Weyl Electrons Research Articles

Weyl disks: Theoretical prediction

A variety of quantum systems exhibits Weyl points in their spectra where two bands cross in a point of three-dimensional parameters space with conical dispersion in the vicinity of the point. We consider theoretically the soft constraint regime where the parameters are dynamical quantum variables. We have shown that in general the soft constraints, in quasi-classical limit, result in Weyl discs where two states are (almost) degenerate in a finite 2d region of the 3d parameter space. We provide concrete calculations for two setups: Weyl point in a four-terminal superconducting structure and a Weyl exciton, i.e., a bound state of Weyl electron and a massive hole.

Corrections to the magnetoresistance formula for semimetals with Dirac electrons: the Boltzmann equation approach validated by the Kubo formula

The magnetoresistance (MR) in semimetals with Dirac (or Weyl) electrons and free holes is investigated on the basis of the Boltzmann theory. The MR is modified from the conventional results with free electrons and holes in a very complex way due to the correction of the Dirac dispersion. The obtained formula explicitly includes the magnetic field dependence, which is very useful for the analysis of experimental results. In order to verify the validity of our results, the results obtained by the Boltzmann approach are compared with those by the Kubo theory. It is revealed that, by taking into account the field dependence of carrier density, the MR obtained by the Boltzmann theory almost perfectly agrees with that based on the Kubo theory even in the high-field region (in the quantum limit) except for the quantum oscillations. It is also shown that the MR in semimetals increases linearly with respect to the field in the quantum limit due to the drastic change of the carrier density, which is a significant characteristic of semimetals.

Surface plasmons in Weyl semimetals

The surface plasmon excitation spectrum is calculated for the Weyl semimetal within the random phase approximation. Recently, a surface plasmon mode has been predicted to exist at the three-dimensional Dirac semimetal surface due to the Dirac plasmon mode in the bulk. In addition, Weyl semimetals possess Fermi arc electron states on their surfaces resulting in an anisotropic Fermi arc plasmon mode. In the present work we consider the modification of the surface plasmon mode due to the Fermi arc plasmon mode. We introduce an effective surface dielectric function of Fermi arc electrons which comprises the Fermi arc plasmon mode and the surface dielectric function that determines the bare surface plasmon mode present due to the plasmon mode in the bulk from Weyl electrons. As a result, we obtain the dispersion of the renormalized surface plasmon mode from the effective surface dielectric function. We find that a renormalization of the bare surface plasmon mode increases with increases in the Fermi arc plasmon frequency. The obtained spectrum will be useful for experimentally exploring the surface spectral properties of Weyl semimetals.

Electronic scattering, focusing, and resonance by a spherical barrier in Weyl semimetals

We solve the Weyl electron scattered by a spherical step potential barrier. Tuning the incident energy and the potential radius, one can enter both quasiclassical and quantum regimes. Transport features related to far-field currents and integrated cross sections are studied to reveal the preferred forward scattering. In the quasiclassical regime, a strong focusing effect along the incident spherical axis is found in addition to optical caustic patterns. In the quantum regime, at energies of successive angular momentum resonances, a polar aggregation of electron density is found inside the potential. The findings will be useful in transport studies and electronic lens applications in Weyl systems.

Anomalous Hall Effect and Topological Defects in Antiferromagnetic Weyl Semimetals: Mn_{3}Sn/Ge.

We theoretically study the interplay between bulk Weyl electrons and magnetic topological defects, including magnetic domains, domain walls, and Z_{6} vortex lines, in the antiferromagnetic Weyl semimetals Mn_{3}Sn and Mn_{3}Ge with negative vector chirality. We argue that these materials possess a hierarchy of energy scales, which allows a description of the spin structure and spin dynamics using an XY model with Z_{6} anisotropy. We propose a dynamical equation of motion for the XY order parameter, which implies the presence of Z_{6} vortex lines, the double-domain pattern in the presence of magnetic fields, and the ability to control domains with current. We also introduce a minimal electronic model that allows efficient calculation of the electronic structure in the antiferromagnetic configuration, unveiling Fermi arcs at domain walls, and sharp quasibound states at Z_{6} vortices. Moreover, we have shown how these materials may allow electronic-based imaging of antiferromagnetic microstructure, and propose a possible device based on the domain-dependent anomalous Hall effect.

Signature of chiral fermion instability in the Weyl semimetal TaAs above the quantum limit

We report the electrical transport properties for Weyl semimetal TaAs in an intense magnetic field. Series of anomalies occur in the longitudinal magnetoresistance and Hall signals at ultra-low temperatures when the Weyl electrons are confined into the lowest Landau level. These strongly temperature-dependent anomalies are ascribed to the electron-hole pairing instability. Our measurements show that the Weyl semimetal TaAs in the ultraquantum regime provides a good platform for studying electron-electron interaction in topological nontrivial semimetals.

Magnetic torque anomaly in the quantum limit of Weyl semimetals.

Electrons in materials with linear dispersion behave as massless Weyl- or Dirac-quasiparticles, and continue to intrigue due to their close resemblance to elusive ultra-relativistic particles as well as their potential for future electronics. Yet the experimental signatures of Weyl-fermions are often subtle and indirect, in particular if they coexist with conventional, massive quasiparticles. Here we show a pronounced anomaly in the magnetic torque of the Weyl semimetal NbAs upon entering the quantum limit state in high magnetic fields. The torque changes sign in the quantum limit, signalling a reversal of the magnetic anisotropy that can be directly attributed to the topological nature of the Weyl electrons. Our results establish that anomalous quantum limit torque measurements provide a direct experimental method to identify and distinguish Weyl and Dirac systems.

Variation of optical conductivity spectra in the course of bandwidth-controlled metal-insulator transitions in pyrochlore iridates

We spectroscopically investigate a series of pyrochlore iridates ${R}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ ($R$: rare-earth and Y ions) where the metal-insulator transitions are induced by systematic bandwidth control via chemical substitutions of $R$ ions. We establish the phase diagram of ${R}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$, as endorsed by the variation of the optical conductivity spectra, in which the competing phases including paramagnetic insulator (PI), paramagnetic metal (PM), and antiferromagnetic insulator (AFI) show up as a function of bandwidth and temperature. For small $R$-ionic radius ($R=$ Y-Sm), i.e., strongly correlated region, pronounced peaks on the edge of the optical gap are discerned below the magnetic transition temperature ${T}_{\mathrm{N}}$, which is attributable to exciton and magnon sideband absorptions. It turns out that the estimated nearest-neighbor exchange interaction increases as $R$-ionic radius increases, whereas ${T}_{\mathrm{N}}$ monotonically decreases, indicating that the all-in all-out magnetic order arises from the interplay among several exchange interactions inherent to extended $5d$ orbitals on the frustrated lattice. For larger $R$-ionic radius ($R=$ Sm-Pr), i.e., relatively weakly correlated region, the optical conductivity spectra markedly change below 0.3 eV in the course of PM-AFI transition, implying that the magnetic order induces the insulating state. In particular, we have found distinct electrodynamics in the composition of $R=\phantom{\rule{4pt}{0ex}}{\mathrm{Nd}}_{0.5}{\mathrm{Pr}}_{0.5}$ which is located on the boundary of the quantum PM-AFI transition, pointing to the possible emergence of unconventional topological electronic phases related possibly to the correlated Weyl electrons.

Electronic properties in a quantum well structure of Weyl semimetal

We investigate the confined states and transport of three-dimensional Weyl electrons around a one-dimensional external rectangular electrostatic potential. The confined states with finite transverse wave vector exist at energies higher than the half well depth or lower than the half barrier height. The rectangular potential appears completely transparent to the normal incident electrons but not otherwise. The tunneling transmission coefficient is sensitive to their incident angle and shows resonant peaks when their energy coincides with the confined spectra. In addition, for the electrons in the conduction (valence) band through a potential barrier (well), the transmission spectrum has a gap of width increasing with the incident angle. Interestingly, the electron linear zero-temperature conductance over the potential can approach zero when the Fermi energy is aligned to the top and bottom energies of the potential, when only electron beams normal to the potential interfaces can pass through. The considered structure can be used to collimate the Weyl electron beams.

Quantum transport in three-dimensional Weyl electron system in the presence of charged impurity scattering

We theoretically study the quantum transport in three-dimensional Weyl electron system in the presence of the charged impurity scattering using a self-consistent Born approximation (SCBA). The scattering strength is characterized by the effective fine structure constant $\alpha$, which depends on the dielectric constant and the Fermi velocity of the linear band. We find that the Boltzmann theory fails at the band touching point, where the conductivity takes a nearly constant value almost independent of $\alpha$, even though the density of states linearly increases with $\alpha$. There the magnitude of the conductivity only depends on the impurity density. The qualitative behavior is quite different from the case of the Gaussian impurities, where the minimum conductivity vanishes below a certain critical impurity strength.

Metallic Interface Emerging at Magnetic Domain Wall of Antiferromagnetic Insulator: Fate of Extinct Weyl Electrons

Topological insulators, in contrast to ordinary semiconductors, accompany protected metallic surfaces described by Dirac-type fermions. Here, we theoretically show another emergent two-dimensional metal embedded in the bulk insulator is realized at a magnetic domain wall. The domain wall has long been studied as ingredients of both old-fashioned and leading-edge spintronics. The domain wall here, as an interface of seemingly trivial antiferromagnetic insulators, emergently realizes a functional interface preserved by zero modes with robust two-dimensional Fermi surfaces, where pyrochlore iridium oxides proposed to host condensed-matter realization of Weyl fermions offer such examples at low temperatures. The existence of ingap states pinned at domain walls, theoretically resembling spin/charge solitons in polyacetylene, and protected as the edge of hidden one-dimensional weak Chern insulators characterized by a zero-dimensional class A topological invariant, solves experimental puzzles observed in R2Ir2O7 with rare earth elements R. The domain wall realizes a novel quantum confinement of electrons and embosses a net uniform magnetization, which enables magnetic control of electronic interface transports beyond semiconductor paradigm.

Quantum transport in a three-dimensional Weyl electron system

Quantum transport in three-dimensional massless Dirac electron system with long-range Gaussian impurities is studied theoretically using a self-consistent Born approximation (SCBA). We find that the conductivity significantly changes the behavior at a certain scattering strength which separates the weak and strong disorder regimes. In the weak disorder regime, the SCBA conductivity mostly agrees with the Boltzmann conductivity, while the agreement fails near the Dirac point where the SCBA conductivity drops to zero linearly to the Fermi energy. In the strong disorder regime, the conductivity is smooth and finite near the Dirac point, and the minimum conductivity becomes larger in increasing the disorder potential, contrary to the usual metallic behavior. The theory applies to three dimensional gapless band structures, including Weyl semimetals.