which can be disguised by linearly polarized light. Qualitative agreement is found for the spin polarization currents of the 1D and 2D ring. Quantitatively, however, the spin polarization currents are weaker in the more realistic 2D ring, especially for weak spin-orbit interaction, but can be considerably enhanced with the aid of a linearly polarized electromagnetic field. Specific spin polarization current symmetries relating the Dresselhaus spin-orbit interaction case to the Rashba one are found to hold for the 2D ring, which is embedded in the photon cavity.     

Anomalous fluctuations of 2D-electron recombination radiation intensity in the quantum Hall regime

Anomalous intensity fluctuations are observed in the spectrum of radiative ecombination of quasi-two-dimensional (2D) electrons with photoexcited holes in a single quantum well. The fluctuations are observed exclusively under the conditions of the quantum Hall effect (QHE). It is shown that, if the QHE conditions are not fulfilled, the radiation intensity fluctuates strictly following the Poisson distribution 〈δN ²〉/〈N〉= 1), whereas in the QHE regime the fluctuation amplitude increases by several orders of magnitude (〈δ N ²〉/〈N〉～10²). It is demonstrated that the maxima of the emission noise amplitude coincide with the maxima of inverse magnetoresistance of 2D electrons in the QHE regime and correspond to establishing an anomalously high uniformity of the system.     

The field of a point source near planar and cylindrical boundaries of a metamaterial

The properties of the two-dimensional electromagnetic fields excited by a filamentary source located near planar and cylindrical boundaries of bodies made of metamaterials with their permittivity and permeability close to minus one are considered. The subwavelength field localization effects, the phenomena associated with the resonances of surface waves, and the nonresonant field enhancement effects are investigated.     

读“等效的磁荷观点”有感

文章在假想的“磁荷世界”中修改了麦克斯韦方程组和洛伦兹力公式.由磁的库仑定律出发,并根据磁荷与电荷产生的电磁场的等效性,得到真空中静磁场的高斯定理和环路定理.仿照“电荷世界”中的电流定义了磁流强度,又根据磁场的相对论变换,由毕奥—萨伐尔定律和法拉第电磁感应定律得到稳恒电场D的高斯定理和环路定理.     

Some uniqueness results for stationary solutions to the Maxwell-Born-Infeld field equations and their physical consequences

Uniqueness is established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell-Born-Infeld equations in boundary-free space under the condition that either the charge or current density vanishes. In addition, it is also shown that the simpler Maxwell-Born equations admit at most one stationary finite-energy electromagnetic field solution, without the above condition. In these theories of electromagnetism the following physical consequences emerge: source-free field solitons moving at speeds less than the vacuum speed of light c do not exist; any electrostatic (resp. magnetostatic) field is the unique stationary electromagnetic field for the same current-density-free (resp. charge-density-free) sources. These results put to rest some interesting speculations in the physics literature.     

Electromagnetic response in kinetic energy driven cuprate superconductors: Linear response approach

Within the framework of the kinetic energy driven superconductivity, the electromagnetic response in cuprate superconductors is studied in the linear response approach. The kernel of the response function is evaluated and employed to calculate the local magnetic field profile, the magnetic field penetration depth, and the superfluid density, based on the specular reflection model for a purely transverse vector potential. It is shown that the low temperature magnetic field profile follows an exponential decay at the surface, while the magnetic field penetration depth depends linearly on temperature, except for the strong deviation from the linear characteristics at extremely low temperatures. The superfluid density is found to decrease linearly with decreasing doping concentration in the underdoped regime. The problem of gauge invariance is addressed and an approximation for the dressed current vertex, which does not violate local charge conservation is proposed and discussed.     

DC corona discharge ozone production enhanced by magnetic field

We have studied the effect of a stationary magnetic field on the production of ozone from air at atmospheric pressure by a negative corona discharge in a cylindrical electrode configuration. We used a stainless steel hollow needle placed at the axis of the cylindrical discharge chamber as a cathode. The outer wall of the cylinder was used as an anode. The vector of magnetic induction was perpendicular to the vector of current density. We found that: (a) the magnetic field extends the current voltage range of the discharge; (b) for the discharge in the Trichel pulses regime and in the pulseless glow regime, the magnetic field has no substantial effect on the discharge voltage or on the concentration of ozone that is produced; (c) for the discharge in the filamentary streamer regime for a particular current, the magnetic field increases the discharge voltage and consequently an approximately 30% higher ozone concentration can be obtained; (d) the magnetic field does not substantially increase the maximum ozone production yield. A major advantage of using a magnetic field is that the increase in ozone concentration produced by the discharge can be obtained without additional energy requirements.     

Imaging of Coulomb-driven quantum Hall edge states

The edges of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime are divided into alternating metallic and insulating strips, with their widths determined by the energy gaps of the QHE states and the electrostatic Coulomb interaction. Local probing of these submicrometer features, however, is challenging due to the buried 2DEG structures. Using a newly developed microwave impedance microscope, we demonstrate the real-space conductivity mapping of the edge and bulk states. The sizes, positions, and field dependence of the edge strips around the sample perimeter agree quantitatively with the self-consistent electrostatic picture. The evolution of microwave images as a function of magnetic fields provides rich microscopic information around the ν=2 QHE state.     

The probe technique far from equilibrium: Magnetic field symmetries of nonlinear transport

The probe technique is a simple mean to incorporate elastic and inelastic processes into quantum transport problems. Using numerical simulations, we demonstrate that this tool can be employed beyond the analytically tractable linear response regime, providing a stable solution for the probe parameters: temperature and chemical potential. Adopting four probes: dephasing, voltage, temperature, and voltage-temperature, mimicking different elastic and inelastic effects, we provide a systematic analysis of magnetic field and gate voltage symmetries of charge current and heat current in Aharonov-Bohm interferometers, potentially far from equilibrium. Considering electron current, we prove that in the linear response regime inelastic scattering processes do not break the Onsager symmetry. Beyond linear response, even (odd) conductance terms obey an odd (even) symmetry with the threading magnetic flux, as long as the system acquires a spatial inversion symmetry. When spatial asymmetry is introduced, particle-hole symmetry assures that nonlinear conductance terms maintain certain symmetries with respect to magnetic field and gate voltage. These analytic results are supported by numerical simulations. Analogous results are obtained for the electron heat current. Finally, we demonstrate that a double-dot Aharonov-Bohm interferometer can act as a charge rectifier when two conditions are met simultaneously: (i) many-body effects are included, here in the form of inelastic scattering; and (ii) time reversal symmetry is broken.     

Playing with quantum Hall effects and single-electron-tunneling effects

The usefulness of quantum Hall effect (QHE) conductors and quantum dot (QD) devices is revealed by reviewing five remarkable effects. The first is the sensitive detection of terahertz (THz) radiation by QHE conductors. The second is the imaging of THz emission from non-equilibrium carriers in QHE conductors, by using scanning THz microscopes. The third is the single-photon detection of THz radiation in strong magnetic fields, which is carried out by incorporating a QHE electron system into a QD. Individual events of single-THz-photon absorption within the QD via cyclotron resonance cause the QD to electrically polarize, which, in turn, is detected as switches of the tunnel conductance through the QD. The fourth is the single-photon detection of THz radiation by using double QDs in the absence of a magnetic field. Both of the photon detectors are implemented in gate-voltage-induced lateral GaAs/AlGaAs QDs, and exploiting the extraordinary sensitivity of single-electron transistors to the charge. The fifth is the coherent control of nuclear spins in QHE conductors. Nuclear spins are (i) electrically polarized by unequally populating spin-split QHE edge channels via the hyperfine interaction, (ii) coherently controlled via pulsed nuclear magnetic resonance induced by local RF magnetic fields, and (iii) finally detected by the edge channels through resistance change of the Hall device. The controlled nuclear spins are limited to those along the edge channels, on the order of 10⁹.     

QHE and far infra-red properties of bilayer graphene in a strong magnetic field

We describe the quantum Hall effect (QHE) and far infra-red (FIR) absorption properties of bilayer graphene in a strong magnetic field and contrast them with the weak field regime. This includes a derivation of the effective low energy Hamiltonian for this system and the consequences of this Hamiltonian for the sequencing of the Landau levels in the material: The form of this effective Hamiltonian gives rise to the presence of a level with doubled degeneracy at zero energy. The effect of a potential difference between the layer of a bilayer is also investigated. It is found that there is a density-dependent gap near the K points in the band structure. The consequences of this gap on the QHE are then described. Also, the magneto-absorption spectrum is investigated and an experiment proposed to distinguish between model ground states of the bilayer quantum Hall effect system based on the different absorption characteristics of right-handed and left-handed polarisation of FIR light. Finally, the effects of trigonal warping are taken into account in the absorption picture.     

粒子模拟场致发射边界的实现

简单地介绍了Marder提出的伪电流修正方法.这种方法可以迅速有效地消除空间网格上电流分配方法带来的电荷误差.在此种方法的基础上,给出了粒子模拟场致发射边界的实现算法,并进行了等离子体融断开关的模拟研究.     

Use of the BFCPIC and BFCRAY codes to describe space charge limited emission in electron guns for gyrotrons

Numerical modelling of an electron gun in the space charge limited regime requires determining the current density distribution as well as the electric fields and electron trajectories. This is a rather complicated self-consistent problem, since the space charge influences the electric field, which in turn influences the electron trajectories. Previous simulations of magnetron electron guns using the BFCPIC and BFCRAY codes used a simple emission model (constant current density) that is approximately valid for thermionic emission. The code has been modified to include space charge limited emission. Several different ways of doing this are considered. One of the models considered uses Gauss’s law to force the electric field on the emitter to vanish; it was used in the original version of BFCPIC for the simulation of ion diodes. A second is based on the use of Child’s law (locally), which may be more appropriate for extension to fully electromagnetic particle-in-cell (PIC) codes. Calculations were performed with both models, and the results compared with each other and with experiments performed at FZK.