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The transition metal dipnictides TaAs2 , TaSb2 , NbAs2 and NbSb2 have recently sparked interest for exhibiting giant magnetoresistance. While the exact nature of magnetoresistance in these materials is still under active investigation, there are experimental results indicating anisotropic negative magnetoresistance. We study the effect of magnetic field on the band structure topology of these materials by applying a Zeeman splitting. In the absence of magnetic field, we find that the materials are weak topological insulators, which is in agreement with previous studies. When the magnetic field is applied, we find that type-II Weyl points form. This result is found first from a symmetry argument, and then numerically for a k.p model of TaAs2 and a tight-binding model of NbSb2. This effect can be of help in search for an explanation of the anomalous magnetoresistance in these materials.
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As one of Weyl semimetals discovered recently, NbP exhibits two groups of Weyl points with one group lying inside the $k_z=0$ plane and the other group staying away from this plane. All Weyl points have been assumed to be type-I, for which the Fermi surface shrinks into a point as the Fermi energy crosses the Weyl point. In this work, we have revealed that the second group of Weyl points are actually type-II, which are found to be touching points between the electron and hole pockets in the Fermi surface. Corresponding Weyl cones are strongly tilted along a line approximately $17^circ$ off the $k_z$ axis in the $k_x - k_z$ (or $k_y - k_z$) plane, violating the Lorentz symmetry but still giving rise to Fermi arcs on the surface. Therefore, NbP exhibits both type-I ($k_z=0$ plane) and type-II ($k_z eq 0$ plane) Weyl points.
Recent experimental observations of Weyl fermions in materials opens a new frontier of condensed matter physics. Based on first-principles calculations, we here discover Weyl fermions in a two-dimensional layered electride material Y$_2$C. We find that the Y 4$d$ orbitals and the anionic $s$-like orbital confined in the interstitial spaces between [Y$_2$C]$^{2+}$ cationic layers are hybridized to give rise to van Have singularities near the Fermi energy $E_{rm F}$, which induce a ferromagnetic (FM) order via the Stoner-type instability. This FM phase with broken time-reversal symmetry hosts the rotation-symmetry protected Weyl nodal lines near $E_{rm F}$, which are converted into the multiple pairs of Weyl nodes by including spin-orbit coupling (SOC). However, we reveal that, due to its small SOC effects, Y$_2$C has a topologically nontrivial drumhead-like surface state near $E_{rm F}$ as well as a very small magnetic anisotropy energy with several ${mu}$eV per unit cell, consistent with the observed surface state and paramagnetism at low temperatures below ${sim}$2 K. Our findings propose that the Brillouin zone coordinates of Weyl fermions hidden in paramagnetic electride materials would fluctuate in momentum space with random orientations of the magnetization direction.
Three-dimensional (3D) topological Weyl semimetals (TWSs) represent a novel state of quantum matter with unusual electronic structures that resemble both a 3D graphene and a topological insulator by possessing pairs of Weyl points (through which the electronic bands disperse linearly along all three momentum directions) connected by topological surface states, forming the unique Fermi-arc type Fermi-surface (FS). Each Weyl point is chiral and contains half of the degrees of freedom of a Dirac point, and can be viewed as a magnetic monopole in the momentum space. Here, by performing angle-resolved photoemission spectroscopy on non-centrosymmetric compound TaAs, we observed its complete band structures including the unique Fermi-arc FS and linear bulk band dispersion across the Weyl points, in excellent agreement with the theoretical calculations. This discovery not only confirms TaAs as the first 3D TWS, but also provides an ideal platform for realizing exotic physical phenomena (e.g. negative magnetoresistance, chiral magnetic effects and quantum anomalous Hall effect) which may also lead to novel future applications.
Characterized by the absence of inversion symmetry, non-centrosymmetric materials are of great interest because they exhibit ferroelectricity, second harmonic generation, emergent Weyl fermions, and other fascinating phenomena. It is expected that if time-reversal symmetry is also broken, additional magneto-electric effects can emerge from the interplay between magnetism and electronic order. Here we report topological conducting properties in the non-centrosymmetric magnet PrAlGe. By photoemission spectroscopy, we observe an arc parametrizing surface-localized states---a topological arc. Using the bulk-boundary correspondence, we conclude that these arcs correspond to projected topological charges of $pm{1}$ in the surface Brillouin zone, demonstrating the presence of magnetic Weyl quasiparticles in bulk. We further observe a large anomalous Hall response, arising from diverging bulk Berry curvature fields associated with the magnetic Weyl band structure. Our results demonstrate a topological phase with robust electronic surface states and anomalous transport in a non-centrosymmetric magnet for the first time, providing a novel material platform to study the interplay between magnetic order, band topology and transport.
A possible connection between extremely large magneto-resistance and the presence of Weyl points has garnered much attention in the study of topological semimetals. Exploration of these concepts in transition metal phosphide WP2 has been complicated by conflicting experimental reports. Here we combine angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations to disentangle surface and bulk contributions to the ARPES intensity, the superposition of which has plagued the determination of the electronic structure in WP2. Our results show that while the hole- and electron-like Fermi surface sheets originating from surface states have different areas, the bulk-band structure of WP2 is electron-hole-compensated in agreement with DFT. Furthermore, the detailed band structure is compatible with the presence of at least 4 temperature-independent Weyl points, confirming the topological nature of WP2 and its stability against lattice distortions.
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