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is shown in Fig.7.13 together with the difference of gate voltage (∆VBG =

∆VBG,max−∆VBG,min) that can be converted into a density. One possible explanation for the screening of the back gate is that the Fermi energy is shifted away from the valance band with increasing electric field (positive electric field is pointing from the WSe2 to the graphene). At some point a trap level is hit and the additional charge induced by the back gate is put into the trap states since the graphene is at the CNP. The number of available trap states is reduced with increasing temperature. This explains the shorter plateau-like feature that is observed at higher temperature.

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Figure 7.13. Screening of back gate for device B:(a) shows R3 at 60 K with a contour line of 15 Ω in red. The extracted maximum of R3 (at the CNP) is shown in (b), where the cut-off of 15 Ω is also indicated. VBG,minand VBG,maxare extracted as indicated and plotted together with their difference in (c).

7.6. Alternative WSe

source and influence of WSe

quality

The interface between the graphene and the WSe2substrate is crucial for the observed enhancement of SOC in graphene. Obviously also the quality of the WSe2 crystal matters as defects and grain boundaries could affect the prox-imity effect on graphene. Crystals from different sources can have different quality as shown in Ref. [240] where the authors investigated topography and defects in WSe2 with a scanning tunnelling microscope. We therefore inves-tigated devices with WSe2 obtained from Nanosurf to compare it to devices with WSe2 obtained from hq graphene. In general, devices with WSe2 from Nanosurf showed more gate instabilities than the devices with WSe2 from hq graphene. In addition, the resistance at the CNP was found to strongly depend on the temperature with a doubling of the resistance at 450 mK compared to 25 K, which was not observed in hBN/Gr/hBN devices nor in hBN/Gr/WSe2

devices with WSe2 from hq graphene, see Fig.7.14. Furthermore, the up and

7. Spin-orbit coupling in graphene/WSe2 heterostructures

down sweep do not overlap and a shift of the CNP reveals a hysteretic gate behaviour. At the CNP large resistance fluctuations are observed that are not reproducible.

Figure 7.14. Alternative source of WSe2, temperature dependence, gate instability: Solid lines correspond to a temperature of 450 mK, whe-reas dashed lines correspond to a temperature of 25 K. (a) shows the two terminal resistance of a WSe2/Gr/hBN device as a function of top gate voltage. (b) shows the two terminal resistance and (c) shows the resistivity of a WSe2/Gr/WSe2device as a function of back gate. Black traces correspond to up sweeps (from negative to positive voltage) and red correspond to down sweeps.

In Fig. 7.15, further characteristics of the device from Fig. 7.14 (a) are shown. A gate gate map of the two-terminal resistance is shown in (a). A varying lever arm of the gates indicates less reproducible device behaviour. A mobility of ≈ 17 000 cm²V⁻¹s⁻¹ was found. Similar mobilities and changes of the resistance at the CNP were found in the other devices fabricated with this material.

The lower device stability (hysteresis and gate instabilities) can be related to a lower WSe2 quality that leads to more charge traps than in high quality WSe2or hBN crystals. On the other hand, larger resistances at the CNP that are strongly temperature dependent could be explained by strong localization due to disorder [252]. However, a more thorough investigation would be needed to conclude about a possible strong localization.

In order to check for the presence of enhanced SOC, magneto conductivity was measured close to the CNP, see Fig. 7.15 (b) and (c). As previously discussed, an ensemble averaging was performed to average out the influence of UCF. The resulting magneto conductivity shows a clear dip around zero magnetic field and shows no feature of weak antilocalization. The absence of any clear sign of weak antilocalization shows that there is no z/-z asymmetric SOC present in the system. Most likely, there is also no z/-z symmetric SOC

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7.6. Alternative WSe2source and influence of WSe2quality

present as this would lead to a reduced weak localization signal. However, it is hard to conclude anything about the SOC in these device as the positive magneto conductance cannot unambiguously be attributed the presence of normal WL or to the presence of z/-z-symmetric SOC.

-2

Figure 7.15. Devices with WSe2from an alternative source: (a) shows the two terminal resistance as a function of top gate and back gate voltage.

(b) shows the magneto conductivity close to the CNP. The back gate voltage was varied within 14 V to 16 V to average out the influence of UCF. (c) shows the average over all gate traces in (b) and a clear weak localization feature is observed. The temperature of all measurements was 300 mK

7.6.1. Fully WSe2 encapsulated graphene

Graphene encapsulated by WSe2 on the bottom and on the top is interesting mainly due to two reasons. First, the symmetry in z-direction of the structure is different from hBN/Gr/WSe2. This could have important consequences on the strength of the different SOC terms. Rashba SOC is expected to be fully absent or at least greatly suppressed [53]. Similar arguments hold for the PIA SOC [53]. On the other hand, one naively could imagine that the other SOC terms would be doubled as the electrons in the graphene experience strong SOC on both sides of the graphene.

To investigate the influence of the symmetry of the structure in z-direction on the SOC, fully WSe2devices were fabricated from WSe2obtained from Na-nosurf. The resistivity of such a device is shown in Fig.7.16(a). A field effect mobility of ∼ 15 000 cm²V⁻¹s⁻¹and a residual doping of ∼ 8 × 10¹⁰cm⁻²was extracted. Due to the lower quality of the WSe2 only a very broad CNP is observed. In addition, this device showed rather inhomogeneous charge trans-port. Nevertheless, the magneto conductivity was measured to investigate possible SOC. To reduce the influence of the UCF, the magneto

conducti-7. Spin-orbit coupling in graphene/WSe2 heterostructures

vity was measured at different gate voltages close to the CNP as shown in Fig.7.16(b). Here, the lower quality of the WSe2 is also visible since several gate jumps occur during the measurement. The average of this map is shown in Fig.7.16(c) that shows a clear dip at Bz = 0 mT but no further sign of typical weak localization nor antilocalization.

2.5

Figure 7.16. Fully WSe2 encapsulated graphene: The resistivity, obtai-ned in a four terminal configuration, of a fully WSee encapsulated device is shown in (a) as a function of top and back gate voltage. (b) shows the mag-neto conductivity close to the CNP. The back gate voltage was varied within 14 volt to 15 volt to average out the influence of UCF. Several gate jumps are visible in this measurement. (c) shows the average over all back gate traces in (b). The conductivity shows a minimum at Bz= 0 mT but does not look like a typical weak localization feature.

In the absence of z/-z asymmetry (fully WSe2 encapsulated graphene), a reduced weak localization is expected in the magneto conductivity that ac-counts for the presence of z/-z symmetric SOC terms [73]. The fact that the magneto conductivity shown in Fig.7.16(c) does not resemble a typical weak localization shape, a clear statement about the presence or absence of any SOC is very hard. Similar results were also found in three further devices that consisted of fully WSe2 encapsulated graphene.

Since the low field magneto conductivity is not a robust measure to detect SOC in symmetric structures, the investigation of Shubnikov-de-Has (SdH) oscillations could prove useful. It is well known that the spin splitting of single band leads to a beating in the SdH oscillations, which was recently observed in bilayer graphene in contact to WSe2[149].

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