Supplementary Information

Transcription

1 Supplementary Information Supplementary Figure 1 AFM and Raman characterization of WS 2 crystals. (a) Optical and AFM images of a representative WS 2 flake. Color scale of the AFM image represents 0-20 nm. Scale bar is 5 μm. The thickness of WS 2 substrates used in this study varied from 5 nm to 15 nm. The surface topography shows that the surface roughness in WS 2 (~110 pm) is comparable to that of Boron Nitride. (b) Raman spectrum of few layers WS 2 with and without graphene. Unlike the peak at 351 cm -1, the intensity of the peak at 418 cm -1 is reduced slightly after the graphene transfer. 1

2 Supplementary Figure 2 Charge transport in few layer WS 2. Two terminal resistance measurement in few layers of WS 2 flakes fabricated with Cr/Au and Ti/Au contacts. With Cr/Au contacts the source drain current remains negligibly small over the entire gate voltage range (I SD <50nA). Thus, Cr/Au contacts are utilized in graphene/ws 2 heterostructure devices so that an Ohmic contact is created to graphene but not to WS 2 directly. This minimizes the chance of having a small but finite, parallel conducting channel. 2

3 Supplementary Figure 3 Charge transport in inverse structure. Conductivity of graphene as a function of top-gate voltage in Top-gate/PVDF/Graphene/WS 2 /SiO 2 /Si heterostructure at room temperature. The inset is the optical image of the measured device. The observation of saturation in conductivity demonstrates: 1-) The saturation in graphene conductivity is not due to parallel conductance of WS 2 as the charge carriers in graphene is tuned through PVDF dielectric rather than WS 2 itself. 2-) The persistence of saturation in graphene conductance even at high V TG show that the density of sulphur vacancies is at least in the order of cm -2. 3

4 Supplementary Figure 4 Charge transport in Graphene/WS 2 heterostructure. (a) Normalized resistance of graphene field effect transistors fabricated on SiO 2, WS 2 and BN substrates at RT. Graphene devices on SiO 2, WS 2 and BN substrates have mobilities of ~8,000, ~ 50,000, and 65,000 cm 2 /Vs respectively (b) Topography of substrates. Scan size is 1 μm x 1μm and height scale bar is 0-3 nm. The roughness of WS 2 (rms ~ 0.08nm) is slightly higher than BN (rms ~ 0.06nm) but much less than SiO 2 (rms ~ 0.17nm) substrate. 4

5 a R XX (kω) R XX (kω) R XX (kω) T 5T 0T V BG (V) b R XY (e 2 /h) R XY (e 2 /h) R XY (kω) T 5T 0T V BG (V) Supplementary Figure 5 Magnetotransport measurements in high fields in Graphene/WS 2 heterostructure. (a-b) Longitudinal and Hall resistance measurements as a function of back gate voltage at fixed magnetic fields at T = 1.5K. Uniquely to this system, on the electron side both R XX and R XY saturates above a V TH ~ 15V. By tuning the Fermi level with B, it is possible to keep the Landau Levels completely filled over an extraordinarily broad range of back gate voltages. The observed phenomenon allows for sustaining a non-dissipative current over a large back gate range, resulting in an unusual robust quantization of the resistance. 5

6 Supplementary Figure 6 Full set of data from another graphene/ws 2 device. (a) Back gate voltage dependence of resistivity and conductivity data at another G/WS 2 reference sample at 2K. A field effect mobility of ~ 50,000 cm 2 /V.s is extracted near the Dirac point. The inset shows the AMF picture of graphene channel on WS 2 substrate. (b) Non-local resistance as a function of V BG. A spin signal of R ~ 2 Ω is observed. (c) Non-local resistance as a function of in-plane applied magnetic field at V BG = 60V, 40V, CNP and -60V. An oscillating signal with applied in-plane magnetic field is only observed at V BG > V TH where we observe the non-local signal from gate dependent measurements as well. This confirms that the origin of signal is spin transport at V BG > V TH. 6

7 Supplementary Figure 7 Non-local measurements with dc current. Current bias dependence of non-local signal. Inset shows the current bias and magnetic field dependence of non-local signal. The linear dependence of measured voltage with applied current bias (both current polarities) excludes the Joule heating as the source of signal. 7

8 Supplementary Figure 8 Non-local measurement with ac and dc techniques. (a) Back gate voltage dependence of the non-local signal at zero magnetic field and T=2.5K. (b) Magnetic field dependence of the non-local signal at V BG = 60V and at T = 2.5K. Both the magnitude and asymmetry of the non-local signal is identical in DC and AC measurements 8

9 Supplementary Figure 9 Temperature dependence of non-local signal. (a) Spin precession measurement at 2.5K, 20K, 40K and 60K. The observation of a clear spin precession effect even at 60K (~ 5.15 mev) acts as an independent confirmation of the enhancement in the strength of the SOC. We note that the strength of SOC obtained from temperature dependent measurement is at the same order with the value extracted from the fitting of the spin precession signal at 2K. (b) Temperature dependence of non-local signal. 9

10 Supplementary Figure 10 Quantum interference measurements in Graphene/WS 2 heterostructure. (a) Conductivity of graphene/ws 2 at zero magnetic field (b) Magnetoconductance of graphene/ws 2 measured at T=1.2 K in perpendicular magnetic field. The magneto conductance is rescaled and shifted to fit to the Maekawa-Fukuyama formula, the measurements show weak localization like behavior at negative backgate and weak antilocalization, associated with strong spin orbit splitting, at V BG >V TH. The black and red dashed lines in back gate voltage dependence of graphene conductivity plot shown in (a) represents the fixed back gate voltages where low field magnetic field dependent measurement was performed. 10

11 Supplementary Figure 11 Charge transport in non-annealed samples. (a-b) Optical and AFM images of a transferred graphene on WS 2 substrate. Red dashed lines represent the border of graphene flake for better clarity. In order to exclude the annealing process as the source of vacancies in substrate, this device was not annealed at any step of the fabrication process. (b) Resistivity and conductivity of graphene as a function of back gate voltage at 2K. A mobility of ~ 5,000 (12,000) cm 2 /V.s is extracted at high (low) charge carrier concentrations. The mobility is limited due to presence of bubbles at the interface, as well as polymer residues on graphene. (c) Landau fan plot of longitudinal resistance as a function of back gate voltage and magnetic field. Similar to the annealed sample shown in the main article, the saturation of conductivity above V TH still exists even externally magnetic field is applied. These results prove that sulphur vacancies form during the growth process and are therefore unavoidable. (d) Non-local resistance as a function of V BG. A spin signal of R ~ 1.5 Ω is observed. 11

12 Supplementary Figure 12 XPS survey scan of WS 2 crystal acquired with Mg Ka line. 12

13 Supplementary Figure 13 First-principle calculations. Geometry of (a) O substituting for S (b) adsorbed oxygen on the S layer (c) adsorbed oxygen in the W layer. Bandstructures of defects in bulk WS 2 : oxygen in the (d-e) S 4 and Mo 1 positions, and (f) substitutional silicon. 13

14 Supplementary Figure 14 Bandstructures of the interfaces of graphene on monolayer WS 2. (a) pristine monolayer WS 2 ; (b) monolayer WS 2 with a sulphur vacancy. The bandstructures were obtained directly from first-principles fully relativistic calculations. 14

15 Supplementary Figure 15 Effective mass calculation of graphene on WS 2 substrate. (a-b) Landau fan plots of longitudinal resistance at 15K and 30K, (c) Amplitude of SdH oscillation as a function magnetic field at different temperature values. (d) Calculated effective mass and carrier concentration as a function of back gate voltage. While m increases slightly in V BG on the hole side, it saturates above the threshold voltage on electron side. 15

16 Supplementary Table 1 The summary of measured samples. While the spin signal presents in all samples, the non-local signal at Dirac point has sample to sample variation. 16

17 Supplementary Note 1 Sample-to-Sample Variation of Non-local Signal. While the overall behavior of the non-local resistance as a function of V BG is similar in all characterized samples, we see sample-to-sample variation in the amplitude of non-local signal especially near Dirac peak. A detailed summary of measured samples is shown in Supplementary Table 1. While samples #3 and #5 have signals at Dirac point comparable to the estimated Ohmic contribution, we observe a non-local resistance near Dirac peak which is higher than the estimated Ohmic contribution in most of the measured devices 1. The absence of spin precession signal near Dirac point suggests that the signal near Dirac peak is artifact. There is no correlation between the signal at Dirac peak and mobility. Further studies are required to explain the origin of signal near Dirac point. However, as discussed in main text, the spin contribution to R NL can be easily estimated in our devices, since the observed proximity effect exhibits a strong electron hole asymmetry. For V BG > V TH we observe a non-local signal due to enhanced spin orbit strength. A new set of transport results of a G/WS 2 heterostructure is shown in Supplementary Fig. 6. As shown in Supplementary Fig. 6a, the sample shows the saturation of conductivity above threshold voltage (V TH ~20V) at electron side. A field effect mobility of ~50,000 cm 2 /V.s is extracted near the Dirac point. From the non-local measurements, we observe a non-local signal once V BG > V TH (Supplementary Fig. 6b). While the background signal at Dirac point is reduced compared to the previously shown samples in manuscript, the signal is higher than the estimated Ohmic contribution. As shown in Supplementary Fig. 6c, the spin precession effect near Dirac point is missing justifying why the signal at Dirac point can not be associated to spin dependent signal. An oscillating signal with applied in-plane magnetic field is only observed at V BG > V TH where we observe the non-local signal from gate dependent measurements as well. This confirms that the origin of signal is spin transport at V BG > V TH. 17

18 Supplementary Note 2 XPS of WS 2 crystal. X-ray photoelectron spectroscopy (XPS) measurements were performed by using non monochromatic Mg Ka radiation (1253.6eV). Supplementary Fig. 12 shows the survey scan of a WS 2 crystal. Along with W and S core levels, O 1s and C 1s peaks are also observed. Next, we focus on the XPS spectra of W 4f and S 2p core levels (Fig. 4A). The W 4f core level peak can be fitted to two sets of doublets corresponding to W (+6) and W (4+) oxidation states. The presence of W (+6) oxidation states indicates that tungsten disulphide has undergone oxidation. The observed peak position for W 4f7/2 for the +6 and +4 oxidations states matches with those reported in the literature 2. The S 2p peak could be fitted to only one set of doublet corresponding to S-W bonding. The stoichiometry of the WS 2 crystal was obtained from: [ W ] σ = [ S] σ S 2 p W 4 f ( hν ) λ ( hν ) λ S 2 p W 4 f I I W 4 f S 2 p (1) where σ S2p (hν) and σ W4f (hν) are photo-ionization cross sections of the 2p and 4f core level of sulphur and tungsten, respectively. The values of σ S2p (hν) and σ W4f (hν) are and 0.18 Mb, respectively, obtained from tabulated data 3. λ S2p and λ W4f are inelastic mean free paths (IMFP) of the photoelectrons with kinetic energies that correspond to the S and W core levels, respectively. The values of λ S2p and λ W4f were estimated to be 1.29 nm and 1.36 nm respectively using the Seah and Dench method 4. I S2p and I W4f are the integrated intensities of the photoelectron peaks of the S 2p and W4 f levels after fitting, respectively. The error arising from the fitting is ~4%. With these values, the [W]/[S] ratio was estimated to be 0.57-/+0.02, which corresponds to 12 % sulphur vacancies in the crystal. Thus, the key findings of the XPS studies are that (1) the WS2 crystals are notably sulphur deficient and (2) the sample is free of metal impurities in detectable concentrations. The origin of sulphur deficiency is partly due to the suspected partial oxidation and polycrystallinity of the sample. However, the estimate of 12 % is an upper limit to the sulphur vacancies for the following reasons: First, our CVD-grown WS 2 crystal consists of 50~500 μm size polycrystalline grains, much smaller than the XPS probe size (~ 1 mm). The suspected presence of W terminated edge 18

19 atoms (i.e. locally sub-stoichiometric) will lead undoubtedly to some errors in the estimation of the sulfur vacancies. It should also be noted that the surface terraces are expected to exhibit high concentration of edge defects. Therefore, in small scale atomically thin cleaved single crystal, WS 2 flakes used for our transport studies, the vacancy concentration is almost certainly smaller. The possible presence of divacancies is also like to further reduce this lower bound 5. With regards to oxidation, we observe a small fraction of W 6+ states along with W 4+ that are expected for ideal WS 2. Based on our fits, this amounts to approximately 4% of the total W atoms. It is conceivable that some of the sulfur vacancies are passivated by O atoms, or conversely, that some of the W signals are coming from WO 3 that may be present in the sample. In either case, this leads to a lower concentration of sulfur sites that are actually vacant, setting a lower bound to around 5 % (~1.2x cm -2 ). Note also that W. Zhou et al. 5 and H. Wiu et al. 6 have recently provided direct evidence that sulphur vacancies are abounded in CVT grown molybdenum disulfide. Since TMDCs have similar structures and properties, a similar concentration of sulphur vacancies is expected in WS 2. In fact, our results based on XPS are in agreement with the TEM imaging results of those authors (with respect to the order of magnitude). Based on all these considerations, we conclude even just assuming the lower bound it is reasonable there is a large concentration of sulphur vacancies of the order of cm -2. This is significantly larger than the concentration of other impurities and thus the vacancies play a dominant role in the phenomenon that is reported in this study. 19

20 Supplementary Note 3 First-principle calculations. Defects Our XPS measurements clearly indicate that WS 2 crystals have oxygen impurities and sulphur deficiency. To check the effect of such defects we have performed non-relativistic DFT calculations by using the method described in reference 7. For the dispersion we used the correction by Grimme 8. Bulk WS 2 was modelled using a supercell, with the experimental c/a ratio. The graphene/ws 2 monolayer interface was modelled in a supercell with 3 3 primitive cells of WS 2 and 4 4 primitive cells of graphene, with the respective lattice vectors aligned. We investigated Si and O replacing for S (noted Si S and O S ), adsorbed oxygen (noted O ad ) and S and W vacancies. The substitutional configuration is shown in Supplementary Fig. 13a. The two configurations found by Ataca et al. [S9] are depicted Supplementary Fig. 13b-c. The O ad configuration II (Mo 1 in Ref. 9) is 1.7eV higher in energy than the O as configuration I (S 4 in Ref. 9). Finally, the S and W vacancies are modelled by removing the respective atoms. In both cases there is little lattice reconstruction. The non-relativistic bandstructure of bulk supercells containing defects with levels in the gap are shown in Supplementary Fig. 13d-f. The position of the conduction band is underestimated by 0.2 ev within the working approximations. This underestimation is systematic and well known. Since the only oxygen defect that is an electron acceptor is metastable, we investigated how likely it is to be present in the samples in that configuration. As the local bonding environment and even the bandstructure of the defects considered here are very similar in bulk and monolayer WS 2, we used a monolayer to model their stability: 1. Above the temperature of mobility of the sulphur vacancy: In thermal equilibrium, the stability of a substitutional atom X S versus an adsorbed atom of the same species X ad can be characterized by the enthalpy change associated with the capture of the impurity atom a sulphur vacancy: V S +X ad > X S where Vs is the sulphur vacancy and X ad is the adatom. For oxygen, this reaction enthalpy is -3.5 ev and -5.2 ev in 20

21 configurations I and II, respectively. For silicon, the reaction enthalpy is -2.8 ev. These values are larger than the formation energy of a sulphur vacancy in a S-poor material. Therefore, Si and O occupy predominantly substitutional positions. 2. Below the temperature of mobility of the sulphur vacancy: We also investigated the hypothesis that, at temperatures at which Vs is immobile, oxygen can be introduced into the metastable position II. The calculated activation energy for the transformation O ad -I -> O ad -II is 4.3 ev in the forward direction. This energy barrier prevents the introduction of O ad into the II site below 590K. Graphene-WS 2 interface Supplementary Figure 15 shows the bandstructures of an interface between graphene and monolayer WS 2. These bandstructures are nearly identical to the superposition of the bandstructures of the two moieties. In particular, it can be noticed that WS 2, either in its pristine form or containing a sulphur vacancy, does not introduce an appreciable spin-orbit splitting of the diract cone bands of graphene. 21

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