Robust Type-II Weyl Semimetal Phase in Transition Metal DiphosphidesXP2(X=Mo, W)

Abstract

The recently discovered type-II Weyl points appear at the boundary between electron and hole pockets. Type-II Weyl semimetals that host such points are predicted to exhibit a new type of chiral anomaly and possess thermodynamic properties very different from their type-I counterparts. In this Letter, we describe the prediction of a type-II Weyl semimetal phase in the transition metal diphosphides MoP2 and WP2. These materials are characterized by relatively simple band structures with four pairs of type-II Weyl points. Neighboring Weyl points have the same chirality, which makes the predicted topological phase robust with respect to small perturbations of the crystalline lattice. In addition, this peculiar arrangement of the Weyl points results in long topological Fermi arcs, thus making them readily accessible in angle-resolved photoemission spectroscopy.Topological semimetals host band degeneracies in the vicinity of the Fermi level (E F ) that are associated with certain integer-valued topological invariants [1][2][3][4][5][6][7][8][9]. Since these invariants cannot continuously change their values, the associated degeneracies are protected against perturbations. One such semimetal phase -the Weyl semimetal (WSM) -hosts point-like linear band crossings of two bands with linear dispersion, the so-called Weyl points (WPs), in the vicinity of E F . These WPs represent sources or sinks of Berry curvature, and their associated topological invariant is the Chern number C = ±1 computed on a surface in momentum space that encloses the WP. Positive (negative) Chern numbers correspond to a source (sink) of the Berry curvature. A variety of topology-driven physical phenomena is predicted and observed in WSMs, ranging from the observation of open Fermi arcs in the surface spectrum [2,10] to the realization of the chiral anomaly of quantum field theory [11][12][13][14][15][16][17].It was recently shown [18] that unlike standard Lorentz-invariant field theory, condensed matter physics has two distinct types of Weyl fermions, and hence WSMs. While standard type-I Weyl fermions with closed Fermi surfaces were discovered in materials of the TaAs family [8,9,[19][20][21][22][23][24][25], the novel type-II Weyl fermions appear at the boundary between electron and hole pockets, leaving an open Fermi surface which results in the anisotropic chiral anomaly [18,26]. Two representatives of type-II WSMs materials considered to date are the orthorhombic low-temperature phases of WTe 2 and MoTe 2 [18,[27][28][29]. Type-II Weyl points were also recently predicted to exist in strained HgTe [30]. Eight (four) type-II WPs appear in WTe 2 (MoTe 2 ) formed by the valence and conduction bands. In WTe 2 some of the carrier pockets become topologically non-trivial, while in MoTe 2 they are all trivial, and the two materials represent very different Fermi arc arrangements [18,28]. In both cases, however, the band structure is very complicated and the arrangement of WPs is sensitive to small changes in the crystal structure, which, in turn, is se...

Fermi surface of the Weyl type-II metallic candidate WP2

“…Nevertheless, the FFT peaks assigned to the electron pockets display a good agreement with the theoretically predicted ones (depicted by blue and magenta lines). Notice that in a simple rigid band-shift scenario, this displacement of the electron-and hole-bands relative to E F would prevent them from touching and therefore would eliminate the predicted Weyl type-II points [19], see Supplementary Fig. S4.…”

“…The reason for such a discrepancy remains unclear, but it does question the validity of both the ARPES measurements and the predictions by density-functional theory calculations. Recently, a type-II WSM ground-state was predicted for the transition-metal diphosphides MoP 2 and WP 2 [19]. WP 2 crystallizes in two distinct structures [20][21][22]: the α-phase which displays the OsGe 2 structure type and the β-phase which is isostructural to MoP 2 and belongs to the non-centrosymmetric orthorhombic space group Cmc2 1 (36) [20] (see Fig.…”

“…1(a)) and is predicted to host Weyl points. Unlike WTe 2 and γ−MoTe 2 , β−WP 2 is not a layered material which leads to a simpler band structure and a more robust arrangement of the Weyl points with respect to small structural changes [19]. Based on DFT calculations it was shown that the electron and hole pockets touch at two inequivalent points located at 0.471 and 0.340 eV below the Fermi energy E F resulting in a total of eight Weyl points across the k x -k y -plane [19].…”

“…Unlike WTe 2 and γ−MoTe 2 , β−WP 2 is not a layered material which leads to a simpler band structure and a more robust arrangement of the Weyl points with respect to small structural changes [19]. Based on DFT calculations it was shown that the electron and hole pockets touch at two inequivalent points located at 0.471 and 0.340 eV below the Fermi energy E F resulting in a total of eight Weyl points across the k x -k y -plane [19]. In addition, a very recent report highlights its unusual electrical transport properties including extremely large magnetoresistivity (MR) possibly related to its underlying Weyl physics [23].…”

Renormalization group approach to stability of two-dimensional interacting type-II Dirac fermions

“…These Weyl nodes can be viewed as magnetic monopoles in momentum space [3,4], which lead to various novel electromagnetic responses such as the chiral anomaly [5][6][7][8][9][10], chiral magnetic effect [11][12][13][14][15][16][17][18], and exotic magnetoresistance [19][20][21][22]. Very recently, a new kind of Weyl/Dirac semimetals with the tilted conic spectrum, named type-II Weyl/Dirac semimetals, have been predicted in a series of materials [23][24][25][26], in which the Fermi surface crossing the Weyl nodes is lines in two dimensions [27] and surface in three dimensions [23] with a finite density of states (DOS). Meanwhile, many experiments have made great efforts to characterize type-II Weyl/Dirac semimetals by angle-resolved photoemission spectroscopy [28][29][30].…”