Domain walls in three-dimensional Weyl semimetals, formed by localized magnetic moments, are investigated. There appear bound states around the domain wall with the discrete spectrum, among which we find "Fermi arc" states with the linear dispersion. The Fermi arc modes contribute to the electric charge and current localized at the domain wall, which reveal a universal behavior depending only on chemical potential and the splitting of the Weyl nodes. This equilibrium current can be traced back to the chiral magnetic effect, or the edge counterpart of the anomalous Hall effect in the bulk. We propose a new way to manipulate the motion of the domain wall, accompanied with the localized charge, by applying an external electric field.

In order to study the temporal and regional variation of lightning occurrences and their relation to sprite activity and climate variability, we have analysed the 1–100 Hz ELF magnetic field waveform data obtained at the Syowa station in Antarctica, Onagawa in Japan and Esrange in Sweden for a one year period from September 2003 to August 2004. We have selected totally 1.7 × 105 events of transient Schumann resonances from the ELF magnetic field data whose amplitude exceeds 40 pT at all stations. Then, the lightning locations are estimated by a triangulation method with an estimation error of 0.5 Mm. It is found that in the summer season (from June to August) the lightning occurrence rates are higher in the northern hemisphere than in the southern hemisphere with large enhancements in North America, South-East Asia and the northern part of Africa. On the other hand, in the winter season (from December to February) these rates are higher in the southern hemisphere with large enhancements in South America, Australia and the southern part of Africa. These features are consistent with the results of global lightning measurements from space conducted by the Optical Transient Detector and the Tropical Rainfall Measuring Mission satellite. Then, we have also calculated the charge moment value (Q · dl) of lightning discharges using ELF magnetic field waveform data and have estimated the distribution function of charge moments for positive cloud-to-ground (+CG) discharges and for negative cloud-to-ground (−CG) discharges. It is found that the shape of the distribution function for both +CG and −CG discharges is almost the same for all seasons and that the distribution function of −CG discharges has a steeper slope at high Q · dl than that of +CG discharges.

[1] Although the Quasi-electrostatic (QE) model has been considered a basic mechanism for describing sprite generation, the relationship between sprite luminosity and the charge moment change (CMC) value, caused by the sprites' parent lightning has not been examined quantitatively. CMC value represents the energy of cloud-to-ground discharge (CG) and the electric field intensity above the thunderstorm. We focused on the data obtained in 2004, in which both ISUAL on board the FORMOSAT-2 satellite and the Tohoku ELF network were operated throughout one year. We could estimate the absolute luminous intensity of sprites free from atmospheric influence with the ISUAL/Array Photometer (AP) and investigated its relationship to the charge moment of parent lightning. Absolute optical energies emitted from sprites were estimated for 14 streamer-type sprites for the first time. The averages of the time-integrated optical energies are 176 kJ and 119 kJ for the N2 1PG and N2 2PG bands, respectively. Furthermore, the optical energies and the charge moments of their parent lightning estimated with ELF data show a high correlation (correlation coefficient = 0.93), that is consistent, qualitatively, with the QE model. This relationship predicts that the 50% occurrence probability is located at ∼600 C km, which coincides with previous statistical studies. Citation: Takahashi, Y., et al. (2010), Absolute optical energy of sprites and its relationship to charge moment of parent lightning discharge based on measurement by ISUAL/AP,

We numerically investigate the electronic properties of magnetic domain walls formed in a Weyl semimetal. Electric charge distribution is computed from the electron wave functions, by numerically diagonalizing the Hamiltonian under several types of domain walls. We find a certain amount of electric charge localized around the domain wall, depending on the texture of the domain wall. This localized charge stems from the degeneracy of Landau states under the axial magnetic field, which corresponds to the curl in the magnetic texture. The localized charge enables one to drive the domain wall motion by applying an external electric field without injecting an electric current, which is distinct from the ordinary spin-transfer torque and is free from Joule heating. arXiv:1805.00383v1 [cond-mat.mes-hall] 1 May 2018