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Spin-orbit interaction induced in graphene by transition metal dichalcogenides

T. Wakamura, F. Reale, P. Palczynski, M. Q. Zhao, A. T. C. Johnson, S. Guéron, C. Mattevi, A. Ouerghi, and H. Bouchiat
Phys. Rev. B 99, 245402 – Published 4 June 2019
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  • INTRODUCTION
  • WEAK ANTILOCALIZATION IN GRAPHENE
  • SAMPLE PREPARATION AND MEASUREMENT…
  • EXPERIMENTAL RESULTS
  • ANALYSIS
  • DISCUSSIONS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We report a systematic study on strong enhancement of spin-orbit interaction (SOI) in graphene induced by transition-metal dichalcogenides (TMDs). Low-temperature magnetotoransport measurements of graphene proximitized to different TMDs (monolayer and bulk WSe2,WS2, and monolayer MoS2) all exhibit weak antilocalization peaks, a signature of strong SOI induced in graphene. The amplitudes of the induced SOI are different for different materials and thickness, and we find that monolayer WSe2 and WS2 can induce much stronger SOI than bulk WSe2,WS2, and monolayer MoS2. The estimated spin-orbit (SO) scattering strength for graphene/monolayer WSe2 and graphene/monolayer WS2 reaches ∼10 meV, whereas for graphene/bulk WSe2, graphene/bulk WS2, and graphene/monolayer MoS2, it is around 1 meV or less. We also discuss the symmetry and type of the induced SOI in detail, especially focusing on the identification of intrinsic (Kane-Mele) and valley-Zeeman (VZ) SOI by determining the dominant spin relaxation mechanism. Our findings pave the way for realizing the quantum spin Hall (QSH) state in graphene.

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    • Received 13 September 2018

    DOI:https://doi.org/10.1103/PhysRevB.99.245402

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    DiffusionElectrical conductivityLocalizationMesoscopicsQuantum interference effectsQuantum transportSpin-orbit couplingSpintronicsSurface & interfacial phenomena
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    T. Wakamura1, F. Reale2, P. Palczynski2, M. Q. Zhao3, A. T. C. Johnson3, S. Guéron1, C. Mattevi2, A. Ouerghi4, and H. Bouchiat1,*

    • 1Laboratoire de Physique des Solides, Univ. Paris-Sud, University Paris-Saclay, 91400 Orsay,France
    • 2Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
    • 3Department of Physics and Astronomy, University of Pennsylvania, 209S 33rd Street, Philadelphia, Pennsylvania 19104-6396, USA
    • 4Centre de Nanosciences et de Nanotechnologies, CNRS, University of Paris-Sud, Universite Paris-Saclay, C2N, Palaiseau 91460, France

    • *helene.bouchiat@u-psud.fr

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    Issue

    Vol. 99, Iss. 24 — 15 June 2019

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    Images

    • Figure 1
      Figure 1

      (a) Magnetoconductivity correction [Δσ(B)≡σ(B)−σ(0)] for mono WSe2 averaged over 50 curves corresponding to 50 values of Vg between 50 and 60 V at 250 mK. A clear WAL peak and flat tails for higher-B regions are observed. The solid curve represents the fit based on the theoretical formula (1). The left inset shows the optical microscope image of the mono WSe2 device. The gate voltage dependence of resistance is displayed in the right inset. (b) Δσ(B) curves at different temperatures, averaged over 50 curves with Vg between −20 and −30 V. Similar tendency as in (a) can be seen in the shape of each curve. The solid lines are theoretical fits.

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    • Figure 2
      Figure 2

      Δσ(B) curves for mono WSe2 for different gate voltage ranges at 1 K. Clear WAL peaks are observed in all Vg ranges. (b) Comparison of Δσ(B) curves from mono WSe2 and bulk WSe2 in the same Vg range. While the curve for mono WSe2 is characterized by flat tails for high-B region, that of bulk WSe2 exhibit instead a striking upturn with magnetic field following the small WAL peak around B=0. This demonstrates that stronger SOI is induced in graphene for mono WSe2 than for bulk WSe2. In the inset, we show R vs Vg curve for bulk WSe2.

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    • Figure 3
      Figure 3

      (a) Δσ(B) for different gate voltage ranges obtained from mono WS2 A at 1 K. The clear WAL peaks demonstrate the strong induced SOI. Interestingly, the peak is sharper for −50 V <Vg<−60 V than for 50 V <Vg<60 V. All curves exhibit flat tails for high-B range. The solid lines are theoretical fits. The inset shows the Vg dependence of R. (b) Comparison of Δσ(B) between mono WS2 A and bulk WS2 B. As seen for the graphene/WSe2 samples, bulk WS2 shows upturns following the WAL peak. The inset displays Vg dependence of R. Theoretical fits are shown by the solid lines.

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    • Figure 4
      Figure 4

      (a) An optical microscope image of mono MoS2 B sample. Graphene is deposited on a CVD grown monolayer MoS2. (b) Resistance as a function of gate voltage at 100 mK of mono MoS2 B. (c) Δσ(B) for Vg between 10 and 20 V, and between −20 and −30 V at 70 mK. In contrast to mono WSe2 and mono WS2, both curves exhibit large upturns when B is large. The solid lines show theoretical fits.

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    • Figure 5
      Figure 5

      (a) Δσ(B) for |B|<35 G. The fits with no symmetric SOI (Bsym=0) and the symmetric SOI equal to the asymmetric SOI (Bsym=Basy) deviate from the best fit (Bsym=70Basy) especially close to the peak. Note that the two fits (Bsym=0 and Bsym=Basy) almost overlap in the figure. (b) In high-field region, there is no striking difference between the fits with different ratio of Bsym to Basy.

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    • Figure 6
      Figure 6

      Removal of temperature independent components. (a) The original data at 500 mK and that at 4 K from mono WS2 A. In the inset, we show Δσ(B) obtained from mono WS2 A after the subtraction of the background signal. The subtraction procedure is written in the main text, and the subtracted regions are marked by the rectangles. (b) Comparison of the Δσ(B) curves at 70 mK and 4 K for mono MoS2 B. It is clear that even for higher-B region, the shape of the two curves is drastically different at the two temperatures, indicating that there does not exist any temperature independent components. Theoretical fits are shown by the solid lines. (Inset) The same curve of Δσ(B) at 4 K as in the main figure with the fit based only on the weak localization term in (1) (namely, τasy→∞ and τso→∞). The upturn is well reproduced therefore it can be attributed to the weak localization contribution.

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    • Figure 7
      Figure 7

      Comparison of the spin-orbit energy (Eso) estimated from the theoretical fits for each graphene/TMD heterostructure. The eight samples can be categorized into the two groups, the group with Eso≳10 mV (mono WSe2 and WS2) and the one with Eso≲1 meV (mono MoS2, bulk WSe2, and WS2). In the inset, we show the temperature dependence of τϕ for the sample mono MoS2 B as an example. The experimental data are consistent with the relation τϕ−1∝T.

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    • Figure 8
      Figure 8

      (a) Simulated curves of Δσ(B) based on equation (2) with Bϕ=ℏ/4eDτϕ=0.01 with different ratio of τϕ/τiv. The shape of Δσ(B) dramatically changes for τiv≳τϕ. (b) Experimental data of Δσ(B) from mono WS2 A. The flat tails in high-field region are observed over a broad range of temperature, indicating that the system is in the limit τiv≪τϕ. The solid lines are the fits based on (1).

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    • Figure 9
      Figure 9

      Sensitivity of the fits to the ratio τsym/τasy. Different fits are shown for different values of τsym/τasy: When there is no symmetric contribution (light blue curve), the fit strongly deviates from the experimental points. In contrast, when τsym≪τasy and Eso≳12 meV, we can well reproduce the experimental data. (Inset) Temperature dependence of 1/τϕ for mono WSe2 for Vg between 50 and 60 V.

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    • Figure 10
      Figure 10

      Extraction of ΔEY and ΔDP to identify the dominant SOI for each heterostructure. (a) Logarithmic-scale plot of ɛF2τp/τso as a function of ɛF2τp2. The nonzero y-axis intercept and the deviation from the linearity are due to the EY-type spin relaxation. The error bars are obtained by considering the standard deviation of the Fermi energy (δEF) due to electron-hole puddles. (b) Using the same experimental data as (a) we plot them in a different way based on (4) to clarify the EY contribution. The positive slope is clearly seen as a result of the EY contribution for the three samples. The inset shows the same plot for mono MoS2 B.

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