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Priya Tiwari, Mohit Kumar Jat, Adithi Udupa, Deepa S. Narang, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Diptiman Sen, Aveek Bid

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[Experimental observation of spin−split energy dispersion in high-mobility single-layer graphene/WSe2 heterostructures](https://mdr.nims.go.jp/datasets/8b760de1-e4c4-4602-a713-1729b9e321cd)

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Experimental observation of spin−split energy dispersion in high-mobility single-layer graphene/WSe2 heterostructuresARTICLE OPENExperimental observation of spin−split energy dispersion inhigh-mobility single-layer graphene/WSe2 heterostructuresPriya Tiwari1, Mohit Kumar Jat1, Adithi Udupa2, Deepa S. Narang1, Kenji Watanabe 3, Takashi Taniguchi 4, Diptiman Sen1,2 andAveek Bid 1✉Proximity-induced spin–orbit coupling in graphene has led to the observation of intriguing phenomena like time-reversal invariantZ2 topological phase and spin-orbital filtering effects. An understanding of the effect of spin–orbit coupling on the band structureof graphene is essential if these exciting observations are to be transformed into real-world applications. In this research article, wereport the experimental determination of the band structure of single-layer graphene (SLG) in the presence of strong proximity-induced spin–orbit coupling. We achieve this in high-mobility hexagonal boron nitride (hBN)-encapsulated SLG/WSe2heterostructures through measurements of quantum oscillations. We observe clear spin-splitting of the graphene bands along witha substantial increase in the Fermi velocity. Using a theoretical model with realistic parameters to fit our experimental data, weuncover evidence of a band gap opening and band inversion in the SLG. Further, we establish that the deviation of the low-energyband structure from pristine SLG is determined primarily by the valley-Zeeman SOC and Rashba SOC, with the Kane–Mele SOCbeing inconsequential. Despite robust theoretical predictions and observations of band-splitting, a quantitative measure of thespin-splitting of the valence and the conduction bands and the consequent low-energy dispersion relation in SLG was missing—our combined experimental and theoretical study fills this lacuna.npj 2D Materials and Applications            (2022) 6:68 ; https://doi.org/10.1038/s41699-022-00348-yINTRODUCTIONGraphene has attracted much attention due to a plethora ofremarkable electronic properties like Dirac energy dispersion,relativistic effects, half-integer quantum Hall effect, and Kleintunneling. Additionally, its van der Waals heterostructures withother 2-dimensional materials1–4 host several single-particle andemergent correlated states that are topologically non-trivial5–8.The ability to precisely transfer and align these atomically thinplanar structures into high-quality heterostructures promisesoutstanding opportunities for both fundamental and appliedresearch9–11. This has made theoretical and experimental studiesof several aspects of graphene-based van der Waals heterostruc-tures of great contemporary interest8,10–19.With a long spin-relaxation length of several μm at roomtemperature, graphene appears a perfect base for low-powerspintronics devices20,21. However, its extremely weak intrinsicspin–orbit coupling (SOC) strength makes spin manipulationchallenging. Decorating the surface of graphene with heavyatoms (such as topological nanoparticles)7,22 or weak hydro-genation of graphene23 improves the SOC in graphene at thecost of introducing disorder and reducing the graphene’smobility. An alternate technique is interfacing graphene withtwo-dimensional transition metal dichalcogenides (TMDC) hav-ing a high SOC11,16,19,21,24–35.Before one conceives increasingly complex graphene/TMDCheterostructures and considers their potential applications, it isimperative to understand the impact of the proximity of TMDCon the electronic properties of graphene. Prominent amongstthese are the breaking of inversion symmetry, breaking of sub-lattice symmetry, and hybridization of the d-orbitals of theheavy element in TMDC with the p-orbitals of SLG, leading tostrong SOC in SLG. This proximity-induced SOC in SLG has threeprimary components, all of which contribute to spin splitting ofthe bands—(i) valley-Zeeman (also called Ising) term, whichcouples the spin and valley degrees of freedom, (ii) Kane–Meleterm36,37, which couples the spin, valley and sublatticecomponents and opens a topological gap at the Dirac point18,38,and (iii) Rashba term39 which couples the spin and sublatticecomponents.In the presence of a strong Ising SOC, the electronic banddispersion of graphene is predicted to be spin–split17,24,39–42, aswas observed recently in bilayer graphene/WSe2 heterostruc-tures10,43. Consequences of this induced SOC include theappearance of helical edge modes and quantized conductancein the absence of a magnetic field in bilayer graphene5 and ofweak antilocalization19, and Hanle precession in SLG27,28,44,44–48.Despite these advances, a quantitative study of the effect of astrong SOC on the electronic energy band dispersion of SLG islacking.In this research article, we report the results of our studies ofquantum oscillations in high-mobility heterostructures of SLG andtrilayer WSe2. Careful analysis of the oscillation frequencies showsspin-splitting of the order of ~5meV for both the valence band(VB) and the conduction band (CB). We find that the bands remainlinear down to at least 70 meV (corresponding ton ~ 2 × 1011cm−2). Close to zero energy, the lower energybranches of the CB and the VB overlap, leading to band inversionand opening of a band gap in the energy dispersion of SLG. We fitour data using a theoretical model that establishes that, to thezeroth order, the magnitude of the spin-splitting of the bands andthat of the band gap are determined by only the valley-Zeemanand Rashba spin–orbit interactions.1Department of Physics, Indian Institute of Science, Bangalore 560012, India. 2Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012, India. 3ResearchCenter for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 4International Center for Materials Nanoarchitectonics, NationalInstitute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. ✉email: aveek@iisc.ac.inwww.nature.com/npj2dmaterialsPublished in partnership with FCT NOVA with the support of E-MRS1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00348-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00348-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00348-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00348-y&domain=pdfhttp://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-2378-7980http://orcid.org/0000-0002-2378-7980http://orcid.org/0000-0002-2378-7980http://orcid.org/0000-0002-2378-7980http://orcid.org/0000-0002-2378-7980https://doi.org/10.1038/s41699-022-00348-ymailto:aveek@iisc.ac.inwww.nature.com/npj2dmaterialsRESULTSExperimental observationsHeterostructures of single-layer graphene and trilayer WSe2,encapsulated by hexagonal boron nitride (hBN) (see deviceschematic Fig. 1a) of thickness ~20–30 nm, were fabricated usingdry transfer technique49,50. One-dimensional Cr/Au electricalcontacts were created by standard nanofabrication techniques—note that this method completely evades contacting the WSe2thus avoiding parallel channel transport (see SupplementaryInformation for details). Electrical transport measurements wereperformed using a low-frequency ac lock-in technique in a dilutionrefrigerator at the base temperature of 20 mK unless specifiedotherwise. Multiple devices of SLG/WSe2 were studied, and thedata from all of them were qualitatively very similar. All the datapresented here are from a device labeled B9S6. The data for twoother similar devices are presented in the SupplementaryInformation. The extracted impurity density from the four-proberesistance of the device as a function of gate voltage (see Fig. 1b)was ~2.2 × 1010 cm−2, and the mobility was ~ 140,000 cm2V−1s−1.The four-probe resistance response as a function of the gatevoltage were identical for different measurement configurations(see Supplementary Information), indicating that the fabricateddevice is spatially homogeneous. Figure 1c shows the quantumHall data at 3 T – the presence of plateaus at ν= ± 2, ± 6, ± 10confirms it as SLG. Along with the signature plateaus of SLG, onecan see a few of the broken symmetry states appearing already at3 T, confirming it to be a high-quality device.Representative data of the Shubnikov-de Haas (SdH) oscillationsmeasured at 20mK are plotted in Fig. 2a. In addition to theexpected decay of the amplitude of the oscillations with increasing1/B, we observe the presence of beating, implying two closelyspaced frequencies. The fast Fourier transforms (FFT) of the dataFig. 2b show that this indeed is the case. We find similar splitting inthe SdH oscillation frequency in all the SLG/WSe2 devices studiedby us—the data for two additional similar devices are presented inthe Supplementary Information. There may be a legitimate concernthat the observed beating can be caused by device inhomogene-ities which lead to different charge carrier density in differentregions of the graphene channel. We rule out this artifact frommeasurements of the four-probe resistance and SdH oscillations inmultiple contact configurations—we find that the data areidentical in each case (see Supplementary Information).Recall that the SdH oscillation frequency, BF is directly related tothe cross-sectional area A kð Þ at the Fermi energy by the relationBF ¼ _A kð Þ=2πe51. For an isotropic dispersion in which the Fermienergy EF is a function of kF ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik2x þ k2yq(where (kx, ky) are definedwith respect to one of the Dirac points, K or K 0, of the SLG), thecross-sectional area of the Fermi surface is given by AðkÞ ¼ πk2F.Figure 2c shows the charge carrier density (n) dependence of BF.The appearance of two closely spaced frequencies at all n (or EF)implies that for each value of the Fermi energy, there are twodistinct values of kF. This is a direct proof of the energy splitting ofboth the CB and the VB of the SLG.From the temperature dependence of the amplitude of the SdHoscillations (Fig. 3), we extracted the effective charge carrier massm*, using the the Lifshitz–Kosevich relation52,53:ΔRxxR0/ 2π2kBTm�=_eBsinh 2π2kBTm�=_eBð Þ ; (1)Here, R0 the longitudinal resistivity at B= 0. On fitting the effectivemass m* versus n using the relation m� ¼ _ð ffiffiffiπp=vFÞnα54 (seeSupplementary Information), we obtain α= 0.5 ± 0.02 and Fermib c-16 -8 0 8 16012-18-12-60612Rxx (k�) Gxy  (e2/h)R (K�) Vg (V)  Vg (V)hBNWSe2hBNSiO 2Si substratebottom hBNWSe 2top hBNagrapheneFig. 1 Transport measurements in hBN encapsulated SLG/WSe2 heterostructures. a A schematic of the device. The bottom right cornershows the sequence of all the layers of the heterostructure. b Four-probe resistance of the device plotted as a function of the back-gatevoltage Vbg; the data were collected at 20mK. An optical image of the device is shown in the inset. The scale bar in the figure is 15 μm. c Plotsof longitudinal resistance Rxx (left-axis) and the Hall conductance Gxy (right-axis) versus Vbg in the quantum Hall regime. The measurementswere done at 20mK in the presence of a 3 T perpendicular magnetic field.EFEFE Ek kNormalized amplitudeBF (T)1/B (1/T)B F (T)∆Rxx (Ω)     n (x1016 m-2 )00 1 2 3-3 -2 -18162432 a   b cFig. 2 Shubnikov-de Haas(SdH) oscillations. a Plot of theShubnikov-de Haas oscillations measured at Vbg=− 9 V andT= 20mK. b The corresponding FFT spectra showing two distinctpeaks. c Charge carrier density (n) dependence of the frequency ofSdH oscillations. The inset shows the schematics of the spin splitconduction and valance bands.P. Tiwari et al.2npj 2D Materials and Applications (2022)    68 Published in partnership with FCT NOVA with the support of E-MRS1234567890():,;velocity vF= 1.29 ± 0.04 × 106 ms−1. The value of α being 0.5establishes the dispersion relation between energy and momen-tum in SLG on WSe2 to be linear51.Figure 4a are the resultant plots of E versus k for both CB andthe VB from our experimental data. Note that our experimentaldata extends down to ≈30meV (corresponding ton ≈ 3.9 × 1010 cm−2). Below this number density, the SdH oscilla-tions are not resolvable – presumably due to the dominance ofcharge puddles on the electrical transport of SLG in this energyrange.We observe that, on extrapolating the E− k plots to E= 0, thelow-energy branches of the spin–split bands of both the CB andthe VB bands enclose a finite area in the k-space at E= 0. Thisleads us to expect that there will be an overlap between the lowerbranches of the CB and VB, ultimately leading to band inversionnear the K (and K 0) points. A verification of this assertion requiresfurther measurements in extremely high quality devices that willallow measurements of SdH oscillations near E= 0.To summarize our experimental observations, we have quanti-fied the spin-splitting of the energy bands in SLG in proximity toWSe2 and mapped out the dispersion relation of the spin–splitbands of SLG. We find that till a certain energy, the dispersionremains linear; below this energy scale, we observe a deviationfrom linearity.Theoretical calculationsUsing the experimental data, we fit a theoretical model to obtainthe dispersion relation close to the Dirac points. The continuumHamiltonian near the Dirac points for SLG with WSe2 has thefollowing terms (see, for instance, ref. 39):H ¼ _vFðηkxσx þ kyσyÞ þ Δσz þ λKMηSzσz þ λVZηSz þ λRðηSyσx � SxσyÞþffiffi3pa2 ½λAPIAðσz þ σ0Þ þ λBPIAðσz � σ0Þ�ðkxSy � kySxÞ(2)In Eq. (2), the Pauli matrices σi and the Si represent the sublatticeand spin degrees of freedom, respectively. The first term denotesthe linear dispersion near the Dirac points, where vF is the Fermivelocity, kx and ky are the momenta with respect to the Diracpoint, and η= ± 1 denotes the valleys K (K 0) respectively (We notethat ℏvF= 3ta/2, where t is the nearest-neighbor hoppingamplitude and the nearest neighbor carbon carbon distance a is1.42 Å). The second term represents a sublattice potential ofstrength Δ. We have considered the four possible spin–orbitcouplings: (i) Kane–Mele SOC with strength λKM, (ii) valley-ZeemanSOC with strength λVZ, (iii) Rashba SOC with strength λR, and (iv)pseudo-spin asymmetric SOC with strengths λAPIA and λBPIA forsublattices A and B respectively.Since this Hamiltonian results in the same dispersion at both thevalleys, we only consider the case η=+ 1 (K point). TheHamiltonian in Eq. (2) is invariant under a simultaneous rotationof (kx, ky), (σx, σy) and (Sx, Sy) by the same angle; this implies thatthe dispersion is isotropic in momentum space, and it is sufficientto take kx= k and ky= 0. The data for the four bands shown in Fig.4a are fitted to the Hamiltonian with t, Δ, λKM, λVZ and λR as the fitparameters. The best fit gives t= 3979.10 ± 3.99 meV implying alarge Fermi velocity in this device of 1.286 × 106 ms−1 (comparedto about 0.86 × 106 ms−1 in pristine SLG55). The parameters in theHamiltonian which give the spin–split band gap in bothconduction and valence bands are λVZ and λR. We find that thebest fit gives the values of λVZ and λR to lie on a circle of radius2.51 meV, such thatλVZ ¼ 2:51 cosθmeV; and λR ¼ 2:51 sin θmeV: (3)where θ can take any value from 0 to 2π, and Δ= λKM= 0. Eq. (3)can be understood by looking at the first-order perturbative effectof the valley-Zeeman and Rashba terms in the Hamiltonian. TakingH0= ℏvFkσx and the perturbation V= λVZSz+ λR(Syσx− Sxσy), wefind that the zeroth order spin-degenerate dispersion E0= ± ℏvFkin the positive and negative energy bands receives first-ordercorrections given byE1;± ¼ ±ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiλ2VZ þ λ2Rq¼ ± 2:51meV (4)for both the bands, thus giving the general relation in Eq. (3). Thisgives a gap equal to twice 2.51 meV which fits the experimentallyobserved value of ~5meV. The two extreme cases are given byθ= 0 with only valley-Zeeman SOC and θ= π/2 with onlyRashba SOC.The overall magnitude of effective SOC of 2.51 meV agrees wellwith previous reports18,19,39,48.The band dispersion for higher energies (E > 5 meV) remainsunaffected for any combination of λVZ and λR which satisfiesRxx (�)-20-10010201 K2.5 K4 K7 K9.5 K15 K20 K25 K1 2 3abRxx/R000 10 20 304812 c-3 -2   0n (x1016 m-2 )0.010.030.02-1 1  2  3T (K)m*/m0B (T)Fig. 3 Temperature dependent SdH oscillations and effectivemass extraction. a SdH oscillations for different temperaturesmeasured at Vbg= 25 V. b The normalized amplitude of the SdHoscillations as a function of temperature (black stars). The solid redline is the fit to Eq. (1) used to extract the effective mass. c Plot of theeffective mass m* versus the charge carrier density n (black stars).The solid red curve is the fit used to extract the relation between m*and n.0 5 10 15 20 25 30 35-300-250-200-150-100-50050100150200250300k (10-3Å-1)E(meV)8 10 12 14 16-125-100-75-505075100125k (10-3Å-1)E(meV)EkkF∆Esa  b5 10 15 20 25 302468101214k (10-3Å-1)�E(meV)Fig. 4 Experimentally obtained dispersion relation. a Dispersionrelation for SLG on WSe2 as extracted from our SdH measurements.The inset shows the zoomed-in plot near the Dirac point. b Plot ofthe magnitude of the energy difference between the two spin–splitbands, ΔEs versus k for the valence band (green open circles) andthe conduction band (red filled circles). The inset shows a schematicof the band-splitting in the CB— ΔEs is the spin-splitting at kF.P. Tiwari et al.3Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022)    68 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiλ2VZ þ λ2Rq¼ 2:51 meV. However, the relative magnitudes of λVZand λR modifies the lower energy band dispersion (E < 5 meV) – aregion inaccessible in our experiments. To evaluate the value ofλVZ and λR explicitly, one needs the value of the band gap at E= 0.As is well known, the presence of finite impurity density(n0 ≈ 2.2 × 1010 cm−2 for this device) leads to the dominance ofcharge puddles on the electrical transport of SLG at the Diracpoint making it extremely difficult to make an accurate estimate ofsuch a small energy gap. In the absence of such information, wetake the theoretically predicted value of λR= 0.56 meV39 whichcorresponds to θ= 13∘ in Eq. (3). This yields the strength of thevalley-Zeeman term to be λVZ= 2.45meV and a maximumexpected band gap of 3.3 meV for λso ~ 2.51 meV. The resultingdispersion is plotted in Fig. 5a. In generating this plot, we haveused Δ= 0.54 meV, λkm= 0.03 meV, λAPIA ¼ �2:69 meV and λBPIA ¼�2:54 meV39. Figure 5b further shows the 3-dimensional plot ofthe energy dispersion for this model.DISCUSSIONSComing to the role of the magnetic field in the extracted energydispersion relation, the SdH oscillations were studied at amagnetic field of the order of 1 T. This field gives a very smallZeeman energy of the order of 0.08meV in the energy. Since theexperimental data points are quite far from E= 0, we can ignorethe magnetic field effect in the Hamiltonian. Further, the fittingdoes not give us the values of Δ, λKM, λAPIA, and λBPIA with anycertainty. While the PIA terms do not alter the dispersion in ourregion of interest, the other two parameters, Δ and λKM will openup a gap at the two values of the energy lying at k= 0. The effectof the Kane–Mele term in this model has been further discussed inthe Supplementary Information. However, we note that thepresence of Δ, λKM, λAPIA and λBPIA does not alter the spin–splitband gap of 5 meV observed between the bands away from zeroenergy.All previous theoretical and experimental studies note that thevalley-Zeeman λVZ and the Rashba λR are the major spin–orbitcoupling (SOC) terms for graphene/TMDs18,19,39,48. These twoterms by themselves give a constant energy gap between thespin–split bands. The other relevant spin–orbit coupling terms areλPIA and λKM. The λPIA terms are negligibly small and do not alterthe band dispersion in the region of interest. On the other hand,we find that including a very large λKM and Δ terms ~20meV inthe standard theoretical models can give a dispersion where theenergy gap between the two spin–split bands increases as oneapproaches the Dirac point. However, such large λKM and Δ mightnot be reasonable and have not been reported to date. To thebest of our knowledge, there is no consistent theoreticalunderstanding of the increase in energy gap between thespin–split bands on approaching the Dirac point; we leave thisas an open question to be explored in near future.Finally, a comment on the relative magnitudes of λVZ and λR:The spin relaxation mechanism in graphene/TMDC heterostruc-tures is extraordinary. It relies on intervalley scattering and canonly occur in materials with spin-valley coupling. In such systems,the lifetime τ and relaxation length λ of spins pointing parallel tothe graphene plane (τks , λks ) can be markedly different from thoseof spins pointing out of the graphene plane (τ?s , λ?s ). Realisticmodeling of experimental studies indicate that the spin lifetimeanisotropy ratio ζ ¼ τks=τ?s ¼ ðλ?s =λks Þ2can be as large as a fewhundred in the presence of intervalley scattering41,44,47. Recall thatthe λVZ provides an out-of-plane spin–orbit field and affects the in-plane spin relaxation time, τks . On the other hand, λR generates anin-plane spin–orbit field and is relevant for determining τ?s47. Thelarge spin lifetime anisotropy ratio (τks=τ?s � 1) seen both fromexperiments and theory41,44,47 show that the value of λVZ canindeed be significantly larger as compared to λR.In conclusion, we have experimentally determined the bandstructure of single-layer graphene in the presence of proximity-induced SOC. We find both the VB and the CB spin–split with aspin-energy gap of ~5meV; the splitting increases as oneapproaches the Dirac point. There are strong indications ofoverlap of the lower energy branches of the conduction and thevalence bands. We also provide precise values of the spin splittingenergy, the Fermi velocity and the effective mass of chargecarriers in graphene/WSe2 hetrostructures. Theoretical modelingof the data establishes that the band dispersion near the Diracpoint and the magnitude of the spin-splitting are determinedprimarily by large valley-Zeeman (Ising) SOC and small RashbaSOC. Our work raises the strong possibility that in this system, thetransport properties near the Dirac point are dominated by chargecarriers of a single spin component, making this system a potentialplatform for realizing spin-dependent transport phenomena, suchas quantum spin-Hall and spin-Zeeman Hall effects.METHODSDevice fabricationThe SLG, WSe2, and hBN flakes were obtained by mechanicalexfoliation on SiO2/Si wafer using scotch tape from thecorresponding bulk crystals. The thickness of the flakes wasverified from Raman spectroscopy. Heterostructures of SLG andWSe2, encapsulated by single-crystalline hBN flakes of thickness~ 20–30 nm was fabricated by dry transfer technique using ahome-built transfer set-up consisting of high-precision XYZ-manipulators. The heterostructure was then annealed at 250 ∘Cfor 3 h. Electron beam lithography followed by reactive ionetching (where the mixture of CHF3 and O2 gas were used withflow rates of 40 sccm and 4 sscm, respectively, at a temperature of25 ∘C at the RF power of 60 W) was used to define the edgecontacts. The electrical contacts were fabricated by depositing Cr/Au (5/60 nm) followed by lift-off in hot acetone and IPA.MeasurementsAll electrical transport measurements were performed using alow-frequency AC lock-in technique in a dilution refrigerator(capable of attaining a lowest temperature of 20mK andmaximum magnetic field of 16 T).DATA AVAILABILITYThe authors declare that the data supports the findings of this study are availablewithin the main text and its Supplementary Information. Other relevant data areavailable from the corresponding author upon reasonable request.-2.0 0.0 2.0-10-50105a bE(k)kxkYE(meV)k (10-3 Å-1 )Fig. 5 Theoretically calculated dispersion relation. a A 2D plot ofthe energy dispersion relation calculated with vF= 1.286 × 106ms−1,and θ= 13∘ (λVZ≃ ± 2.45 meV and λR= ± 0.56 meV). The value of λR istaken from ref. 39. The value of λVZ comes from fitting theexperimental spin split band gap energy. Further, the otherparameters in this graph have been set as follows: Δ= 0.54 meV,λKM= 0.03 meV, λAPIA ¼ �2:69 meV and λBPIA ¼ �2:54 meV. b The 3Ddispersion of this model for the same set of parameters as in (a).P. Tiwari et al.4npj 2D Materials and Applications (2022)    68 Published in partnership with FCT NOVA with the support of E-MRSReceived: 2 May 2022; Accepted: 27 September 2022;REFERENCES1. Geim, A. K. & Grigorieva, I. V. Van der waals heterostructures. Nature 499, 419–425(2013).2. Lotsch, B. V. Vertical 2d heterostructures. Ann. Rev. Mater. Res. 45, 85–109 (2015).3. Wang, H. et al. Two-dimensional heterostructures: fabrication, characterization,and application. Nanoscale 6, 12250–12272 (2014).4. Zhou, X. et al. 2d layered material-based van der waals heterostructures foroptoelectronics. Adv. Funct. Mater. 28, 1706587 (2018).5. Tiwari, P., Srivastav, S. K., Ray, S., Das, T. & Bid, A. Observation of time-reversalinvariant helical edge-modes in bilayer graphene/wse2 heterostructure. ACSNano 15, 916–922 (2020).6. Cao, Y. et al. Unconventional superconductivity in magic-angle graphenesuperlattices. Nature 556, 43–50 (2018).7. Hatsuda, K. et al. Evidence for a quantum spin hall phase in graphene decoratedwith bi2te3 nanoparticles. Sci. Adv. 4, eaau6915 (2018).8. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle gra-phene superlattices. Nature 556, 80–84 (2018).9. Amin, K. R. & Bid, A. Effect of ambient on the resistance fluctuations of graphene.Appl. Phys. Lett. 106, 183105 (2015).10. Tiwari, P., Srivastav, S. K. & Bid, A. Electric-field-tunable valley zeeman effect inbilayer graphene heterostructures: Realization of the spin-orbit valve effect. Phys.Rev. Lett. 126, 096801 (2021).11. Avsar, A. et al. Spin-orbit proximity effect in graphene. Nat. Commun. 5, 1–6(2014).12. Ingla-Aynés, J., Herling, F., Fabian, J., Hueso, L. E. & Casanova, F. Electrical controlof valley-zeeman spin-orbit-coupling–induced spin precession at room tem-perature. Phys. Rev. Lett. 127, 047202 (2021).13. Sierra, J. F., Fabian, J., Kawakami, R. K., Roche, S. & Valenzuela, S. O. Van der waalsheterostructures for spintronics andopto-spintronics. Nat. Nanotechnol. 16,856–868 (2021).14. Zollner, K., Gmitra, M. & Fabian, J. Swapping exchange and spin-orbit coupling in2d van der waals heterostructures. Phys. Rev. Lett. 125, 196402 (2020).15. Zollner, K. et al. Scattering-induced and highly tunable by gate damping-likespin-orbit torque in graphene doubly proximitized by two-dimensional magnetcr 2 ge 2 te 6 and monolayer ws 2. Phys. Rev. Res. 2, 043057 (2020).16. Safeer, C. et al. Room-temperature spin hall effect in graphene/mos2 van derwaals heterostructures. Nano Lett. 19, 1074–1082 (2019).17. Cysne, T. P., Garcia, J. H., Rocha, A. R. & Rappoport, T. G. Quantum hall effect ingraphene with interface-induced spin-orbit coupling. Phys. Rev. B 97, 085413(2018).18. Garcia, J. H., Vila, M., Cummings, A. W. & Roche, S. Spin transport in graphene/transition metal dichalcogenide heterostructures. Chem. Soc. Rev. 47, 3359–3379(2018).19. Wang, Z. et al. Strong interface-induced spin–orbit interaction in graphene onws2. Nat. Commun. 6, 1–7 (2015).20. Avsar, A. et al. Colloquium: Spintronics in graphene and other two-dimensionalmaterials. Rev. Mod. Phys. 92, 021003 (2020).21. Benítez, L. A. et al. Tunable room-temperature spin galvanic and spin hall effectsin van der waals heterostructures. Nat. Mater. 19, 170–175 (2020).22. Weeks, C., Hu, J., Alicea, J., Franz, M. & Wu, R. Engineering a robust quantum spinhall state in graphene via adatom deposition. Phys. Rev. X 1, 021001 (2011).23. Balakrishnan, J., Koon, G. K. W., Jaiswal, M., Neto, A. C. & Özyilmaz, B. Colossalenhancement of spin–orbit coupling in weakly hydrogenated graphene. Nat.Phys. 9, 284–287 (2013).24. Gmitra, M. & Fabian, J. Proximity effects in bilayer graphene on monolayer wse2:Field-effect spin valley locking, spin-orbit valve, and spin transistor. Phys. Rev. Lett.119, 146401 (2017).25. Gmitra, M., Konschuh, S., Ertler, C., Ambrosch-Draxl, C. & Fabian, J. Band-structuretopologies of graphene: Spin-orbit coupling effects from first principles. Phys. Rev.B 80, 235431 (2009).26. Yang, B. et al. Strong electron-hole symmetric rashba spin-orbit coupling ingraphene/monolayer transition metal dichalcogenide heterostructures. Phys. Rev.B 96, 041409 (2017).27. Wang, Z. et al. Origin and magnitude of ‘designer’ spin-orbit interaction in gra-phene on semiconducting transition metal dichalcogenides. Phys. Rev. X 6,041020 (2016).28. Xu, J., Zhu, T., Luo, Y. K., Lu, Y.-M. & Kawakami, R. K. Strong and tunable spin-lifetime anisotropy in dual-gated bilayer graphene. Phys. Rev. Lett. 121, 127703(2018).29. Garcia, J. H., Cummings, A. W. & Roche, S. Spin hall effect and weak antilocali-zation in graphene/transition metal dichalcogenide heterostructures. Nano Lett.17, 5078–5083 (2017).30. Han, W., Kawakami, R. K., Gmitra, M. & Fabian, J. Graphene spintronics. Nat.Nanotechnol. 9, 794–807 (2014).31. Wakamura, T. et al. Strong anisotropic spin-orbit interaction induced in grapheneby monolayer ws 2. Phys. Rev. Lett. 120, 106802 (2018).32. Ghiasi, T. S., Ingla-Aynés, J., Kaverzin, A. A. & van Wees, B. J. Large proximity-induced spin lifetime anisotropy in transition-metal dichalcogenide/grapheneheterostructures. Nano Lett. 17, 7528–7532 (2017).33. Offidani, M. & Ferreira, A. Microscopic theory of spin relaxation anisotropy ingraphene with proximity-induced spin-orbit coupling. Phys. Rev. B 98, 245408(2018).34. Luo, Y. K. et al. Opto-valleytronic spin injection in monolayer mos2/few-layergraphene hybrid spin valves. Nano Lett. 17, 3877–3883 (2017).35. Ghiasi, T. S., Kaverzin, A. A., Blah, P. J. & van Wees, B. J. Charge-to-spin conversionby the rashba–edelstein effect in two-dimensional van der waals heterostructuresup to room temperature. Nano Lett. 19, 5959–5966 (2019).36. Kane, C. L. & Mele, E. J. Quantum spin hall effect in graphene. Phys. Rev. Lett. 95,226801 (2005).37. Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin hall effect.Phys. Rev. Lett. 95, 146802 (2005).38. Ilić, S., Meyer, J. S. & Houzet, M. Weak localization in transition metal dichalco-genide monolayers and their heterostructures with graphene. Phys. Rev. B 99,205407 (2019).39. Gmitra, M., Kochan, D., Högl, P. & Fabian, J. Trivial and inverted dirac bands andthe emergence of quantum spin hall states in graphene on transition-metaldichalcogenides. Phys. Rev. B 93, 155104 (2016).40. Khoo, J. Y., Morpurgo, A. F. & Levitov, L. On-demand spin-orbit interaction fromwhich-layer tunability in bilayer graphene. Nano Lett. 17, 7003–7008 (2017).41. Cummings, A. W., Garcia, J. H., Fabian, J. & Roche, S. Giant spin lifetime anisotropyin graphene induced by proximity effects. Phys. Rev. Lett. 119, 206601 (2017).42. Gmitra, M. & Fabian, J. Graphene on transition-metal dichalcogenides: A platformfor proximity spin-orbit physics and optospintronics. Phys. Rev. B 92, 155403(2015).43. Island, J. et al. Spin–orbit-driven band inversion in bilayer graphene by the vander waals proximity effect. Nature 571, 85–89 (2019).44. Omar, S. & van Wees, B. J. Spin transport in high-mobility graphene on ws2substrate with electric-field tunable proximity spin-orbit interaction. Phys. Rev. B97, 045414 (2018).45. Offidani, M., Milletarì, M., Raimondi, R. & Ferreira, A. Optimal charge-to-spinconversion in graphene on transition-metal dichalcogenides. Phys. Rev. Lett. 119,196801 (2017).46. Leutenantsmeyer, J. C., Ingla-Aynés, J., Fabian, J. & van Wees, B. J. Observation ofspin-valley-coupling-induced large spin-lifetime anisotropy in bilayer graphene.Phys. Rev. Lett. 121, 127702 (2018).47. Benítez, L. A. et al. Strongly anisotropic spin relaxation in graphene–transitionmetal dichalcogenide heterostructures at room temperature. Nat. Phys. 14,303–308 (2018).48. Zihlmann, S. et al. Large spin relaxation anisotropy and valley-zeeman spin-orbitcoupling in wse2/graphene/h-bn heterostructures. Phys. Rev. B 97, 075434 (2018).49. Pizzocchero, F. et al. The hot pick-up technique for batch assembly of van derwaals heterostructures. Nat. Commun. 7, 1–10 (2016).50. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material.Science 342, 614–617 (2013).51. Novoselov, K. S. et al. Two-dimensional gas of massless dirac fermions in gra-phene. Nature 438, 197–200 (2005).52. Küppersbusch, C. & Fritz, L. Modifications of the lifshitz-kosevich formula in two-dimensional dirac systems. Phys. Rev. B 96, 205410 (2017).53. Lifshitz, I. & Kosevich, A. Theory of magnetic susceptibility in metals at lowtemperatures. Sov. Phys. JETP 2, 636–645 (1956).54. Neto, A. C., Guinea, F., Peres, N. M., Novoselov, K. S. & Geim, A. K. The electronicproperties of graphene. Rev. Mod. Phys. 81, 109 (2009).55. Hwang, C. et al. Fermi velocity engineering in graphene by substrate modifica-tion. Sci. Rep. 2, 1–4 (2012).ACKNOWLEDGEMENTSThe authors acknowledge fruitful discussions with Saurabh Kumar Srivastav andRamya Nagarajan and facilities in CeNSE, IISc. AB acknowledges funding from DSTFIST program and DST (No. DST/SJF/PSA01/2016-17). DS acknowledges funding fromSERB (JBR/2020/000043). K.W. and T.T. acknowledge support from the ElementalStrategy Initiative conducted by the MEXT, Japan (Grant Number JPMXP0112101001)and JSPS KAKENHI (Grant Numbers JP19H05790 and JP20H00354). DSN thanks DSTfor Woman Scientist fellowship (WOS-A) (Grant No. SR/WOS-A//PM-98/2018).P. Tiwari et al.5Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022)    68 AUTHOR CONTRIBUTIONSP.T. and A.B. conceived the idea of this research. P.T. and D.S.N. fabricated thedevices; P.T., M.K.J., and A.B. performed the measurements; A.U. and D.S. providedtheoretical support; K.W. and T.T. grew the material; P.T., M.K.J., and A.B. did theexperimental data analysis. P.T., A.U., and A.B. co-wrote the manuscript. All authorsdiscussed the results and commented on the manuscript.COMPETING INTERESTSThe authors declare no competing interests.ADDITIONAL INFORMATIONSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41699-022-00348-y.Correspondence and requests for materials should be addressed to Aveek Bid.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claimsin published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022P. Tiwari et al.6npj 2D Materials and Applications (2022)    68 Published in partnership with FCT NOVA with the support of E-MRShttps://doi.org/10.1038/s41699-022-00348-yhttp://www.nature.com/reprintshttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Experimental observation of spin&#x02212;split energy dispersion in high-mobility single-layer graphene/WSe2 heterostructures Introduction Results Experimental observations Theoretical calculations Discussions Methods Device fabrication Measurements DATA AVAILABILITY References Acknowledgements Author contributions Competing interests ADDITIONAL INFORMATION