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Máté Kedves, Bálint Szentpéteri, Albin Márffy, Endre Tóvári, Nikos Papadopoulos, Prasanna K. Rout, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Srijit Goswami, Szabolcs Csonka, Péter Makk

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[Stabilizing the Inverted Phase of a WSe<sub>2</sub>/BLG/WSe<sub>2</sub> Heterostructure via Hydrostatic Pressure](https://mdr.nims.go.jp/datasets/81c05ca4-63e8-43f8-be44-cc088fcf9667)

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Stabilizing the Inverted Phase of a WSe2/BLG/WSe2 Heterostructure via Hydrostatic PressureStabilizing the Inverted Phase of a WSe2/BLG/WSe2 Heterostructurevia Hydrostatic PressureMáté Kedves, Bálint Szentpéteri, Albin Márffy, Endre Tóvári, Nikos Papadopoulos, Prasanna K. Rout,Kenji Watanabe, Takashi Taniguchi, Srijit Goswami, Szabolcs Csonka, and Péter Makk*Cite This: Nano Lett. 2023, 23, 9508−9514 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Bilayer graphene (BLG) was recently shown to hosta band-inverted phase with unconventional topology emerging fromthe Ising-type spin−orbit interaction (SOI) induced by theproximity of transition metal dichalcogenides with large intrinsicSOI. Here, we report the stabilization of this band-inverted phase inBLG symmetrically encapsulated in tungsten diselenide (WSe2) viahydrostatic pressure. Our observations from low temperaturetransport measurements are consistent with a single particlemodel with induced Ising SOI of opposite sign on the twographene layers. To confirm the strengthening of the invertedphase, we present thermal activation measurements and show thatthe SOI-induced band gap increases by more than 100% due to theapplied pressure. Finally, the investigation of Landau level spectra reveals the dependence of the level-crossings on the appliedmagnetic field, which further confirms the enhancement of SOI with pressure.KEYWORDS: bilayer graphene, WSe2, spin−orbit interaction, band inversion, pressure, transport measurementsVan der Waals (VdW) engineering provides a powerfulmethod to realize electronic devices with novelfunctionalities via the combination of multiple 2D materials.1An exciting example is the case of graphene connected tomaterials with large intrinsic spin−orbit interaction (SOI),which allows the generation of an enhanced SOI in graphenevia proximity effect.2−26 This, on the one hand, is compellingin the case of spintronics devices since the large spin diffusionlength in graphene heterostructures27−29 could be comple-mented with electrical tunability30−32 or charge-to-spinconversion effects.33 Moreover, it is also interesting from afundamental point of view since graphene with intrinsic SOIwas predicted to be a topological insulator.34 The observationof increased SOI was demonstrated in the past few years inboth single layer12−20 and recently in bilayer graphene(BLG).14,21−26 It was found that one of the dominatingspin−orbit terms is the Ising-type valley-Zeeman term which isan effective magnetic field acting oppositely in the two valleys,and could enable such exciting applications as a valley-spinvalve in BLG.35 Recent compressibility measurements21 haveshown that BLG encapsulated in tungsten-diselenide (WSe2)from both sides hosts a band-inverted phase if the sign ofinduced SOI is different for the two WSe2 layers. In practice,this can be achieved if the twist angle between the two WSe2layers is, for example, 180°.7,11,36In this article, we experimentally investigate the SOI inducedin BLG symmetrically encapsulated in WSe2 (WSe2/BLG/WSe2) via transport measurements. We present resistancemeasurements as a function of charge carrier density (n) andthe transverse displacement field (D) at ambient pressure anddemonstrate the appearance of the inverted phase (IP). Inorder to stabilize this phase, we employ our recently developedsetup37,38 to apply a hydrostatic pressure (p), which allows usto decrease the distance between the WSe2 layers and bilayergraphene and to boost the SOI as we have recentlydemonstrated on single layer graphene.39 The sample is placedin a piston−cylinder pressure cell, where kerosene acts as thepressure mediating medium. More details about this can alsobe found in Methods. To confirm the increased SOI, wepresent thermal activation measurements where the evolutionof the SOI-induced band gap can be estimated as a function ofD and p. Finally, we further investigate the induced SOI withquantum Hall measurements by tracking the Landau levelcrossings as a function of the magnetic field.To reveal the band-inverted phase arising from the Ising SOIin BLG, we show the low-energy band structure of WSe2/BLG/WSe2 in Figure 1, calculated using a continuum modelReceived: August 15, 2023Revised: October 6, 2023Published: October 16, 2023Letterpubs.acs.org/NanoLett© 2023 The Authors. Published byAmerican Chemical Society9508https://doi.org/10.1021/acs.nanolett.3c03029Nano Lett. 2023, 23, 9508−9514This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on October 27, 2023 at 00:00:22 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ma%CC%81te%CC%81+Kedves"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ba%CC%81lint+Szentpe%CC%81teri"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Albin+Ma%CC%81rffy"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Endre+To%CC%81va%CC%81ri"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Nikos+Papadopoulos"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Prasanna+K.+Rout"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Srijit+Goswami"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Szabolcs+Csonka"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Pe%CC%81ter+Makk"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.nanolett.3c03029&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/nalefd/23/20?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/20?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/20?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/20?ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c03029?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org/NanoLett?ref=pdfhttps://acsopenscience.org/open-access/licensing-options/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/by following in the footsteps of ref.7 The effect of the WSe2layers in the proximity of BLG can be described by the IsingSOI terms λIt and λIb that couple only to the top or bottom layerof BLG and act as a valley-dependent effective magnetic field.For WSe2 layers rotated with respect to each other with 180°,the induced SOI couplings will have opposite sign.7,11,36 This istaken into account by the opposite signs of λIt and λIb. Thetransverse displacement field (D) in our measurements can bemodeled by introducing an interlayer potential difference=u Ded0 BLG, where e is the elementary charge, ϵ0 is the vacuumpermittivity, d = 3.3 Å is the separation of BLG layers, and ϵBLGis the effective out-of-plane dielectric constant of BLG.Figure 1a−c shows the calculated band structure around theK-point for different values of u, using the parameter values λIt= −λIb = 2 meV. Details of the modeling can be found in theSupporting Information. First of all, for |u| > |λIt| = |λIb|, we cansee the opening of a band gap (Figure 1a), as expected for BLGin a transverse displacement field.40,41 On the other hand, asopposed to pristine BLG, the bands are spin-split, and thedirection of this spin splitting is opposite for the valence andconduction bands. This is a direct consequence of the oppositesign of λIt and λIb as the valence and conduction bands arelocalized on different layers due to the large u. The bandstructure in the K′-valley is similar except that the spin-splittingis reversed due to time reversal symmetry. For |u| = |λIt,b|(Figure 1b), the u-induced band gap approximately equals thespin splitting induced by the Ising SOI and the bands touch.Finally, for |u| < |λIt,b| (Figure 1c), a band gap reopens and weobserve spin-degenerate bands for u = 0, separated by a gapcomparable in size to the Ising SOI terms (Δ ≈ |λIt − λIb|/2).This gapped phase is distinct from the band insulating phase atlarge u in that the valence and conduction bands are no longerlayer polarized, hence it is usually referred to as inverted phase(IP). It is worth mentioning that the IP at |u| < |λIt| is weaklytopological unlike the trivial band insulating phase.42,43Our device consists of a BLG flake encapsulated in WSe2and hexagonal boron nitride (hBN) on both sides, asillustrated in Figure 2a. To enable transport measurements,we fabricated NbTiN edge contacts in a Hall bar geometry.The device also features a graphite bottomgate and a metallictopgate that allow the independent tuning of n and D. See theSupporting Information for more details about samplefabrication and geometry. The results on similar devices withvery similar findings are also shown in the SupportingInformation.Figure 2c shows the resistance measured in a four-terminalgeometry as a function of n and D at ambient pressure at 1.4 Ktemperature. As expected for BLG, we observe the opening of aband gap at large displacement fields along the chargeneutrality line (CNL) at n = 0, indicated by an increase ofresistance. In accordance with the theoretical model andprevious compressibility measurements,21 we also observe twolocal minima separated by a resistance peak at D = 0 inagreement with the closing and reopening of the band gapsignaling the transition between the band insulator and the IP.This observation is further emphasized in Figure 2b, where aline trace (blue) of the resistance is shown as a function of D,measured along the CNL. It is important to note that duringthe fabrication process the rotation of WSe2 layers was notcontrolled. However, from theoretical predictions,7,11,36 weonly expect to observe signatures of the IP for a suitable rangeof rotation angles between the two WSe2 layers (e.g., ∼180°).This is further supported by the fact that not all devicesfabricated showed the IP. An example for this case is shown inthe Supporting Information, where only the band insulatingregime can be observed in the resistance map.To boost the induced SOI and stabilize the IP, we applied ahydrostatic pressure of p = 1.65 GPa and repeated the previousmeasurement. Figure 2d shows the n−D map of the resistanceafter applying the pressure. Although the basic features of theresistance map are similar, two consequences of applying thepressure are clearly visible. First, as also illustrated in Figure 2b,the peak resistance in the IP at D = 0 increased by ∼25%.Second, the displacement field required to close the gap of theIP increased significantly, by about 70%. Both of theseobservations can be accounted for by an increase in the IsingSOI term that results in a larger gap at D = 0 and subsequentlyFigure 1. (a−c) Calculated band structure around the K-point fordifferent values of the interlayer potential difference u. Color scalecorresponds to the spin polarization of the bands.Figure 2. (a) Schematic representation of the measured device.Bilayer graphene is symmetrically encapsulated in WSe2 and hBN. (b)Line trace of the four-terminal resistance along the CNL for ambientpressure (blue) and p = 1.65 GPa (red). (c, d) Four-terminalresistance map as a function of charge carrier density n anddisplacement field D measured at (c) ambient pressure and (d) anapplied pressure of 1.65 GPa. The alternating low and high resistanceregions along the CNL indicate the closing and reopening of a bandgap in the bilayer graphene.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c03029Nano Lett. 2023, 23, 9508−95149509https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig2&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c03029?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asin a larger displacement field needed to close the gap. Althoughthe shift of resistance minima could be explained by theincrease of ϵBLG or the decrease of interlayer separation d, thesealtogether are not expected to have greater effect than∼20%.44,45 It is also worth mentioning that the lever armsalso change due to the applied pressure, changing theconversion from gate voltages to n and D; however, we havecorrected for this effect by experimentally determining themfrom quantum Hall measurements (see the SupportingInformation).To quantify the increase in the SOI gap due to hydrostaticpressure, we performed thermal activation measurements alongthe CNL for several values of D. Figure 3a demonstrates theevolution of resistance as a function of 1/T for selected valuesof D at ambient pressure. From this, we extract the band gapusing a fit to the high-temperature, linear part of the datawhere thermal activation−ln(R) ∝ Δ/2kBT − dominates overhopping-related effects.46 Figure 3b shows the extracted gapvalues as functions of D with and without applied pressure.First of all, a factor of 2 increase is clearly visible in the gap atD = 0 for p = 1.65 GPa, which is consistent with the observedincrease of resistance. Second, the higher D needed to reachthe gap minima is also confirmed. We also note that the bandgap cannot be fully closed which we attribute to spatialinhomogeneity in the sample.The experimentally determined band gaps allow us toquantify the SOI parameters. By adjusting the theoreticalmodel to match the positions of the gap minima and theopening of the trivial gap for p = 0, we extract λIt = −λIb = 2.2 ±0.4 meV. Similarly, we can extract the SOI parameters at p =1.65 GPa. For these, we obtain λIt = −λIb = 5.6 ± 0.6 meV. TheSOI parameters extracted from the minima give the same orderof magnitude estimate as the gaps at D = 0 extracted fromthermal activation directly. A more detailed discussion of theextraction and possible errors is given in the SupportingInformation. We expect that all layer distances (e.g., hBN-hBN,BLG-WSe2, and d) change due to the applied pressure as it isalso reflected in the change of lever arms. The extractedincrease of SOI strength due to the change of BLG-WSe2distances is consistent with theoretical predictions in ref 37,where almost a factor of 3 increase was predicted for an appliedpressure of 1.8 GPa. Importantly, we have found similar resultsin two further devices shown in the Supporting Information.The quantum Hall effect in BLG provides us another tool toinvestigate the Ising SOI induced by the WSe2 layers. The 2-fold degeneracy of valley isospin (ξ = +, − ), the first twoFigure 3. Thermal activation measurements along the chargeneutrality line. (a) Arrhenius plot of the resistance at ambientpressure for selected values of D. Solid lines are fits to the linear partsof the data from which the band gap values were obtained. (b) Gap Δas a function of displacement field at ambient pressure (blue) and anapplied pressure of 1.65 GPa. Arrows indicate the D values for whichthe activation data are shown in a.Figure 4. (a) Low energy Landau level spectrum at B = 8.5 T obtained from single-particle continuum model with λIt = −λIb = 2 meV. (b) Four-terminal resistance as a function of n and D measured at B = 8.5 T out-of-plane magnetic field and ambient pressure. Resistance plateauscorrespond to different ν filling factors. Abrupt changes in resistance at a given ν value as a function of D indicate the crossings of LLs. (c, e)Measurements of LL crossings as a function of B for ν = 0 and ν = 1, respectively, for p = 0. Symbols denote LL crossings shown in a. (d, f) Criticaldisplacement field D* corresponding to LL crossings for ν = 0 and ν = 1 extracted from D − B maps measured at p = 0 (blue, see c, e) and p = 1.65GPa (red).Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c03029Nano Lett. 2023, 23, 9508−95149510https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?fig=fig4&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c03029?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asorbitals (N = 0, 1) and spin (σ = ↑, ↓) give rise to an 8-folddegenerate Landau level (LL) near zero-energy.47−49 Thisdegeneracy is weakly lifted by the interlayer potentialdifference, Zeeman energy, coupling elements between theBLG layers50 and the induced Ising SOI.22 We can obtain theenergy spectrum of this set of eight closely spaced sublevels,labeled by |ξ, N, σ⟩, by introducing a perpendicular magneticfield in our continuum model, as detailed in.50 This is shown inFigure 4a for B = 8.5 T as a function of the interlayer potential(u). LLs with different ξ reside on different layers of the BLG,and therefore u induces a splitting between these levels.Second, the finite magnetic field causes the Zeeman-splitting oflevels with different σ. Finally, the Ising SOI induces anadditional effective Zeeman field associated with a given layer,further splitting the levels. The key feature that should benoted here is that for a given filling factor ν, crossings of LLscan be observed and the position of crossing points along the uaxis depend on SOI parameters as well as on the magneticfield. These level crossings manifest as sudden changes ofresistance in our transport measurements as is illustrated inFigure 4b. Here, the n−D map of the resistance is shown asmeasured at B = 8.5 T with fully developed resistance plateaus(due to the unconventional geometry, see the SupportingInformation) corresponding to the sublevels of ν ∈ [−4,4].For a given filling factor ν, we observe 4 − |ν| different D valueswhere the resistance deviates from the surrounding plateaucorresponding to the crossing of LLs, as expected from themodel.The evolution of LL crossings with B can be observed byperforming measurements at fixed filling factors, as shown inFigure 4c and e for ν = 0 and ν = 1, respectively. During thelatter measurement, carrier density n was tuned such that thefilling factor given by ν = nh/eB was kept constant. On bothpanels, we can observe 4 − ν LL crossings that evolve as B istuned, until they disappear at low magnetic fields where we canno longer resolve LL plateaus. This B-dependent behaviorenables us to investigate the effect of SOI on the LL structure.Figure 4d and f shows the critical displacement field D* values,where LL crossings can be observed, extracted from Figure 4cand e and similar maps measured at p = 1.65 GPa (see theSupporting Information). For ν = 0 (Figure 4d), the mostimportant observation is that the crossing points do notextrapolate to zero as B → 0 T, which is a direct consequenceof the induced Ising SOI. It is also clearly visible that due tothe applied pressure, |D*| is generally increased, especially atlower B-fields, indicating that the Ising SOI has increased, inagreement with our thermal activation measurements. For ν =1 (Figure 4f), similar trends can be observed. The two LLcrossings at finite D saturate for small B, while the thirdcrossing remains at D = 0. We note that the D*(B) curves for p= 1.65 GPa cannot be scaled down to the p = 0 curves, whichconfirms that our observations cannot simply be explained byan increased ϵBLG or decreased interlayer separation distance,but are the results of enhanced SOI. We also point out thatsome lines which extrapolate to D = 0 can also be observed(e.g., Figure 4e, gray arrow). This could also be explained bysample inhomogeneity. It is also important to note that oursingle-particle model fails to quantitatively predict the B-dependence of the LL crossings indicating the importance ofelectron−electron interactions (see the Supporting Informa-tion).In conclusion, we showed that the IP observed in BLGsymmetrically encapsulated between twisted WSe2 layers canbe stabilized by applying hydrostatic pressure, which enhancesthe proximity induced SOI. We presented thermal activationmeasurements as a means to quantify the Ising SOI parametersin this system and showed an increase of approximately 150%due to the applied pressure. In order to gain more informationon the twist angle dependence of the SOI, a more systematicstudy with several samples with well-controlled twist angles isneeded. The enhancement of Ising SOI with pressure wasfurther confirmed from quantum Hall measurements. How-ever, to extract SOI strengths from these measurements, morecomplex models are needed that also take into accountinteraction effects. Our study shows that the hydrostaticpressure is an efficient tuning knob to control the inducedIsing SOI and thereby the topological phase in WSe2/BLG/WSe2.The IP has a distinct topology from the band insulator phaseat large D, and the presence of edge states are expected.42 Thepresence of these states should be studied in better definedsample geometries51,52 or using supercurrent interferome-try.53,54 Opposed to the weak protection of the edge states inthis system, a strong topological insulator phase is predicted inABC trilayer graphene.43,55 Furthermore, pressure could alsobe used in case of magic-angle twisted BLG, in whichtopological phase transitions between different Chern insulatorstates are expected as a function of SOI strength.56■ METHODSSample Fabrication. The dry-transfer technique with PC/PDMS hemispheres is employed to stack hBN (35 nm)/WSe2(19 nm)/BLG/WSe2 (19 nm)/hBN (60 nm)/graphite. Tofabricate electrical contacts to the Hall bar, we use e-beamlithography patterning followed by a reactive ion etching stepusing CHF3/O2 mixture and finally deposit Ti (5 nm)/NbTiN(100 nm) by dc sputtering. We deposit Al2O3 (30 nm) usingALD which acts as the gate dielectric and isolates the ohmiccontacts from the top gate. Finally, the top gate is defined by e-beam lithography and deposition of Ti (5 nm)/Au (100 nm).Transport Measurements. Transport measurements werecarried out in an Oxford cryostat equipped with a variabletemperature insert (VTI) at a base temperature of 1.4 K(unless otherwise stated). Measurements were performedusing the lock-in technique at 1.17 kHz frequency.Pressurization. The sample is first bonded to a highpressure sample holder and placed in a piston−cylinderpressure cell, where kerosene acts as the pressure mediatingmedium. To change the applied pressure, the sample iswarmed up to room temperature where the pressure is appliedusing a hydraulic press and the sample is cooled down again.Our pressure cell is described in more detail in ref.39■ ASSOCIATED CONTENTData Availability StatementSource data of the measurements and the Python code for thesimulation are publicly available at 10.5281/zenodo.8406628.*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029.Details of device fabrication, optical image of the device,measurement setup, n−D conversion, determination oflever arms, details of band structure calculation,extended activation data, details of the method toextract SOI strength, additional quantum Hall measure-Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c03029Nano Lett. 2023, 23, 9508−95149511https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03029/suppl_file/nl3c03029_si_001.pdfhttps://doi.org/10.5281/zenodo.8406628https://pubs.acs.org/doi/10.1021/acs.nanolett.3c03029?goto=supporting-infopubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c03029?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asment data, and measurements on two-terminal devices(PDF)■ AUTHOR INFORMATIONCorresponding AuthorPéter Makk − Department of Physics, Institute of Physics,Budapest University of Technology and Economics, BudapestH-1111, Hungary; MTA-BME Correlated van der WaalsStructures Momentum Research Group, Budapest H-1111,Hungary; Email: makk.peter@ttk.bme.huAuthorsMáté Kedves − Department of Physics, Institute of Physics,Budapest University of Technology and Economics, BudapestH-1111, Hungary; MTA-BME Correlated van der WaalsStructures Momentum Research Group, Budapest H-1111,Hungary; orcid.org/0000-0002-2057-4891Bálint Szentpéteri − Department of Physics, Institute ofPhysics, Budapest University of Technology and Economics,Budapest H-1111, Hungary; MTA-BME Correlated van derWaals Structures Momentum Research Group, Budapest H-1111, Hungary; orcid.org/0000-0003-1587-1098Albin Márffy − MTA-BME Correlated van der WaalsStructures Momentum Research Group, Budapest H-1111,Hungary; MTA-BME Superconducting NanoelectronicsMomentum Research Group, H-1111 Budapest, HungaryEndre Tóvári − Department of Physics, Institute of Physics,Budapest University of Technology and Economics, BudapestH-1111, Hungary; MTA-BME Correlated van der WaalsStructures Momentum Research Group, Budapest H-1111,Hungary; orcid.org/0000-0002-0000-3805Nikos Papadopoulos − QuTech and Kavli Institute ofNanoscience, Delft University of Technology, Delft 2600 GA,The Netherlands; orcid.org/0000-0002-9972-699XPrasanna K. Rout − QuTech and Kavli Institute ofNanoscience, Delft University of Technology, Delft 2600 GA,The NetherlandsKenji Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0003-3701-8119Takashi Taniguchi − International Center for MaterialsNanoarchitectonics, National Institute for Materials Science,Tsukuba 305-0044, Japan; orcid.org/0000-0002-1467-3105Srijit Goswami − QuTech and Kavli Institute of Nanoscience,Delft University of Technology, Delft 2600 GA, TheNetherlandsSzabolcs Csonka − Department of Physics, Institute of Physics,Budapest University of Technology and Economics, BudapestH-1111, Hungary; MTA-BME SuperconductingNanoelectronics Momentum Research Group, H-1111Budapest, HungaryComplete contact information is available at:https://pubs.acs.org/10.1021/acs.nanolett.3c03029Author ContributionsN.P. and P.K.R. fabricated the device. Measurements wereperformed by M.K., B.Sz., and P.K.R. with the help of M.A.,P.M. M.K. and B.Sz. did the data analysis. B.Sz. did thetheoretical calculation. M.K., B.Sz., E.T., and P.M. wrote thepaper and all authors discussed the results and worked on themanuscript. K.W. and T.T. grew the hBN crystals. The projectwas guided by Sz.Cs., S.G., and P.M.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThis work acknowledges support from the Topograph,MultiSpin, and 2DSOTECH FlagERA networks, the OTKAK138433 and PD 134758 grants, and the VEKOP 2.3.3-15-2017-00015 grant. This research was supported by theMinistry of Culture and Innovation and the National Research,Development and Innovation Office within the QuantumInformation National Laboratory of Hungary (Grant No.2022-2.1.1-NL-2022-00004), by the FET Open AndQCnetwork. We acknowledge COST Action CA 21144 super-QUMAP. P.M. and E.T. received funding from BolyaiFellowship. This project was supported by the ÚNKP-22-3-IINew National Excellence Program of the Ministry forInnovation and Technology from the source of the NationalResearch, Development and Innovation Found. K.W. and T.T.acknowledge support from JSPS KAKENHI (Grant Numbers19H05790, 20H00354, and 21H05233). The authors thankPablo San-Jose, Elsa Prada, and Fernando Peñaranda forfruitful discussions.■ REFERENCES(1) Geim, A. K.; Grigorieva, I. V. Van der Waals heterostructures.Nature 2013, 499, 419−425.(2) Konschuh, S.; Gmitra, M.; Kochan, D.; Fabian, J. Theory of spin-orbit coupling in bilayer graphene. Phys. Rev. B 2012, 85, 115423.(3) Gmitra, M.; Fabian, J. Graphene on transition-metaldichalcogenides: A platform for proximity spin-orbit physics andoptospintronics. Phys. Rev. B 2015, 92, 155403.(4) Khoo, J. Y.; Morpurgo, A. F.; Levitov, L. On-Demand Spin−Orbit Interaction from Which-Layer Tunability in Bilayer Graphene.Nano Lett. 2017, 17, 7003−7008.(5) Garcia, J. H.; Vila, M.; Cummings, A. 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