Current Charge Distribution Research Articles

Probing optical anapoles with fast electron beams

Optical anapoles are intriguing charge-current distributions characterized by a strong suppression of electromagnetic radiation. They originate from the destructive interference of the radiation produced by electric and toroidal multipoles. Although anapoles in dielectric structures have been probed and mapped with a combination of near- and far-field optical techniques, their excitation using fast electron beams has not been explored so far. Here, we theoretically and experimentally analyze the excitation of optical anapoles in tungsten disulfide (WS2) nanodisks using Electron Energy Loss Spectroscopy (EELS) in Scanning Transmission Electron Microscopy (STEM). We observe prominent dips in the electron energy loss spectra and associate them with the excitation of optical anapoles and anapole-exciton hybrids. We are able to map the anapoles excited in the WS2 nanodisks with subnanometer resolution and find that their excitation can be controlled by placing the electron beam at different positions on the nanodisk. Considering current research on the anapole phenomenon, we envision EELS in STEM to become a useful tool for accessing optical anapoles appearing in a variety of dielectric nanoresonators.

Exploring Locality in Molecular Dirac-Coulomb-Breit Calculations: A Perspective.

The Dirac-Coulomb-Breit (DCB) operator is widely recognized for its ability to accurately capture relativistic effects and spin-physics in molecular calculations. However, due to its high computational cost, there is a need to develop low-scaling approximations without compromising accuracy. To tackle this challenge, it becomes essential to gain a deeper understanding of the DCB operator's behavior. This work aims to explore local integral approximations, shedding light on the locality of the parts of the charge-current distribution due to the small component. In particular, we propose an atomic Breit approximation that leverages an analysis of the behavior observed in a series of gold chains. Through benchmark studies of metal complexes, we evaluated the accuracy and performance of the proposed atomic Breit approximation. This work provides a comprehensive understanding of the behavior of the charge-current distribution in terms of its contributions from its AO basis constituents, facilitating the development of low-scaling methods that strike a balance between computational efficiency and accuracy.

Multipolar quantum electrodynamics of localized charge-current distributions: Spectral theory and renormalization

We formulate a nonrelativistic quantum field theory to model interactions between quantized electromagnetic fields and localized charge-current distributions. The electronic degrees of freedom are encoded in microscopic polarization and magnetization field operators whose moments are identified with the multipole moments of the charge-current distribution. The multipolar Hamiltonian is obtained from the minimal coupling Hamiltonian through a unitary transformation, often referred to as the Power-Zienau-Woolley transformation; we renormalize this Hamiltonian using perturbation theory, the result of which is used to compute the leading-order radiative corrections to the electronic energy levels due to interactions between the electrons and quantum vacuum fluctuations in the electromagnetic field. Our renormalized energy shift constitutes a generalization of the Lamb shift in atomic hydrogen, valid for general localized assemblies of atoms and molecules, possibly with net charge but absent a free current. By expanding the fields in a series of multipole moments, our results can be used to study contributions to this energy shift coming from specific multipole moments of arbitrary order.

Dynamic toroidizability as ubiquitous property of atoms and molecules in optical electric fields.

The continuous search for metamaterials with special properties, suitable for new technological applications, is presently being driven by a preceding theoretical development, which took place after the introduction of new physical entities, anapole and a family of toroidal multipoles, having a border in common with those considered in the more familiar electric and magnetic multipole expansions. The related concept of toroidization, i.e., toroidal moment per unit volume, has been advocated in analogy to electric polarization and magnetization operated by electromagnetic fields and should be considered on the same footing regarding its relevance and practicality for understanding certain properties, e.g., ferrotoroidicity in condensed matter physics, and for rationalizing the behavior of charge-current distributions that neither radiate nor interact with external fields in classical and quantum electrodynamics. Toroidizability, i.e., the ability of sustaining toroidal moments, can also be defined by an analogy with electric polarizability and magnetizability. The present study shows that such a property is general and characterizes atoms and molecules and that the optical electric field of a light beam induces an oscillating anapole moment, i.e., the superposition of toroidal moment with an electric dipole moment. However, values of anapole polarizabilities induced by monochromatic light, estimated by time-dependent perturbation theory for rare gas atoms and a few molecules, are quite small and possibly hard to detect experimentally.

Disentangling Spin, Anomalous, and Planar Hall Effects in Ferromagnet–Heavy-Metal Nanostructures

Ferromagnetic (FM)/heavy metal (HM) nanostructures can be used for the magnetic state readout in the proposed magneto-electric spin-orbit logic by locally injecting a spin-polarized current and measure the spin-to-charge conversion via the spin Hall effect. However, this local configuration is prone to spurious signals. In this work, we address spurious Hall effects that can contaminate the spin Hall signal in these FM/HM T-shaped nanostructures. The most pronounced Hall effects in our Co50Fe50/Pt nanostructures are the planar Hall effect and the anomalous Hall effect generated in the FM nanowire. We find that the planar Hall effect, induced by misalignment between magnetization and current direction in the FM wire, is manifested as a shift in the measured baseline resistance, but does not alter the spin Hall signal. In contrast, the anomalous Hall effect, arising from the charge current distribution within the FM, adds to the spin Hall signal. However, the effect can be made insignificant by minimizing the shunting effect via proper design of the device. We conclude that local spin injection in FM/HM nanostructures is a suitable tool for measuring spin Hall signals and, therefore, a valid method for magnetic state readout in prospective spin-based logic.

Nonradiating anapole states in nanophotonics: from fundamentals to applications

Nonradiating sources are nontrivial charge–current distributions that do not generate fields outside the source domain. The pursuit of their possible existence has fascinated several generations of physicists and triggered developments in various branches of science ranging from medical imaging to dark matter. Recently, one of the most fundamental types of nonradiating sources, named anapole states, has been realized in nanophotonics regime and soon spurred considerable research efforts and widespread interest. A series of astounding advances have been achieved within a very short period of time, uncovering the great potential of anapole states in many aspects such as lasing, sensing, metamaterials, and nonlinear optics. In this review, we provide a detailed account of anapole states in nanophotonics research, encompassing their basic concepts, historical origins, and new physical effects. We discuss the recent research frontiers in understanding and employing optical anapoles and provide an outlook for this vibrant field of research.

Analytic calculation of radio emission from parametrized extensive air showers: A tool to extract shower parameters

The radio intensity and polarization footprint of a cosmic-ray induced extensive air shower is determined by the time-dependent structure of the current distribution residing in the plasma cloud at the shower front. In turn, the time dependence of the integrated charge-current distribution in the plasma cloud, the longitudinal shower structure, is determined by interesting physics which one would like to extract such as the location and multiplicity of the primary cosmic-ray collision or the values of electric fields in the atmosphere during thunderstorms. To extract the structure of a shower from its footprint requires solving a complicated inverse problem. For this purpose we have developed a code that semi-analytically calculates the radio footprint of an extensive air shower given an arbitrary longitudinal structure. This code can be used in a optimization procedure to extract the optimal longitudinal shower structure given a radio footprint. On the basis of air-shower universality we propose a simple parametrization of the structure of the plasma cloud. This parametrization is based on the results of Monte-Carlo shower simulations. Deriving the parametrization also teaches which aspects of the plasma cloud are important for understanding the features seen in the radio-emission footprint. The calculated radio footprints are compared with microscopic CoREAS simulations.

Inclined Pulsar Magnetospheres in General Relativity: Polar Caps for the Dipole, Quadrudipole, and Beyond

Abstract In the canonical model of a pulsar, rotational energy is transmitted through the surrounding plasma via two electrical circuits, each connecting to the star over a small region known as a “polar cap.” For a dipole-magnetized star, the polar caps coincide with the magnetic poles (hence the name), but in general, they can occur at any place and take any shape. In light of their crucial importance to most models of pulsar emission (from radio to X-ray to wind), we develop a general technique for determining polar cap properties. We consider a perfectly conducting star surrounded by a force-free magnetosphere and include the effects of general relativity. Using a combined numerical-analytical technique that leverages the rotation rate as a small parameter, we derive a general analytic formula for the polar cap shape and charge-current distribution as a function of the stellar mass, radius, rotation rate, moment of inertia, and magnetic field. We present results for dipole and quadrudipole fields (superposed dipole and quadrupole) inclined relative to the axis of rotation. The inclined dipole polar cap results are the first to include general relativity, and they confirm its essential role in the pulsar problem. The quadrudipole pulsar illustrates the phenomenon of thin annular polar caps. More generally, our method lays a foundation for detailed modeling of pulsar emission with realistic magnetic fields.

Novel Power Allocation Method to Distribute the Working Current of Parallel-Connected Lithium-Ion Battery Packs

Owing to the growing environmental awareness, finding alternative energy sources of petroleum has become an important issue. Out of the total petroleum consumption, vehicle transportation accounts for up to half of it. Therefore, electric vehicles have swept the globe, and lithium-ion battery is among the best electric energy-storage candidates because of its high working voltage, high energy density, and long cycle life without memory effect. For high power equipment, a battery pack which is composed of large number of batteries in series and parallel is necessary. However, after cyclic charging and discharging loops, the uniformity in the parallel-connected battery pack is destroyed; consequently, electrical current appears in the pack between any two batteries with potential difference. Therefore, it can be easily expected that analysis of paralleled batteries becomes more and more complicated while the number of batteries increases. For example, in a set of 100 parallel-connected batteries, 4950 directional branch currents are needed to be manipulated to satisfy Kirchhoff Circuit Laws. Obviously, heavy computational load makes the analysis of mass batteries based on the electrochemical model impossible. In this study, we propose a novel solution in combination with the ESP (enhanced single particle) model as proposed in Ref. [1] to enable an electrochemical analysis even with a huge amount of batteries in the pack. The main idea of the novel solution originates from the “power allocation”, which means that when an electron leaving a certain battery owns a larger kinetic energy, the current dedicated by this battery accounts for a higher proportion of the total output current. Since the kinetic energy of an electron amounts to the electrical potential difference, the current distribution of a certain battery k in a parallel-connected battery pack with a total of n batteries can be assumed to be Eq.(1), where is the summation of equilibrium currents between the battery k and all the other batteries, and it can be obtained from the view of electrical work as Eq. (2), where is a weighting factor which is related to the convergence. Accordingly, the working current of the battery k at the next time interval () can be calculated from the current and voltage information at the time t, i.e., Eq. (3). From the simulated discharge-charge curve shown in Fig. 1, it can be seen that by employing this method, the working voltage of the parallel-connected battery pack with 100S120P reaches the same in a dozens of time steps. The corresponding discharge and charge current distributions within each parallel string are presented in Fig. 2 and 3, respectively. This method finds an approximate solution instead of the exact solution from KCL, however, the deviation of the result is only within 10-3~10-5 volt, which is a tolerable error range. REFERENCES [1] N. Baba, H. Yoshida, M. Nagaoka, C. Okuda, and S. Kawauchi, J. Power Sources, 252, 214 (2014). Figure 1

Current distributions in stripe Majorana junctions

We calculate current and density distributions in stripe (2D planar) junctions between normal and Majorana nanowires having a finite ($y$) transverse length. In presence of a magnetic field with vertical and in-plane components, the $y$-symmetry of the charge current distribution in the normal lead changes strongly across the Majorana phase transition: from center-symmetric if a Majorana mode is present to laterally-shifted (as expected by the Hall effect) if the field is tilted such as to destroy the Majorana mode due to the projection rule. We compare quasi-particle and charge distributions of current and density, as well as spin magnetizations. The Majorana mode causes opposite spin accumulations on the junction and the emergence of a spin current.

Persistent Hall voltages across thin planar charged quantum rings on the surface of a three-dimensional topological insulator

We study theoretically, the electromagnetic response due to localized charge current distributions above a topological insulator (coated with a thin ferromagnetic layer) using the electromagnetic duality symmetry. We show that the localized current induces an electric field which depends on the current —this is a manifestation of the topological magnetoelectric (TME) effect. We also show that if the charge carriers have spin, then they acquire Aharanov-Casher phases which depend on the current. As an application, we consider thin planar charged quantum rings with persistent currents on the surface of a TI and show that the TME manifests itself as persistent Hall voltages across the charged ring. If the spin is also taken into account, then persistent spin Hall voltages develop across the ring.

Response to “Comment on ‘The electromagnetic momentum of static charge-current distributions’ [Am. J. Phys. 83, 279 (2015)

Response to “Comment on ‘The electromagnetic momentum of static charge-current distributions’ [Am. J. Phys. <b>83</b>, 279 (2015)

The electromagnetic momentum of static charge-current distributions

The origin of electromagnetic momentum for general static charge-current distributions is examined. The electromagnetic momentum for static electromagnetic fields is derived by implementing conservation of momentum for the sum of mechanical momentum and electromagnetic momentum. The external force required to keep matter at rest during the production of the final static configuration produces the electromagnetic momentum. Examples of the electromagnetic momentum in static electric and magnetic fields are given. The center-of-energy theorem is shown to be violated by electromagnetic momentum. Hidden momentum is shown to be generally absent and not to cancel electromagnetic momentum.

Statistics of charge transfer through impurities in strongly correlated 1D metals

We study the counting statistics of charge transport in the Anderson impurity model (AIM) employing both Keldysh perturbation theory in a Fermi liquid picture and the Bethe ansatz. In the Fermi liquid approach, the object of our principal interest is the generating function for the cumulants of the charge current distribution. We derive an exact analytic formula relating the full counting statistic (FCS) generating function to the self-energy of the system in the presence of a measuring field. We first check that our approach reproduces correctly known results in simple limits, like the FCS of the resonant level system (AIM without Coulomb interaction). We then proceed to study the FCS for the AIM perturbatively in the Coulomb interaction. By comparing this perturbative analysis with a strong coupling expansion, we arrive at a conjecture for an expression for the FCS generating function at 𝒪(V3) (V is the voltage across the impurity) valid at all orders in the interaction. In the second part of the article, we examine a Bethe ansatz analysis of the current noise for the AIM. Unlike the Fermi liquid approach, here the goal is to obtain qualitative, not quantitative, results for a wider range of voltages both in and out of a magnetic field. Particularly notable are finite field results showing a double peaked structure in the current noise for voltages satisfying eV ∼ μB H. This double peaked structure is the “smoking gun” of Kondo physics in the current noise and is directly analogous to the single peak structure predicted in the differential conductance of the AIM.

Counting statistics for the Anderson impurity model: Bethe ansatz and Fermi liquid study*

AbstractWe study the counting statistics of charge transport in the Anderson impurity model (AIM) employing both Keldysh perturbation theory in a Fermi liquid picture and the Bethe ansatz. In the Fermi liquid approach, the object of our principal interest is the generating function for the cumulants of the charge current distribution. We derive an exact analytic formula relating the full counting statistic (FCS) generating function to the self‐energy of the system in the presence of a measuring field. We first check that our approach reproduces correctly known results in simple limits, like the FCS of the resonant level system (AIM without Coulomb interaction). We then proceed to study the FCS for the AIM perturbatively in the Coulomb interaction. By comparing this perturbative analysis with a strong coupling expansion, we arrive at a conjecture for an expression for the FCS generating function at 𝒪(V3) (V is the voltage across the impurity) valid at all orders in the interaction. In the second part of the article, we examine a Bethe ansatz analysis of the current noise for the AIM. Unlike the Fermi liquid approach, here the goal is to obtain qualitative, not quantitative, results for a wider range of voltages both in and out of a magnetic field. Particularly notable are finite field results showing a double peaked structure in the current noise for voltages satisfying eV ∼ μB H. This double peaked structure is the “smoking gun” of Kondo physics in the current noise and is directly analogous to the single peak structure predicted in the differential conductance of the AIM.

Counting statistics for the Anderson impurity model: Bethe ansatz and Fermi liquid study

We study the counting statistics of charge transport in the Anderson impurity model (AIM) employing both Keldysh perturbation theory in a Fermi liquid picture and the Bethe ansatz. In the Fermi liquid approach, the object of our principal interest is the generating function for the cumulants of the charge current distribution. We derive an exact analytic formula relating the full counting statistic (FCS) generating function to the self-energy of the system in the presence of a measuring field. We first check that our approach reproduces correctly known results in simple limits, like the FCS of the resonant level system (AIM without Coulomb interaction). We then proceed to study the FCS for the AIM perturbatively in the Coulomb interaction. By comparing this perturbative analysis with a strong coupling expansion, we arrive at a conjecture for an expression for the FCS generating function at O(V^3) (V is the voltage across the impurity) valid at all orders in the interaction. In the second part of the article, we examine a Bethe ansatz analysis of the current noise for the AIM. Unlike the Fermi liquid approach, here the goal is to obtain qualitative, not quantitative, results for a wider range of voltages both in and out of a magnetic field. Particularly notable are finite field results showing a double peaked structure in the current noise for voltages satisfying eV ~ mu H$. This double peaked structure is the ``smoking gun'' of Kondo physics in the current noise and is directly analogous to the single peak structure predicted for the differential conductance of the AIM.

Full counting statistics for transport through a molecular quantum dot magnet: Incoherent tunneling regime

Full counting statistics (FCS) for the transport through a molecular quantum dot magnet is studied theoretically in the incoherent tunneling regime. We consider a model describing a single-level quantum dot, magnetically coupled to an additional local spin, the latter representing the total molecular spin s. We also assume that the system is in the strong Coulomb blockade regime, i.e., double occupancy on the dot is forbidden. The master equation approach to FCS introduced in Ref. [12] is applied to derive a generating function yielding the FCS of charge and current. In the master equation approach, Clebsch-Gordan coefficients appear in the transition probabilities, whereas the derivation of generating function reduces to solving the eigenvalue problem of a modified master equation with counting fields. To be more specific, one needs only the eigenstate which collapses smoothly to the zero-eigenvalue stationary state in the limit of vanishing counting fields. We discovered that in our problem with arbitrary spin s, some quartic relations among Clebsch-Gordan coefficients allow us to identify the desired eigenspace without solving the whole problem. Thus we find analytically the FCS generating function in the following two cases: i) both spin sectors lying in the bias window, ii) only one of such spin sectors lying in the bias window. Based on the obtained analytic expressions, we also developed a numerical analysis in order to perform a similar contour-plot of the joint charge-current distribution function, which have recently been introduced in Ref. [13], here in the case of molecular quantum dot magnet problem.

Liouville and Fokker–Planck dynamics for classical plasmas and radiation

We consider a nonequilibrium statistical system formed by many classical non-relativistic particles of opposite electric charges (plasma) and by the classical dynamical electromagnetic (EM) field. The charges interact with one another directly through instantaneous Coulomb potentials and with the dynamical degrees of freedom of the transverse EM field. The system may also be subject to external influences of: i) either static, but spatially inhomogeneous, electric and magnetic fields (case 1)), or ii) weak distributions of electric charges and currents (case 2)). The particles and the dynamical EM field are described, for any time t > 0, by the classical phase-space probability distribution functional (CPSPDF) f and, at the initial time (t = 0), by the initial CPSPDF fin. The CPSPDF f and fin, multiplied by suitable Hermite polynomials (for particles and field) and integrated over all canonical momenta, yield new moments. The Liouville equation and fin imply a new nonequilibrium linear infinite hierarchy for the moments. In case 1), fin describes local equilibrium but global nonequilibrium, and we propose a long-time approximation in the hierarchy, which introduces irreversibility and relaxation towards global thermal equilibrium. In case 2), the statistical system, having been at global thermal equilibrium, without external influences, for t ≤ 0, is subject to weak external charge-current distributions: then, new hierarchies for moments and their long-time behaviours are discussed in outline. As examples, approximate mean-field (Vlasov) approximations are treated for both cases 1) and 2).

Towards full counting statistics for the Anderson impurity model

We analyze the full counting statistics (FCS) of the charge transport through the Anderson impurity model (AIM) and similar systems with a single conducting channel. The object of principal interest is the generating function for the cumulants of charge current distribution. We derive an exact analytic formula relating the FCS generating function to the self energy of the system in the presence of the measuring field. We first check that our approach reproduces correctly known results in simple limits, such as the FCS of the resonant level system (AIM without Coulomb interaction). We then proceed to study the FCS for the AIM both perturbatively in the Coulomb interaction and in the Kondo regime at the Toulouse point (we also study a related model of a spinless single-site quantum dot coupled to two half-infinite metallic leads in the Luttinger liquid phase at a special interaction strength). At zero temperature the FCS turns out to be binomial for small voltages. For the generic case of arbitrary energy scales the FCS is shown to be captured very well by generalizations of the Levitov-Lesovik type formula. Surprisingly, the FCS for the AIM indicates a presence of coherent electron pair tunnelling in addition to conventional single-particle processes. By means of perturbative expansions around the Toulouse point we succeeded in showing the universality of the binomial FCS at zero temperature in linear response. Based on our general formula for the FCS we then argue for a more general binomial theorem stating that the linear response zero-temperature FCS for any interacting single-channel setup is always binomial.

Full Counting Statistics for the Kondo Dot

The generating function for the cumulants of charge current distribution is calculated for two generalized Majorana resonant level models: the Kondo dot at the Toulouse point and the resonant level embedded in a Luttinger liquid with the interaction parameter g=1/2. We find that the low-temperature nonequilibrium transport in the Kondo case occurs via tunneling of physical electrons as well as by coherent transmission of electron pairs. We calculate the third cumulant ("skewness") explicitly and analyze it for different couplings, temperatures, and magnetic fields. For the g=1/2 setup the statistics simplifies and is given by a modified version of the Levitov-Lesovik formula.