Fermi Arcs and Their Topological Character in the Candidate Type-II Weyl Semimetal ${\mathrm{MoTe}}_2$

We report a combined experimental and theoretical study of the candidate type-II Weyl semimetal ${\mathrm{MoTe}}_2$. Using laser-based angle-resolved photoemission, we resolve multiple distinct Fermi arcs on the inequivalent top and bottom (001) surfaces. All surface states observed experimentally are reproduced by an electronic structure calculation for the experimental crystal structure that predicts a topological Weyl semimetal state with eight type-II Weyl points. We further use systematic electronic structure calculations simulating different Weyl point arrangements to discuss the robustness of the identified Weyl semimetal state and the topological character of Fermi arcs in ${\mathrm{MoTe}}_2$.

Popular Summary

Crystalline solids have particlelike, low-energy excitations—so-called quasiparticles—that describe collective states of many electrons interacting with the atomic nuclei. In 2015, scientists predicted the existence of an exotic new quasiparticle, dubbed a type-II Weyl fermion, that breaks the Lorentz invariance of special relativity and has no direct analog in the standard model of particle physics. The primary signature of this new particle is an electronic surface state that forms an open Fermi arc connecting Weyl points with opposite chirality. Here, we report multiple open Fermi arcs in semimetallic ${\mathrm{MoTe}}_2$.

Using angle-resolved photoemission, we show that the inequivalent top and bottom (001) surfaces of ${\mathrm{MoTe}}_2$ host distinct Fermi arc surface states. Employing systematic electronic structure calculations, we show that some of these arcs likely arise from type-II Weyl points and are topologically nontrivial; other arcs are not related to the topological properties of the band structure.

Our work reveals that ${\mathrm{MoTe}}_2$is a strong candidate for the realization of a type-II Weyl semimetal phase. However, it also illustrates the numerous potential pitfalls to identifying type-II Weyl fermions, providing a framework for future spectroscopic studies of new topological materials

Figure 1

Crystal structure and Weyl points of ${\mathrm{MoTe}}_2$. (a) Crystal structure of the $1{\mathrm{T}}^{\prime }$ phase (space group $Pmn{2}_1$) determined by x-ray diffraction. The two inequivalent surfaces, labeled $A$ and $B$, are indicated. (b),(c) Momentum-resolved density of states of the (001) surface at $E-E_F=0.062$ and 0.006 eV, respectively, illustrating the touching points W1,4 and W2,3 of electron and hole pockets. W1(W2) is a mirror image of W4(W3).

Figure 2

Electronic structure of ${\mathrm{MoTe}}_2$. (a) Stack of constant energy maps measured with 62 eV photon energy and $p$ polarization. (b) Left: ARPES Fermi surface at 62 eV photon energy. Right: Fermi surface contours extracted from Fermi surface maps measured at different photon energies. The largest extension of electron and hole pockets corresponding to the projected bulk band structure is indicated in blue and green, respectively. The thin black arc between hole and electron pockets is a surface state. (c) $k_z$ dependence of the electronic states at the Fermi level in the $k_y=0$ plane. The straight lines at $k_x=\pm 0.195{\AA }^{-1}$ marked by black arrows are the signature of a two-dimensional electronic state at the surface of ${\mathrm{MoTe}}_2$. Values of $k_z$ are calculated for free-electron final states with an inner potential of 13 eV. (d) Overview of the surface band structure measured along the high-symmetry direction $k_y=0$ taken with $h\nu =62$ and 6.01 eV (blue inset).

Figure 3

Fermi arcs on the surface of ${\mathrm{MoTe}}_2$. (a),(b) Detailed view of the Fermi surface measured with 6.01 eV photon energy and $p$ polarization on the $A$ and $B$ surface terminations of ${\mathrm{MoTe}}_2$. The photoemission intensity has been symmetrized with respect to the $k_x$ axis. (c),(d) Surface density of states for the two surface terminations calculated 10 meV below the Fermi level. (e),(f) Zoom into the areas enclosed by a dashed rectangle in (a) and (c), respectively. (g) Numerical results for the surface density of states along an elliptical contour (with $r_{kx}=0.0018{\AA }^{-1}$, $r_{ky}=0.005{\AA }^{-1}$) enclosing the Weyl point W2. The topological surface state is connecting valence to conduction bands and produces CTSS in the calculations.

Figure 4

(a) Dispersion plots taken on surface $A$ parallel to $k_y$ for different values of $k_x$. (b) Calculated surface energy dispersion along equivalent cuts in momentum space for the same surface termination.

Figure 5

Trivial and topological Fermi arcs on the $B$-type surface of ${\mathrm{MoTe}}_2$. (a) Position of the four Weyl points calculated for the experimental crystal structure reported in Ref. [7]. (b) Using the structure determined in our work, we find eight Weyl points. (c),(d) Theoretical Fermi surfaces for the structures used in (a) and (b), respectively. The large Fermi arc has a virtually identical dispersion in the two scenarios but is topological in (c) and trivial in (d).

Figure 6

Temperature dependence of the lattice constants of ${\mathrm{MoTe}}_2$ in the $1{\mathrm{T}}^{\prime }$ phase (space group $Pmn{2}_1$). Open circles and squares are the lattice constants of ${\mathrm{MoTe}}_2$ obtained with different sample growth procedures as reported in Refs. [4, 7]. All values have been normalized by the lattice parameters of our samples measured at 230 K ($a=3.4762\AA$, $b=6.3239\AA$, $c=13.837\AA$).

Figure 7

False-color plot of the energy gap between valence and conduction bands in the $k_z=0$ plane illustrating how the number and position of Weyl points evolve for different unit cell parameters: (a) Structure in Ref. [7] which has a 0.3% smaller lattice constant $a$; (b)–(d) lattice constants at 10, 100, and 230 K obtained from a linear extrapolation based on the experimental data in Fig. 11. The coordinates of the Weyl points found for the unit cell parameters at 100 K used in the main text are $(0.1855,\pm 0.0539,0){\AA }^{-1}$ and $E-E_F=0.062\mathrm{eV}$ for W1,4 and $(0.1906,\pm 0.0152,0){\AA }^{-1}$ and $E-E_F=0.006\mathrm{eV}$ for W2,3. The remaining four points are mirror symmetric with respect to $k_x$

Figure 8

(a),(b) Detailed view of the Fermi surface measured with 6.01 eV photon energy and $p$ polarization on the $A$- and $B$-type surfaces of ${\mathrm{MoTe}}_2$, displayed on a logarithmic color scale. This photon energy corresponds to $k_z$ values around $0.6\pi /c$ in the fifth Brillouin zone assuming a free-electron final state with an inner potential of 13 eV. Note, however, that a free-electron final state model is not fully appropriate at such low photon energies, which results in a substantial uncertainty of $k_z$ values. (c),(e) Surface energy dispersion along the $k_y=0$ direction calculated for the top and bottom surface, respectively. (d),(f) Dispersion plots measured on surface $A$ and $B$ parallel to the $k_y=0$ direction at the $k_y$ values “i”–“iii” marked in (a) and (b), respectively.

Figure 9

Momentum-resolved surface density of states illustrating the evolution of the topological Fermi arc (CTSS) around the energy of the W2 Weyl point.

Figure 10

Evolution of the large Fermi arcs for different values of the spin-orbit coupling (SOC) constant, which artificially modify the band structure of ${\mathrm{MoTe}}_2$ resulting in 8, 4, or 0 Weyl points (WP) in the $k_z=0$ plane. (a) False-color plot of the energy gap between valence and conduction bands in the $k_z=0$ plane illustrating the number and position of Weyl points. (b) Momentum-resolved surface density of states at the Fermi level.

Figure 11

Large Fermi arc of ${\mathrm{WTe}}_2$ for different numbers of Weyl points. (a) Momentum-resolved surface density of states at the Fermi level calculated using the room temperature structure [45], which results in no Weyl points. (b) Momentum-resolved surface density of states at the Fermi level calculated using the low-temperature structure ($T=113\mathrm{K}$, Ref. [46]) and 200% spin-orbit coupling, which produces only four Weyl points. (c) Momentum-resolved surface density of states at the Fermi level calculated using the low-temperature structure ($T=113\mathrm{K}$ Ref. [46]) and 100% spin-orbit coupling, which produces eight Weyl points.