Abstract
Weyl semimetal is a new quantum state of matter^{1,2,3,4,5,6,7,8,9,10,11,12} hosting the condensed matter physics counterpart of the relativistic Weyl fermions^{13} originally introduced in highenergy physics. The Weyl semimetal phase realized in the TaAs class of materials features multiple Fermi arcs arising from topological surface states^{10,11,14,15,16} and exhibits novel quantum phenomena, such as a chiral anomalyinduced negative magnetoresistance^{17,18,19} and possibly emergent supersymmetry^{20}. Recently it was proposed theoretically that a new type (typeII) of Weyl fermion^{21,22} that arises due to the breaking of Lorentz invariance, which does not have a counterpart in highenergy 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 typeII Weyl semimetal MoTe_{2} (refs 23,24,25). The topological surface states are confirmed by directly observing the surface states using bulk and surfacesensitive angleresolved photoemission spectroscopy, and the quasiparticle interference pattern between the putative topological Fermi arcs in scanning tunnelling microscopy. By establishing MoTe_{2} as an experimental realization of a typeII Weyl semimetal, our work opens up opportunities for probing the physical properties of this exciting new state.
Main
In the Brillouin zone of a typeI Weyl semimetal, the linearly dispersing and nondegenerate bands cross each other at the Weyl points (Fig. 1a). These bandtopology protected Weyl points can be created or annihilated only in pairs according to the nogo theorem^{1}. When projected onto the surface, the Weyl points are connected by the topologically protected Fermi arcs (Fig. 1a)^{2}. In contrast to the typeI Weyl fermions in the TaAs class or compressively strained HgTe^{12} that have a pointlike Fermi surface, the typeII 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 E_{F}. 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 fields^{21}.
TypeII Weyl fermion has been predicted in the orthorhombic T_{d} phase of WTe_{2} (ref. 21), which breaks the inversion symmetry and shows unusual transport properties^{26}. However, the small momentum separation of the Weyl points (0.7% of the Brillouin zone) and the extremely small size of the arcs^{21} make it exceptionally challenging to resolve the topological Fermi arcs in WTe_{2} by angleresolved photoemission spectroscopy (ARPES). A promising solution is provided by the prediction that the topological Fermi arcs can be significantly enlarged in MoTe_{2} (refs 23,24) or Mo_{x}W_{1−x}Te_{2} (ref. 27). Among these candidate materials, MoTe_{2} is particularly interesting because of the reported superconductivity^{28} and the predicted topological phase transition induced by temperature or strain^{23}. Although the electronic structures of WTe_{2} (refs 29,30,31) and Mo_{x}W_{1−x}Te_{2} (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 surfacesensitive 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 T_{d} phase of MoTe_{2}, establishing it as a typeII Weyl semimetal.
MoTe_{2} is polymorphic with three different structures: hexagonal (αphase, or 2H phase), monoclinic (βphase, or 1T′ phase) and orthorhombic (γphase, or T_{d} phase). The 1T′ phase has a distorted CdI_{2} structure (Fig. 1c) that crystallizes in the centrosymmetric space group P2_{1}/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 octahedra^{33,34}, causing the c axis to incline at an angle of ∼93.9° (ref. 33). A temperatureinduced phase transition from the hightemperature 1T′ to the lowtemperature T_{d} phase has been reported between 240 K to 260 K (ref. 33). The T_{d} phase (Fig. 1d) shares the same inplane crystal structure (Fig. 1e) as the 1T′ phase but has a vertical (90°) stacking and belongs to the noncentrosymmetric space group Pmn2_{1}. Weyl fermions are possible in the T_{d} phase only where the inversion symmetry is broken. The Brillouin zone of the T_{d} phase is shown in Fig. 1f.
Figure 1g shows the Xray diffraction intensity of the highquality MoTe_{2} single crystal at room temperature (1T′ phase). The Raman spectrum in Fig. 1h shows A_{g} vibrational modes at ∼160 and 260 cm^{−1} (ref. 35). The resistance measurement (Fig. 1i) confirms the firstorder phase transition between the T_{d} and 1T′ phases at ∼260 K, in agreement with previous results^{33}. The high crystallinity of the samples is revealed by the sharp diffraction spots (Fig. 1j) in the lowenergy electron diffraction pattern measured on a freshly cleaved sample in the T_{d} phase. The atomically resolved STM topography in Fig. 1k further confirms the high quality of the MoTe_{2} 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 MoTe_{2} in the T_{d} phase measured by ARPES with band structure calculation along the aaxis (––) direction. In band structure calculation, the bands with significant k_{z} 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 firstprinciples 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 ppolarization light (Fig. 2b), while the spolarization 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 belllike shapes on both sides away from the Γ point and part of the bowtieshaped outer contour around the Γ point is contributed by the hole pockets at E_{F}. These bulk states are better observed with a bulksensitive 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 bowtieshaped 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 chiralities^{21,23,24}. 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 semimetallic state. The characteristic electronic structure of T_{d} phase MoTe_{2} 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 surfacesensitive UV source (penetration depth of a few ångströms). The intensity contribution from bulk bands is largely suppressed by using selected specific surfacesensitive photon energy with different polarizations, and the surface states inbetween the bulk electron and hole pockets can thus become more accessible experimentally.
Figure 3e–h shows the highresolution ARPES intensity maps taken at 32.5 eV photon energy. The arcs (indicated by red arrows) are clearly observed. At E_{F} (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 zoomin 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 twodimensional crystal surface. We performed more experimental studies, including variable incident photon energy measurement and quasiparticle interference in real space, to support the surface nature of the observed electronic feature. Bulk states with different k_{z} 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 E_{F} 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 surfacesensitive probe STM provides further independent experimental evidence to support the surface nature of the arcs. Universal signatures of topological Fermi arcs in quasiparticle 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 k_{i} and k_{f} on a twodimensional constant energy contour, where k_{i} and k_{f} are the initial and final wavevectors, contribute dominantly to the spatial interference pattern of the local electron density of states^{36}. 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 = k_{f} − k_{i} of the extremal pairs. QPI is more sensitive to the surface states or states with small k_{z} dependence than to the bulk ones with strong k_{z} dependence since the latter cannot host the ‘extreme pairs’. In this sense, QPI is advantageous in studying typeII Weyl semimetal MoTe_{2}, 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 q_{1}, q_{2} and q_{3}, might be expected to appear in QPI. Among them, q_{3} is forbidden due to the requirement of the timereversal symmetry in the system. Similar forbidden scattering was also experimentally observed in the surface states of topological insulators with timereversal symmetry^{37}. The scattering wavevectors should generate visible features centred between q_{1} and q_{2} 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 energydependent scattering wavevector (panel k) are in very good agreement with the q_{1} and q_{2} extracted from band structure calculation, providing further independent and strong evidence for the existence of topological surface states. By combining two complementary surfacesensitive 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 typeII Weyl semimetal.
Note added in proof: During revision of this manuscript for resubmission, we became aware of related work^{38,39}.
Methods
Sample growth.
Highquality βMoTe_{2} single crystals were grown by chemical vapour transport using polycrystalline MoTe_{2} as precursors. Polycrystalline MoTe_{2} was synthesized by directly heating the stoichiometric mixture of highpurity Mo foil (99.95%, Alfa Aesar) and Te ingot (99.99%, Alfa Aesar) at 1,073 K in a vacuumsealed silica ampoule for 3 days. The asgrown MoTe_{2} was then recrystallized by the chemical vapour transport method using powder TeCl_{4} (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 largesize βMoTe_{2} single crystals.
ARPES measurement.
Bulksensitive laserARPES measurements have been performed in the home laboratory at Tsinghua University with a fourth harmonic generation light source. Surfacesensitive 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 T_{d} phase.
STM measurement.
STM experiments were conducted on a Unisoku ultrahighvacuum lowtemperature (down to 4.2 K) system equipped with an in situ cleaving stage. The MoTe_{2} 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 lockin amplifier at a frequency of 913 Hz.
Firstprinciples calculations.
The ab initio calculations are carried out in the framework of the Perdew–Burke–Ernzerhoftype 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 kpoint mesh is taken as 12 × 10 × 6 for the bulk calculations. The spin–orbit coupling effect is selfconsistently included. The lattice constants are taken from experiments^{23}, 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 tightbinding model of semiinfinite 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 semiinfinite system.
Data availability.
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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Acknowledgements
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. DEAC0205CH11231.
Author information
Author notes
 Ke Deng
 , Guoliang Wan
 & Peng Deng
These authors contributed equally to this work.
Affiliations
State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
 Ke Deng
 , Guoliang Wan
 , Peng Deng
 , Kenan Zhang
 , Shijie Ding
 , Eryin Wang
 , Mingzhe Yan
 , Huaqing Huang
 , Hongyun Zhang
 , Zhilin Xu
 , Haitao Yang
 , Wenhui Duan
 , Shoushan Fan
 , Xi Chen
 & Shuyun Zhou
Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
 Jonathan Denlinger
 & Alexei Fedorov
TsinghuaFoxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China
 Haitao Yang
 , Yang Wu
 & Shoushan Fan
Collaborative Innovation Center of Quantum Matter, Beijing, China
 Wenhui Duan
 , Hong Yao
 , Shoushan Fan
 , Xi Chen
 & Shuyun Zhou
Institute for Advanced Study, Tsinghua University, Beijing 100084, China
 Hong Yao
National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
 Haijun Zhang
Collaborative Innovation Center of Advanced Microstructures, Nanjing, China
 Haijun Zhang
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Contributions
S.Z., X.C. and Y.W. conceived the research project. K.D. and K.Z. grew and characterized the samples under the supervision of Y.W. K.D., G.W., K.Z., S.D., E.W., M.Y. and Hongyun Z. performed the ARPES measurements and analysed the ARPES data. J.D. and A.F. provided support for the ARPES experiments. P.D. and Z.X. performed the STM measurements. Haijun Z. performed the firstprinciples calculations presented in the manuscript. H.H. and W.D. repeated the calculation. K.D., H.Yao, Y.W., X.C. and S.Z. wrote the manuscript, and all authors commented on the manuscript.
Competing interests
The authors declare no competing financial interests.
Corresponding authors
Correspondence to Yang Wu or Xi Chen or Shuyun Zhou.
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