Observation of intervalley quantum interference in epitaxial monolayer tungsten diselenide

The extraordinary electronic structures of monolayer transition metal dichalcogenides, such as the spin–valley-coupled band edges, have sparked great interest for potential spintronic and valleytronic applications based on these two-dimensional materials. In this work, we report the experimental observation of quasi-particle interference patterns in monolayer WSe2 using low-temperature scanning tunnelling spectroscopy. We observe intervalley quantum interference involving the Q valleys in the conduction band due to spin-conserving scattering processes, while spin-flipping intervalley scattering is absent. Our results establish unequivocally the presence of spin–valley coupling and affirm the large spin splitting at the Q valleys. Importantly, the inefficient spin-flipping scattering implies long valley and spin lifetime in monolayer WSe2, which is a key figure of merit for valley-spintronic applications.

Ultrathin WSe 2 films are grown on highly ordered pyrolytic graphite (HOPG) by molecular-beam epitaxy (MBE). The electronic structure and QPI in ML WSe 2 are probed by STM/S at 77 K. LT-STS is a known powerful method for probing electronic structures of thin films and its studies have already been implemented to extract the quasiparticle band gaps and band edges in ML TMDs [14][15][16][17][18] . Quantum interference has been also studied by STM/S for metals 19 , topological insulators 20,21 and graphene 22   This has given us an opportunity to study the quantum interference effect in ultrathin WSe 2 by STM/S, thereby allows probing the electronic structure as well as the spin-splitting in ML-TMDs. The inset in Fig. 1a is a close-up atomic resolution image of the ML region of the sample. Fig. 1b shows the differential conductance spectrum measured at a fix point on ML WSe 2 by STS at 77 K. It reveals an energy gap of 2.59 ± 0.07 eV, in agreement with the previous report 16 . The Fermi level is found slightly above the mid-gap energy, suggesting the sample is slightly electron-doped, likely by some native defects such as Se vacancies.
To search for the QPI in ML WSe 2 , we firstly locate a surface area that contains point defects. An example is given in Fig. 1c, which shows two point defects in the field of view. In this region of the surface, quantum interference stands high chance to be observed by LT-STM/S. We began our search of the QPIs by taking the STS maps at energies close to the valence band maximum (≤ -1.4 eV). The absence of intervalley QPI in the valence band implies that spin-flip scattering between K and K ̅ valleys is inefficient. In ML WSe 2 , the ultra-strong spin-orbit coupling in the 5d orbitals of the metal atoms give rise to large spin splitting in both the conduction and valence bands, which are dictated by the mirror symmetry and time-reversal symmetry to be in the opposite out-of-plane directions at a time reversal pair of either K or Q valleys 3 . In Fig. 2a, we show electronic bands of ML WSe 2 calculated by the density functional theory (DFT), in which the red solid and dashed blue lines represent the spin-split bands due to spin-orbital coupling. The valence band edge at the K points has a spin splitting of ~ 0.4 eV with opposite signs at K and K ̅ as required by the time reversal symmetry 17,25 . Consequently quasi-particle interference between K and K ̅ valleys will be prohibited by the time-reversal symmetry if the scattering defects are nonmagnetic. Moreover, a recent study has shown that STM/S is not very sensitive to the K-valley states as compared to the  and Q valleys 17 , which can be another cause for the absence of QPI in the STS near the valence band maximum.
Conduction band electron has a completely different story. The spin-splitting is much smaller at the K-point (~ 0.03 eV), and the largest spin-split of ~ 0.2 eV occurs in the Q-valley (c.f. Fig. 2a). The energy minimum at Q is close to that of the K valleys in ML WSe 2 3,11,17,25 . Besides, Q valley can have a much larger weight in STM/S than K valley due to the larger density of states (DOS) as well as a larger tunneling coefficient 3,17 . Therefore the Q valleys are expected to play a significant role in the STS mapping of the empty-states. As illustrated in Fig. 2b, the six-fold degenerate Q valleys form two groups. Q 1 , Q 2 and Q 3 have the same spin and Q ̅ 1 , Q ̅ 2 and Q ̅ 3 are their time reversals. QPIs by the spin-conserved intervalley scattering are possible within each group. In addition, as the spin-split is small at K while the energy difference between Q and K is also small, QPIs by the spin-conserved scatterings between K and K ̅ , and between Q and K-valleys may also occur (c.f. Fig.   3d). A possible complication, however, is the presence of scattering between Q and K-valleys, which would result in a wavevector ( 3 in Fig. 3d) that is very similar to 4 . With the resolution of the experimental data, we cannot discriminate one from the other, and indeed both could occur. Nevertheless, according to the band structure calculations 11,26 , the Q-valley is situated slightly off the mid-point of -K and closer to K (see Fig. 2a), so 4 would be slightly larger than |M|, which appears consistent with the experimental data. Moreover, as noted earlier, the STM/S measurement should be more sensitive to Q states than the K valleys, therefore the Q-Q QPI has a larger chance to be picked up in the STM/S images compared to the Q-K one. We therefore believe that Q-Q scattering ( 4 ) is the dominating contributor to the experimentally observed spot next to M in Figs. 3b and 3c.
With the presence of both spin-up and down CEC at K valleys and the six-fold degenerate Q valleys, Q-K QPI at another two wavevectors, 2 and 5 , and K − K ̅ QPI at wavevector 1 are also possible through the spin-conserved scattering (see Fig. 3d). Though weak, intensity spots are indeed observable at 2 and 5 as shown in Figs. 3b and 3c. Intensity spot at wavevector 1 may not be discernable in Fig. 3b or 3c, which again may be attributed to the sensitivity of STM/S to K-valley electrons.
However, we did observe hint of such scatterings at some other energies (see and 3e also provides an experimental evidence for the presence of an appreciable spin-splitting at Q-valleys in ML WSe 2 , as otherwise the scattering would resemble that of Fig. 3f, where Q ̅ − Q scattering channels would be present (i.e., the black arrow in Fig. 4c). This is clearly not the case in the experiment.
By examining the STS maps obtained at different energies, we derive an energy dependence of the | |'s (peak-to-peak distances in FT-STS maps), and Fig. 4f summarizes the data for the wavevector 4 . There are apparently two branches, corresponding to | 4 | ~ 1.06 Å -1 and 1.14 Å -1 , respectively. According to first-principle band structures, the exterma of the upper and lower spin-subbands at the Q-valley do show a relative shift in momentum (as indicated by two short vertical arrows in Fig. 2a). Therefore we are tempted to attribute the two branches in Fig. 4f to be scatterings dominantly in the lower and upper spin-subbands, respectively. If this is indeed the case, we may further estimate the magnitude of the spin-split  SO at Q, which is about 0.2 eV. This value compares reasonably well with the first-principle calculation estimations 11 . However, a discrepancy exists, where most first-principle calculations suggest the upper spin-subband at Q has a smaller momentum than the lower one, which is opposite to the finding of Fig. 4f. Besides, the experimental data can have contributions of the other scattering channels (e.g. the Q-K scattering 3 ).
Hence the two momentum branches observed in Fig. 4f may reflect a change of dominance of the different scattering processes when the energy is changed. Further studies by higher resolution STM/S may resolve this ambiguity.
Lastly, we draw attention of the seemingly ring feature in the FT-STS map at the center ( Fig. 3b and 3c). It may have reflected intra-valley scattering of electrons.  and its high symmetry points (K and M) are also shown for reference.