The discovery of the first Weyl semimetal tantalum monoarsenide has greatly promoted physical research on the niobium and tantalum pnictide compounds. Crystallizing into the NbAs- and OsGe₂-type structures, these mono- and di-pnictide semimetals manifest exotic electrical transport properties in magnetic field, which only occur in their single-crystalline forms. All the unusual electrical properties correspond to their poor carriers, which are indeed vulnerable to various crystal defects. In this review article, we present a comprehensive comparison of the crystal growth and electrical transport properties of the two semimetal families. We then discuss in detail the possible characteristic transport features, such as the chiral anomaly of Weyl quasiparticles. We emphasize the importance of crystal growth and sample manipulation for exploring the unique topological properties of Weyl semimetals in the future.

Monocrystalline SrMnBi₂ thin films were grown by molecular beam epitaxy (MBE), and their transport properties were investigated. A high and unsaturated linear magnetoresistance (MR) was observed, which exhibited a transition from a semi-classical weak-field B² dependence to a high-field linear dependence. An unusual nonlinear Hall resistance was also observed because of the anisotropic Dirac fermions. The two-carrier model was adopted to analyze the unusual Hall resistance quantitatively. The fitting results yielded carrier densities and mobilities of 3.75×10¹⁴ cm⁻² and 850 cm²·V⁻¹s⁻¹, respectively, for holes, and 1.468×10¹³ cm⁻², 4118 cm²·V⁻¹·s⁻¹, respectively, for electrons, with a hole-dominant conduction at 2.5 K. Hence, an effective mobility can be achieved, which is in reasonable agreement with the effective hole mobility of 1800 cm²·V⁻¹·s⁻¹, extracted from the MR. Further, the angle-dependent MR, proportional to cosθ, where θ is the angle between the external magnetic field and the perpendicular orientation of the sample plane, also implies a high anisotropy of the Fermi surface. Our results about SrMnBi₂ thin films, as one of a new class of AEMnBi₂ and AEMnSb₂ (AE= Ca, Sr, Ba, Yb, Eu) materials, suggest that they have a lot of exotic transport properties to be investigated, and that their high mobility might facilitate electronic device applications.

Unsaturated magnetoresistance (MR) has been reported in type-II Weyl semimetal WTe₂, manifested as a perfect compensation of opposite carriers. We report linear MR (LMR) in WTe₂ crystals, the onset of which was identified by constructing the MR mobility spectra for weak fields. The LMR further increased and became dominant for fields stronger than 20 T, while the parabolic MR gradually decayed. The LMR was also observed in high-pressure conditions.

Chiral anomaly-induced negative magnetoresistance (NMR) has been widely used as critical transport evidence for the existence of Weyl fermions in topological semimetals. In this mini-review, we discuss the general observation of NMR phenomena in non-centrosymmetric NbP and NbAs. We show that NMR can arise from the intrinsic chiral anomaly of Weyl fermions and/or extrinsic effects, such as the superimposition of Hall signals; field-dependent inhomogeneous current flow in the bulk, i.e., current jetting; and weak localization (WL) of coexistent trivial carriers. The WL-controlled NMR is heavily dependent on sample quality and is characterized by a pronounced crossover from positive to negative MR growth at elevated temperatures, resulting from the competition between the phase coherence time and the spin-orbital scattering constant of the bulk trivial pockets. Thus, the correlation between the NMR and the chiral anomaly need to be scrutinized without the support of complimentary techniques. Because of the lifting of spin degeneracy, the spin orientations of Weyl fermions are either parallel or antiparallel to the momentum, which is a unique physical property known as helicity. The conservation of helicity provides strong protection for the transport of Weyl fermions, which can only be effectively scattered by magnetic impurities. Chemical doping with magnetic and non-magnetic impurities is thus more convincing than the NMR method for detecting the existence of Weyl fermions.

Topological semimetals are newly discovered states of quantum matter, which have extended the concept of topological states from insulators to metals and attracted great research interest in recent years. In general, there are three kinds of topological semimetals, namely Dirac semimetals, Weyl semimetals, and nodal line semimetals. Nodal line semimetals can be considered as precursor states for other topological states. For example, starting from such nodal line states, the nodal line structure might evolve into Weyl points, convert into Dirac points, or become a topological insulator by introducing the spin–orbit coupling (SOC) or mass term. In this review paper, we introduce theoretical materials that show the nodal line semimetal state, including the all-carbon Mackay–Terrones crystal (MTC), anti-perovskite Cu3PdN, pressed black phosphorus, and the CaP3 family of materials, and we present the design principles for obtaining such novel states of matter.

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.