Fermi Arcs and DC Transport in Nanowires of Dirac and Weyl Semimetals

The transport properties and electron states in cylinder nanowires of Dirac and Weyl semimetals are studied paying special attention to the structure and properties of the surface Fermi arcs. The latter make the electric charge and current density distributions in nanowires strongly nonuniform as the majority of the charge density is accumulated at the surface. It is found that a Weyl semimetal wire also supports a magnetization current localized mainly at the surface because of the Fermi arcs contribution. By using the Kubo linear response approach, the direct current (DC) conductivity is calculated and it is found that its spatial profile is nontrivial. By explicitly separating the contributions of the surface and bulk states, it is shown that when the electric chemical potential and/or the radius of the wire is small, the electron transport is determined primarily by the Fermi arcs and the electrical conductivity is much higher at the surface than in the bulk. Due to the rise of the surface-bulk transition rate, the relative contribution of the surface states to the total conductivity gradually diminishes as the chemical potential increases. In addition, the DC conductivity at the surface demonstrates noticeable peaks when the Fermi level crosses energies of the surface states.     

Laser Pump-Probe Fiber-Optic Technique for Characterization of Near-Surface Layers of Solids: Development and Application Prospects for Studying Semiconductors and Weyl Semimetals

A fiber-optic setup incorporating the pump-probe thermoreflectance (TR) technique with Fabry–Perot (FP) interferometer is presented. It includes both heat pump and probe lasers, producing wavelengths of 1470 and 1530 nm, respectively, together with a reflected radiation detector. Heat pump pulse duration varies from a few microseconds to tens of microseconds. The potential of the pump-probe TR-FP technique to investigate the subsurface region of semiconductors with a range of electron spectra is demonstrated. A pronounced dip in time dependence of the TR-FP signal is discovered at the liquid nitrogen temperature in the gapless semiconductor compound HgSe—a candidate for the family of Weyl semimetals with broken inversion symmetry. This finding implies the developed pulsed TR-FP method for the detection of Weyl nodes and surface Fermi arcs in solids.     

RKKY interaction in three-dimensional tilted Dirac and Weyl semimetals

We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities of the tilted Dirac and Weyl semimetals in three dimensions. In accordance with the untilted scenario, the RKKY interaction contains three terms, namely the Heisenberg term, the Ising term, and the Dzyaloshinsky-Moriya term. The main influence of tilt on the RKKY Hamiltonian is a modulation to the oscillation frequencies of range functions. Our results enrich the knowledge of the magnetic properties of materials with tilted Dirac cones and may see an important application in spintronics.     

Hybrid Weyl semimetal under crossed electric and magnetic fields: Field tuning of spectrum type

There are two types (WSM-I and WSM-II) of the WSMs. The WSMs of different types have various topological and transport properties. Besides pure WSM-I and WSM-II, there exists a novel type, dubbed “hybrid Weyl semimetal”, which contains the Weyl points of both types. In this Letter we consider the hybrid WSM under crossed magnetic and electric fields. The electromagnetic field induces transition between different types of spectrum in Weyl point (WP). Thus, hybrid phase of the WSM can be tunable using the electromagnetic field. Finally, we proposed a new field-induced type of hybrid WSM in which two different regimes of spectrum coexist. In this case, the spectrum near the first WP corresponds to electric regime (no Landau levels) and the spectrum in the second WP with opposite chirality corresponds to magnetic regime (there are Landau levels).     

Magnetic Textures and Dynamics in Magnetic Weyl Semimetals

Recent theoretical and experimental attempts have been successful in finding magnetic Weyl semimetal phases, which show nodal-point structure in the electronic bands as well as magnetic orders. Beyond uniform ferromagnetic or antiferromagnetic orders, nonuniform magnetic textures, such as domain walls and skyrmions, enrich the properties of the Weyl electrons even more in such materials. Here, a topical review on interplay between Weyl electrons and magnetic textures in those magnetic Weyl semimetals is given. The basics of magnetic textures in nontopological magnetic metals are reviewed first, and then the effect of magnetic textures in Weyl semimetals is discussed, regarding the recent theoretical and experimental progress therein. The idea of the fictitious “axial gauge fields” is pointed out, which effectively describes the effect of magnetic textures on the Weyl electrons and can well account for the properties of the electrons localized around magnetic domain walls.     

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.     

Tunable anisotropic anomalous Nernst effect and orbital magnetization in Floquet Weyl semimetals

Weyl semimetals and nodal line semimetals display a host of novel properties. Floquet Weyl semimetals with tunable Weyl points can be obtained from nodal line semimetals under the circularly polarized off-resonant light. Here we theoretically investigate the anomalous Nernst effect and orbital magnetization in Floquet Weyl semimetals. Due to the anisotropy of the band structure in Floquet Weyl semimetals, highly anisotropic Berry phase mediated anomalous Nernst effect and orbital magnetization in the absence of magnetic field are observed, indicating orientation-dependent applications in the design of nanodevices. The amplitude and sign of anomalous Nernst coefficient and orbital magnetization can be tuned by the light direction, amplitude and polarization. The effect of the chemical potential on anomalous Nernst coefficient and orbital magnetization is also discussed. The light-modulated anomalous Nernst effect and orbital magnetization make Floquet Weyl semimetals potential candidates for thermoelectric devices.     

Floquet Transmission in Weyl/Multi-Weyl and Nodal-Line Semimetals through a Time-Periodic Potential Well

A quantum pumping protocol through which the quasiparticles of Weyl/multi-Weyl and nodal-line semimetals are subjected to a time-periodic rectangular potential well is considered. The presence of an oscillating potential of frequency ω creates equispaced Floquet side-bands with spacing $\hslash \omega$. As a result, a Fano resonance is observed when the difference in the Fermi energy (i.e., the energy of the incident quasiparticle), and the energy of one of the (quasi)bound state levels of the well, coincides with the energy of an integer number of photons (each carrying energy quantum $\hslash \omega$). Using the Floquet theory and the scattering matrix approach in the zero-temperature non-adiabatic pumping limit, characteristic Fano resonance patterns are found in the transmission coefficients. The inflection points in the pumped shot noise spectra also serve as a proxy for the corresponding Fano resonances. Therefore, the pumped shot noise is also numerically evaluated. Finally, the existence of the Fano resonance points is correlated to the (quasi)bound states of the well, by explicitly calculating the bound states of the static well (which are a subset of the bound states of the driven system). Since semimetals with anisotropic dispersions are considered, all the features observed depend on the orientation of the potential well.     

Photoinduced Weyl semimetal phase and anomalous Hall effect in a three-dimensional topological insulator

Motivated by the fact that Weyl fermions can emerge in a three-dimensional topological insulator on breaking either time-reversal or inversion symmetries, we propose that a topological quantum phase transition to a Weyl semimetal phase occurs under the off-resonant circularly polarized light, in a three-dimensional topological insulator, when the intensity of the incident light exceeds a critical value. The circularly polarized light effectively generates a Zeeman exchange field and a renormalized Dirac mass, which are highly controllable. The phase transition can be exactly characterized by the first Chern number. A tunable anomalous Hall conductivity emerges, which is fully determined by the location of the Weyl nodes in momentum space, even in the doping regime. Our predictions are experimentally realizable through pump-probe angle-resolved photoemission spectroscopy and raise a new way for realizing Weyl semimetals and quantum anomalous Hall effects.     

Weak antilocalization and interaction-induced localization of Dirac and Weyl Fermions in topological insulators and semimetals

Weak localization and antilocalization are quantum transport phenomena that arise from the quantum interference in disordered metals.At low temperatures,they can give distinct temperature and magnetic field dependences in conductivity,allowing the symmetry of the system to be explored.In the past few years,they have also been observed in newly emergent topological materials,including topological insulators and topological semimetals.In contrast from the conventional electrons,in these new materials the quasiparticles are described as Dirac or Weyl fermions.In this article,we review our recent efforts on the theories of weak antilocalization and interaction-induced localization for Dirac and Weyl fermions in topological insulators and topological semimetals.     

Quintessence and Dark Matter Created by Weyl–Dirac Geometry

A spatially closed universe undergoing at present accelerated expansion, having a non-vanishing cosmological constant, and filled with luminous- and dark matter is described in terms of the Integrable Weyl–Dirac theory. It is shown that, during the dust-dominated period, dark matter and the quintessence pressure, the latter giving rise to acceleration: both are created by the Dirac gauge function. The behavior of two models: a nearly flat one and a well closed are considered in appropriate gauges, and plausible scenarios are obtained. The outcome of the present paper, together with results of a previous work,⁽³¹⁾ provide a geometrically based, classical, singularity-free model of the universe, that has originated from a pure geometric Weyl–Dirac entity, passed a prematter period, the radiation-dominated era, and continues its development in the present dust period.     

Wilson Loops and Topological Phases in Closed String Theory

Using covariant phase space formulations for the natural topological invariants associated with the world-surface in closed string theory, we find that certain Wilson loops defined on the world-surface and that preserve topological invariance, correspond to wave functionals for the vacuum state with zero energy. The differences and similarities with the 2-dimensional QED proposed by Schwinger early are discussed. PACS Numbers : 81T30, 81T45     

Topological transport in Dirac electronic systems:A concise review

Various novel physical properties have emerged in Dirac electronic systems, especially the topological characters protected by symmetry. Current studies on these systems have been greatly promoted by the intuitive concepts of Berry phase and Berry curvature, which provide precise definitions of the topological phases. In this topical review, transport properties of topological insulator(Bi2Se3), topological Dirac semimetal(Cd3As2), and topological insulator-graphene heterojunction are presented and discussed. Perspectives about transport properties of two-dimensional topological nontrivial systems,including topological edge transport, topological valley transport, and topological Weyl semimetals, are provided.     

A General Method for Obtaining Degenerate Solutions to the Dirac and Weyl Equations and a Discussion on the Experimental Detection of Degenerate States

In this work, a general method is described for obtaining degenerate solutions of the Dirac equation, corresponding to an infinite number of electromagnetic 4-potentials and fields, which are explicitly calculated. More specifically, using four arbitrary real functions, one can automatically construct a spinor that satisfies the Dirac equation for an infinite number of electromagnetic 4-potentials, defined by those functions. An interesting characteristic of these solutions is that, in the case of Dirac particles with nonzero mass, the degenerate spinors should be localized, both in space and time. The method is also extended to the cases of massless Dirac and Weyl particles, where the localization of the spinors is no longer required. Finally, two experimental methods are proposed for detecting the presence of degenerate states.     

Hexagonal wurtzite MnO in ferromagnetic state: A magnetic topological spin-gapless Weyl semimetal

Magnetic topological materials have attracted increasingly attentions in recent years due to their exotic electronic behaviors emerging from the couplings of topological, magnetic, and crystalline symmetries. In this work, based on the first-principles calculations, we propose that hexagonal wurtzite MnO is a magnetic topological spin-gapless semi-half-metal with two pairs of type-I Weyl fermions near the Fermi level in ferromagnetic state, which is a promising candidate material in spintronic and piezoelectric applications. In the absence of spin-orbit coupling (SOC), it hosts one triple degeneracy point (TP) in the irreducible Brillouin zone. Owing to weak SOC, the TP splits into two type-I Weyl points that are very close to each other. The Fermi arc surface states connecting the projected Weyl points with opposite chirality are observed. Our results therefore provide a wonderful platform to study the interplay of magnetism and topology.