Abstract
Weyl semimetals display a novel topological phase of matter where the Weyl nodes emerge in pairs of opposite chirality and can be seen as either a source or a sink of Berry curvature. The exotic effects in Weyl semimetals, such as surface Fermi arcs and the chiral anomaly, make them a new playground for exploring novel functionalities. Further exploiting their potential applications requires clear understanding of their topological electronic properties. Here we report a Fourier transform scanning tunneling spectroscopy (FTSTS) study on a typeII Weyl semimetal candidate MoTe_{2} whose Weyl points are predicated to be located above Fermi level. Although its electronic structure below the Fermi level has been identified by angle resolved photo emission spectroscopy, by comparing our experimental data with firstprinciples calculations, we are able to identify the origins of multiple scattering channels both below and above Fermi level. Our calculations also show the existence of both trivial and topological arclike states above the Fermi energy. In the FTSTS experiments, we have observed strong signals from intraarc scatterings as well as from the scattering between the arclike surface states and the projected bulk states. A detailed comparison between our experimental observations and calculated results reveals the trivial and nontrivial scattering channels are difficult to distinguish in this compound. Interestingly, we find that the broken inversion symmetry changes the terminating states on the two inequivalent surfaces, which in turn changes the relative strength of the scattering channels observed in the FTSTS images on the two surfaces.
Introduction
Transition metal dichalcogenides (TMDs) provide a fertile ground for exploring exotic collective quantum phenomena, such as superconductivity and charge density waves.^{1,2,3} Recently, the Mo_{x}W_{1x}Te_{2} class of TMDs has attracted great interest due to the topological nature of the electronic states and as a topological Weyl semimetal (TWS).^{4,5,6,7} Their lowenergy excitations behave as Weyl fermions that always appear in pairs with opposite chirality. TWSs are classified into typeI and typeII: typeI TWSs have point like Fermi surfaces and respect Lorentz invariance, while typeII with tilted Weyl cones break Lorentz invariance.^{5,8,9} TypeI TWSs were first predicted and experimentally discovered in the (Ta, Nb) (As, P) family compounds.^{8,9,10,11} TypeII TWSs have been proposed to exist in the Mo_{x}W_{1x}Te_{2} family TMDs^{4,5,6,7} and LaAlGe.^{12} In this system, the tilted Weyl cones that arise from topologically protected crossings of valence and conduction bands cause touching points between electron and hole pockets near the Fermi level. Exotic Fermi arcs states that join these touching points, are expected on the surfaces of these materials. In the last few years, there have been a series of experimental studies aimed at verifying the existence of the Fermi arcs.^{13,14,15,16,17,18,19,20,21}
For the Mo_{x}W_{1x}Te_{2} family, the Weyl nodes are usually located at energies above the Fermi level which makes it difficult to be accessed by conventional angle resolved photo emission spectroscopy (ARPES).^{13,14,15,17,20} Fourier transform scanning tunneling spectroscopy (FTSTS) contains information on the scattering vectors between electronic states in momentum space and can provide the information on both the occupied and unoccupied states^{22} which makes it a particularly powerful probe for the topological states of the Mo_{x}W_{1x}Te_{2}. There have been several FTSTS studies on the Mo_{x}W_{1x}Te_{2.}^{15,23,24,25,26,27,28} However, due to the complex band structure and the low signal strength in the FTSTS images, the existence of Fermi arcs in Mo_{x}W_{1x}Te_{2} system still remains to be clarified.
Here we use lowtemperature scanning tunneling microscopy (STM) and firstprinciples calculations to directly visualize and identify the electronic states in MoTe_{2}, an end member of the Mo_{x}W_{1x}Te_{2} system. The other end member, WTe_{2} was the first predicated typeII Weyl semimetal, but the small momentum separation between the opposite Weyl points that are located about 50 mV above the Fermi level, made experimental confirmation by conventional ARPES difficult.^{5,14} MoTe_{2} was later predicated as another candidate of typeII Weyl semimetal where the Weyl points have six times larger momentum separation which makes experimental probe of Weyl nodes much easier.^{6,7} For MoTe_{2}, previous ARPES works have found evidence for the trivial and topologically protected Fermi arcs at energies below Fermi level.^{18,19,20} However, for various reasons such as the size of the STS maps or the properties of the scattering impurities, previous FTSTSs on MoTe_{2} did not show sufficient signal strength to perform a clear analysis of the FTSTS data, and have not arrived at an unequivocal conclusion about the nature of the Weyl states. In this work, we present FTSTS data with much higher signal strength that allows us to compare the various scattering channels observed in the experimental data with theory, and reach a robust conclusion on the origins of the scattering channels. Interestingly, based on this higher resolution FTSTS data, we come to different conclusions compared to the previous work:^{15,23,24,26} the trivial and nontrivial scattering channels are indistinguishable in the FTSTS images. Moreover, the broken inversion symmetry in this compound is reflected in the FTSTS images taken on two inequivalent surfaces.
Results
The T_{d} phase crystal has an orthorhombic structure with van der Waals stacking of TeMoTe sandwich layers along the caxis direction as shown in Fig. 1a. Due to the weak van der Waals interaction between the Te layers, the MoTe_{2} sample cleaves at the Te layers and the cleaved surface is Teterminated. The bulk, and surface Brillouin zones for this termination, is shown in Fig. 1b. In highresolution STM topographies, the two inequivalent Te atomic rows in the top Te layer can be clearly resolved (Fig. 1d). There are mainly two kinds of atomic defects and they look different in the STM topographies taken with positive bias voltages (as shown in the red and black circles in Fig. 1e). The defects lie on the Te sites and are likely to be Te vacancies/impurities in the two Te atomic rows at the top Te layer. In addition, in the negative bias topography, there are other faint defects that may be attributed to vacancies/impurities in the layers underneath (more details can be found in Supplementary Fig. S1 and Fig. S2).
Figure 1f shows the position dependent dI/dV spectra taken on a 50 nm by 50 nm area on MoTe_{2} in the energy range of ±500 mV. In general, the dI/dV spectra are parabolashaped with minimum around 10 mV above the Fermi level. Despite the presence of impurities, the low energy density of states as well as the overall parabolashape of the spectra remains homogeneous and there are no clear impurityinduced resonance states in this energy range.^{26} However, the scattering pattern of quasiparticles by the atomic impurities can be clearly seen in the dI/dV maps, Fig. 1c. The next step is to study the Fourier transforms of the dI/dV maps to look for signatures of the electronic states in momentum space.
Figure 2a–i shows FTSTS images at a few energies below and above the Fermi level (also see Figs. S6 and S7). There is a distinct change in the FTSTS as we go from negative to positive energies. With increasing the bias above the Fermi level, several strong scattering vectors gradually emerge. To identify the origin of the scattering vectors we carried out firstprinciples density functional theory (DFT) calculations of band structures of MoTe_{2} which were then used to calculate FTSTS images. Using the iterative Green’s function method, we obtained the surface states of MoTe_{2} under different terminations (details in Supplementary Section 8 which were then used to simulate the FTSTS patterns using spindependent scattering probability method).
As can be seen in Fig. 3, the simulated FTSTS matches well with the measured FTSTS over a wide range of energies. In the measured FTSTS at energies below −100 mV (right panel in Fig. 3a), there is a liplike feature with a bright center. By comparing with the simulated FTSTS at −140 mV, we conclude that this liplike feature is due to the scattering of the bulk states of MoTe_{2} (Supplementary Fig. S5). At −40 mV, the measured FTSTS shows two short arclike features at the left or right side of the bright center spot (right panel of Fig. 3b). Due to the multiple scattering vectors seen in the simulated FTSTS at negative bias voltages, it is difficult to unambiguously identify the origin of these two short arcs. However, by comparing the momentumspace position of these short arcs, we conclude that they most likely arise from the scattering processes from the trivial surface states to the holepockets. At positive bias voltages, the scattering patterns become much clearer (Fig. 2i). By comparing the calculated FTSTS with the measured FTSTS at +40 mV and +100 mV (Fig. 3c, d and Supplementary Fig. S9), we can for the first time identify all the scattering patterns as: Q_{1} is induced by the intrascattering of the topologically trivial surface states; Q_{2} is caused by the scattering between the surface states and the electron pockets. Q_{3} and Q_{4} are due to the scattering between the surface states and the projected bulk states at the \(\bar Y\) point.
Although, the highresolution FTSTS data clearly show multiple scattering vectors from the surface states and our experimental measurements match the numerical calculations, these data alone do not provide unambiguous evidence for the existence of nontrivial Fermi arcs. According to our calculations, the Weyl points for MoTe_{2} are located at 4 mV and 57 mV. As the energy increased from the Fermi level to +100 mV, the scattering vectors (Q_{1}–Q_{4}) gradually emerge in the measured FTSTSs (Fig. 2f–i), and there is no sudden change in the FTSTSs near the energy positions of the Weyl nodes. This suggests that there are no clear features induced by the nontrivial Fermi arcs in the FTSTSs on MoTe_{2}. We note that our conclusions are in contrast with previous studies.^{15,23,24,26,27} Most previous STM studies have claimed that Mo_{x}W_{1x}Te_{2} family material is a Weyl semimetal based on the existence of the long Fermi arcs in the FTSTS data. However, based on our theoretical and experimental studies we find that the long arcs arise primarily from topologically trivial scattering channels. In addition, for Mo_{0.66}W_{0.34}Te_{2} samples, the absence of the scattering vector (Q_{3}) between the arclike feature and projected bulk states was taken as proof of the existence of the topological Fermi arc.^{27} In contrast, in our highresolution data on MoTe_{2}, we clearly detect this scattering vector (Q_{3}) thereby determining that the scattering process from trivial surface states forms an important component of the scattering seen in our FTSTS data.
Discussion
This leads to the question: why is it difficult to detect the nontrivial Fermi arcs in MoTe_{2} even with highresolution FTSTS measurements? Weyl fermions are local singularities in momentum space (Fig. S10). Therefore, at energies or momentum space away from the Weyl nodes, the nontrivial properties induced by Weyl fermions are negligible. In Fig. 4 we show the calculated surface states of MoTe_{2} at three different energies, below, at, and above the Fermi level. Figure 4a–c shows constant energy contours at −40 mV, 0 mV, and +40 mV, respectively. Figure 4d–f is the zoomin of Fig. 4a–c in the momentum region around the positions of the Weyl nodes (the orange rectangle area shown in Fig. 4a–c). Figure 4d clearly shows that the long topologically trivial arc in Fig. 4a lies far from the Weyl nodes in momentum space, and it is therefore not related to the Weyl nodes. With increasing energy, the topologically trivial arc moves toward the Weyl nodes and starts to touch the Weyl nodes at the Fermi level (Fig. 4e). In the constant energy contour of E = +40 meV, the long trivial arc is disconnected with the Weyl nodes and a small topological Fermi arc (arc 2) can be seen in between the two Weyl nodes, as shown in Fig. 4f (also see Fig. S10). However, the separation in momentum space between the nontrivial arc (arc 2) and the trivial arcs (arc 1 and 3) is only about 0.008 Å^{−}^{1}, which makes it extremely difficult to distinguish the scattering features in FTSTS induced by the nontrivial arc and those induced by the long trivial arc. Thus, by comparing the STM data with calculations, we conclude that the trivial and nontrivial scattering channels are difficult to distinguish in this compound.
Finally, our STM data show signatures of the broken inversion symmetry that’s critical to the physics of MoTe_{2}. Due to the bulk broken inversion symmetry, the two surfaces obtained after cleaving are inequivalent (Supplementary Fig. S11). As shown in Fig. S11, while the surface structure itself is the same, the atomic arrangement in the second layer is different between the two surfaces. An earlier ARPES study had suggested that this might affect the electronic structure.^{20} The two inequivalent surfaces were revealed in our data when different cleaves showed slightly different FTSTS patterns (Fig. 5, Supplementary Fig. S12 and Fig. S13). Our FTSTS calculations for the second surface, also show that the terminating electronic states are measurably different for the two surfaces. The differences arise from the different weights of bulk and surface states on the two terminations which makes the scattering channels in the measured FTSTS images taken on these two surfaces have different relative strengths. While the match between the calculations and data are not as good for this second surface, both STM as well as theory indicate that the broken inversion symmetry makes the two surfaces electronically inequivalent (Fig. 5).
In conclusion, we have performed a detailed lowtemperature STM/STS study on the MoTe_{2} sample. In the spatially resolved dI/dV maps, the quasiparticle interference patterns can be clearly resolved. We thoroughly characterized the electronic structure of MoTe_{2} with FTSTSs taken at energies both below and above the Fermi level. In the highresolution FTSTSs above Fermi level, the scattering vectors between the trivial arcs and the projected bulk states can be clearly resolved. Due to the small momentumspace separation between the nontrivial arc and the trivial arc, it is difficult to clearly identify the nontrivial arc features in the FTSTSs. Our data show that the bulk broken inversion symmetry has a measurable effect on the surface electronic properties.
Methods
Sample synthesis
The MoTe_{2} single crystals were grown by using a chemical vapor transport method. A mixture of stoichiometric Mo and Te powder were sealed into an evacuated quartz tube with iodine used as a transport agent. The quartz tube was then placed in a double zone furnace with temperature gradient from 900 °C to 800 °C. Largesingle crystals of centimeter size were obtained after 2 weeks. The composition and structure of MoTe_{2} single crystals were checked using Xray diffraction and an energydispersive Xray spectrometer.
Scanning tunneling spectroscopy measurements
Highquality MoTe_{2} samples were cleaved at 77 K and immediately inserted into the STM scanner at 6 K. Differential conductance (dI/dV) spectra were acquired at 6 K using a standard lockin technique with ~4 mV_{rms} modulation at a frequency of 987.5 Hz.
Data availability
All data are available upon request from the corresponding authors.
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Acknowledgements
STM work was supported by the US Department of Energy, Scanned Probe Division under Award Number DESC0014335. S.Y. acknowledges the financial support from Science and Technology Commission of Shanghai Municipality (STCSM) (Grant No. 18QA1403100) and the startup funding from ShanghaiTech University. The work at Tulane University was supported by the US Department of Energy under Grant No. DESC0014208 (support for single crystal growth).
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S.Y. and V.M. conceived the experiment. Samples were grown by J.H. and obtained from Z.M. S.Y. and D.I. carried out the STM studies. G.C., T.R.C., and H.L. did all the calculations. S.Y., V.M., and D.I. wrote the paper.
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Iaia, D., Chang, G., Chang, T. et al. Searching for topological Fermi arcs via quasiparticle interference on a typeII Weyl semimetal MoTe_{2}. npj Quant Mater 3, 38 (2018). https://doi.org/10.1038/s4153501801125
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