Weyl semimetal is a new quantum state of matter1,2,3,4,5,6,7,8,9,10,11,12 hosting the condensed matter physics counterpart of the relativistic Weyl fermions13 originally introduced in high-energy physics. The Weyl semimetal phase realized in the TaAs class of materials features multiple Fermi arcs arising from topological surface states10,11,14,15,16 and exhibits novel quantum phenomena, such as a chiral anomaly-induced negative magnetoresistance17,18,19 and possibly emergent supersymmetry20. Recently it was proposed theoretically that a new type (type-II) of Weyl fermion21,22 that arises due to the breaking of Lorentz invariance, which does not have a counterpart in high-energy physics, can emerge as topologically protected touching between electron and hole pockets. Here, we report direct experimental evidence of topological Fermi arcs in the predicted type-II Weyl semimetal MoTe2 (refs 23,24,25). The topological surface states are confirmed by directly observing the surface states using bulk- and surface-sensitive angle-resolved photoemission spectroscopy, and the quasi-particle interference pattern between the putative topological Fermi arcs in scanning tunnelling microscopy. By establishing MoTe2 as an experimental realization of a type-II Weyl semimetal, our work opens up opportunities for probing the physical properties of this exciting new state.
In the Brillouin zone of a type-I Weyl semimetal, the linearly dispersing and non-degenerate bands cross each other at the Weyl points (Fig. 1a). These band-topology protected Weyl points can be created or annihilated only in pairs according to the no-go theorem1. When projected onto the surface, the Weyl points are connected by the topologically protected Fermi arcs (Fig. 1a)2. In contrast to the type-I Weyl fermions in the TaAs class or compressively strained HgTe12 that have a point-like Fermi surface, the type-II Weyl fermions emerge at the boundary between electron and hole pockets when the cones are tilted significantly (Fig. 1b), and there is a finite density of states at the Fermi energy EF. The distinction between the Fermi surfaces of these two types of Weyl semimetal is expected to lead to different physical properties and response to magnetic fields21.
Type-II Weyl fermion has been predicted in the orthorhombic Td phase of WTe2 (ref. 21), which breaks the inversion symmetry and shows unusual transport properties26. However, the small momentum separation of the Weyl points (0.7% of the Brillouin zone) and the extremely small size of the arcs21 make it exceptionally challenging to resolve the topological Fermi arcs in WTe2 by angle-resolved photoemission spectroscopy (ARPES). A promising solution is provided by the prediction that the topological Fermi arcs can be significantly enlarged in MoTe2 (refs 23,24) or MoxW1−xTe2 (ref. 27). Among these candidate materials, MoTe2 is particularly interesting because of the reported superconductivity28 and the predicted topological phase transition induced by temperature or strain23. Although the electronic structures of WTe2 (refs 29,30,31) and MoxW1−xTe2 (ref. 32) have been experimentally studied, so far there is no conclusive evidence on the existence of topological Fermi arcs. Here, by combining two complementary surface-sensitive probes—ARPES and scanning tunnelling microscopy (STM), we provide direct experimental evidence of the topological Fermi arcs at the boundary between electron and hole pockets in the Td phase of MoTe2, establishing it as a type-II Weyl semimetal.
MoTe2 is polymorphic with three different structures: hexagonal (α-phase, or 2H phase), monoclinic (β-phase, or 1T′ phase) and orthorhombic (γ-phase, or Td phase). The 1T′ phase has a distorted CdI2 structure (Fig. 1c) that crystallizes in the centrosymmetric space group P21/m. The Mo atoms are coordinated by six Te atoms but shifted from the centre of the Te octahedra, resulting in the zigzag chains along the b axis. The bonding between the shifted Mo atoms corrugates the Te sheets and distorts the Te octahedra33,34, causing the c axis to incline at an angle of ∼93.9° (ref. 33). A temperature-induced phase transition from the high-temperature 1T′ to the low-temperature Td phase has been reported between 240 K to 260 K (ref. 33). The Td phase (Fig. 1d) shares the same in-plane crystal structure (Fig. 1e) as the 1T′ phase but has a vertical (90°) stacking and belongs to the non-centrosymmetric space group Pmn21. Weyl fermions are possible in the Td phase only where the inversion symmetry is broken. The Brillouin zone of the Td phase is shown in Fig. 1f.
Figure 1g shows the X-ray diffraction intensity of the high-quality MoTe2 single crystal at room temperature (1T′ phase). The Raman spectrum in Fig. 1h shows Ag vibrational modes at ∼160 and 260 cm−1 (ref. 35). The resistance measurement (Fig. 1i) confirms the first-order phase transition between the Td and 1T′ phases at ∼260 K, in agreement with previous results33. The high crystallinity of the samples is revealed by the sharp diffraction spots (Fig. 1j) in the low-energy electron diffraction pattern measured on a freshly cleaved sample in the Td phase. The atomically resolved STM topography in Fig. 1k further confirms the high quality of the MoTe2 crystal. The cleaved surface is terminated by Te atoms. The image shows a rectangular lattice with the lattice constants of a = 3.5 Å, b = 6.3 Å. The centre and corner atoms of a rectangular unit are different in height and exhibit distinct contrast. The dI/dV spectrum on the surface is shown in the Supplementary Information.
Figure 2a–c compares the electronic structure of MoTe2 in the Td phase measured by ARPES with band structure calculation along the a-axis (––) direction. In band structure calculation, the bands with significant kz dispersion overlap to form continuously filled contours, while those with strong surface state characteristics show up as sharp features in the intensity maps. The ARPES spectral intensity is affected by the dipole matrix elements and thereby depends on both the electron wavefunction and light polarization. To resolve the dispersions of multiple pockets, we use UV light with both horizontal (p) and vertical (s) polarizations. The measured dispersions (Fig. 2b, c) are in good agreement with the first-principles calculations (Fig. 2a). The trivial surface states (marked by the black broken curve) together with the smaller electron pocket (blue broken curve) are better resolved with the p-polarization light (Fig. 2b), while the s-polarization light (Fig. 2c) clearly resolves both bulk electron pockets (blue solid and dotted curves) and the pocket surrounding the Γ point. In the calculated spectral function (Fig. 2d), the spectral weight of the electron pockets forms bell-like shapes on both sides away from the Γ point and part of the bowtie-shaped outer contour around the Γ point is contributed by the hole pockets at EF. These bulk states are better observed with a bulk-sensitive laser source at 6.3 eV (penetration depth of ≈30 Å) in ARPES. Figure 2e, f shows the measured Fermi surface maps with light polarizations perpendicular to the b and a axis respectively. The bulk electron pockets are clearly observed in Fig. 2e and have an overall uniform intensity contour (blue broken curve), while the bowtie-shaped hole pocket is more clearly observed in Fig. 2f (green curve).
According to band structure calculation (Fig. 2g), the above observed electron and hole pockets touch each other at eight Weyl points with energies of ≈0.005 eV (W1) and ≈0.045 eV (W2), respectively. Topological Fermi arcs (highlighted by yellow curves in Fig. 2g) are expected to emerge between the Weyl points with opposite chiralities21,23,24. At the energy of W2, part of the arcs is shadowed by the pockets and only a small portion is observed. In addition to the topological surface states, there are also trivial surface states (indicated by white arrows). Theoretical calculation also shows that in the centrosymmetric 1T′ phase, the electron and hole pockets have no touching points, and only the trivial surface states remain (see Supplementary Fig. 1). The disappearance of the Fermi arcs in the 1T′ phase further confirms their origin from the Weyl semi-metallic state. The characteristic electronic structure of Td phase MoTe2 is schematically summarized in Fig. 2h with the energies of the Weyl points as examples.
Since both the topological and the trivial surface states are squeezed in the narrow gap between the electron and hole pockets (Fig. 3a–d), resolving the different features in ARPES measurement is the most challenging aspect to correctly identify the topological Fermi arcs. We search for the topological Fermi arcs in ARPES intensity maps with a surface-sensitive UV source (penetration depth of a few ångströms). The intensity contribution from bulk bands is largely suppressed by using selected specific surface-sensitive photon energy with different polarizations, and the surface states in-between the bulk electron and hole pockets can thus become more accessible experimentally.
Figure 3e–h shows the high-resolution ARPES intensity maps taken at 32.5 eV photon energy. The arcs (indicated by red arrows) are clearly observed. At EF (panels a, e, i) and −0.02 eV (panels b, f, j), the arcs and the trivial surface states are not well separated. However, as the electron pocket shrinks with decreasing energy, the separation between the topological Fermi arcs (red arrow in panel g and yellow arrow in panel k) and the trivial surface states (indicated by the grey arrow in panels c, g and h) becomes more pronounced. At −0.06 eV where the electron pocket completely disappears (panel d), the trivial surface states form a loop (panels d, h) and are clearly separated from the hole pocket. The evolution of the topological and trivial surface states in ARPES measurement is in good agreement with that from the band structure calculation. Furthermore, a comparison with the zoom-in calculated maps shows that the termination points of the observed arcs (panels e–h) line up with those of the calculated ones (yellow broken curves in panels i–l), explicitly supporting the presence of topological Fermi arcs.
The observed topological Fermi arcs reside on the two-dimensional crystal surface. We performed more experimental studies, including variable incident photon energy measurement and quasi-particle interference in real space, to support the surface nature of the observed electronic feature. Bulk states with different kz values selectively respond to different incident photon energy, which helps to separate the contributions from bulk and surface states. Figure 4a–h shows ARPES data measured along the –– direction with photon energies from 32.5 eV to 90 eV. The dispersions near the point change significantly with incident photon energy, suggesting that they are from bulk states. In contrast, the previously identified surface band (between EF and −0.1 eV and indicated by red arrows in panels b and c) appears at the same position with different photon energies. Consistently, this surface band is most clearly observed at 45 eV and 53 eV, where the penetration depth of photons reaches the minimum.
The complementary surface-sensitive probe STM provides further independent experimental evidence to support the surface nature of the arcs. Universal signatures of topological Fermi arcs in quasi-particle interference (QPI) on the surface of Weyl semimetals have been theoretically established by ref. 25. Various defects on the surface elastically scatter the electrons and induce the QPI pattern. In the surface Brillouin zone, the extremal pairs of ki and kf on a two-dimensional constant energy contour, where ki and kf are the initial and final wavevectors, contribute dominantly to the spatial interference pattern of the local electron density of states36. The spatial variation of the local density of states at a certain energy is the sum of the contributions from all of the extremal pairs on the constant energy contour and measured by the differential conductance (dI/dV) mapping with spatial resolution. The features in the Fourier transform of dI/dV mapping correspond to the scattering vector Q = kf − ki of the extremal pairs. QPI is more sensitive to the surface states or states with small kz dependence than to the bulk ones with strong kz dependence since the latter cannot host the ‘extreme pairs’. In this sense, QPI is advantageous in studying type-II Weyl semimetal MoTe2, where the topological Fermi arcs and the projected bulk pockets are very close in energy.
Figure 5a–i displays the fast Fourier transform (FFT) of the dI/dV maps between −10 mV and −90 mV. For a pair of topological Fermi arcs, three scattering wavevectors (Fig. 5j), labelled q1, q2 and q3, might be expected to appear in QPI. Among them, q3 is forbidden due to the requirement of the time-reversal symmetry in the system. Similar forbidden scattering was also experimentally observed in the surface states of topological insulators with time-reversal symmetry37. The scattering wavevectors should generate visible features centred between q1 and q2 and along the Γ–X direction (Fig. 5j). Such features are clearly resolved and indicated by red arrows in FFT. The existence of such a pattern beyond the band bottom of the trivial surface states (−60 mV) excludes the possibility of trivial surface states as the origin. Moreover, the dispersions extracted from the energy-dependent scattering wavevector (panel k) are in very good agreement with the q1 and q2 extracted from band structure calculation, providing further independent and strong evidence for the existence of topological surface states. By combining two complementary surface-sensitive experimental probes—STM, ARPES—with theoretical calculations, we provide direct and strong experimental evidence for the existence of the topological surface states, establishing it as a type-II Weyl semimetal.
High-quality β-MoTe2 single crystals were grown by chemical vapour transport using polycrystalline MoTe2 as precursors. Polycrystalline MoTe2 was synthesized by directly heating the stoichiometric mixture of high-purity Mo foil (99.95%, Alfa Aesar) and Te ingot (99.99%, Alfa Aesar) at 1,073 K in a vacuum-sealed silica ampoule for 3 days. The as-grown MoTe2 was then recrystallized by the chemical vapour transport method using powder TeCl4 (99%, Aladdin) as the transporting agent with a concentration of ≤2.7 mg ml−1. Material transport occurred in a sealed silica ampoule in a tube furnace for 3 days. After the reaction, the ampoule was immediately quenched in cold water to obtain large-size β-MoTe2 single crystals.
Bulk-sensitive laser-ARPES measurements have been performed in the home laboratory at Tsinghua University with a fourth harmonic generation light source. Surface-sensitive ARPES measurements have been performed at BL.4.0.1 and BL.12.0.1 of the Advanced Light Source using photon energies from 30.5 eV to 90 eV. The overall experimental energy resolution at 32.5 eV is better than 18 meV. The samples were cleaved and measured at 10–20 K in the Td phase.
STM experiments were conducted on a Unisoku ultrahigh-vacuum low-temperature (down to 4.2 K) system equipped with an in situ cleaving stage. The MoTe2 single crystals were cleaved in ultrahigh vacuum (5 × 10−11 torr) at room temperature and then transferred to STM to perform measurement at 4.2 K with a PtIr tip. QPI maps and dI/dV spectra were acquired using a lock-in amplifier at a frequency of 913 Hz.
The ab initio calculations are carried out in the framework of the Perdew–Burke–Ernzerhof-type generalized gradient approximation of the density functional theory through employing the Vienna Ab initio simulation package (VASP)40 with the projected augmented wave (PAW) method. The kinetic energy cutoff is fixed to 400 eV, and the k-point mesh is taken as 12 × 10 × 6 for the bulk calculations. The spin–orbit coupling effect is self-consistently included. The lattice constants are taken from experiments23, but the atoms in the unit cell are fully relaxed with the force cutoff 0.01 eV Å−1. Maximally localized Wannier functions are employed to obtain the ab initio tight-binding model of semi-infinite systems with the (001) surface as the boundary to exhibit surface states and topological Fermi arcs. An iterative method is used to obtain the surface Green’s function of the semi-infinite system.
The data that support the plots within this paper and other findings of this study are available from the corresponding author on request.
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This work is supported by the National Natural Science Foundation of China (grant no. 11274191, 11334006), Ministry of Science and Technology of China (no. 2015CB92100, 2016YFA0301004 and 2012CB932301) and Tsinghua University Initiative Scientific Research Program (no. 2012Z02285). The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231.
The authors declare no competing financial interests.
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Deng, K., Wan, G., Deng, P. et al. Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2. Nature Phys 12, 1105–1110 (2016). https://doi.org/10.1038/nphys3871
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