# Fileset

[Seiler_2025_2D_Mater._12_035009.pdf](https://mdr.nims.go.jp/filesets/28ef6405-dd27-4702-aa56-e69e61217aae/download)

## Creator

Anna M Seiler, Yaroslav Zhumagulov, Klaus Zollner, Chiho Yoon, David Urbaniak, Fabian R Geisenhof, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Jaroslav Fabian, Fan Zhang, R Thomas Weitz

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Layer-selective spin-orbit coupling and strong correlation in bilayer graphene](https://mdr.nims.go.jp/datasets/98fcdbd1-6dae-40e1-9bba-646f38592745)

## Fulltext

Layer-selective spin-orbit coupling and strong correlation in bilayer graphene2D Materials     PAPER • OPEN ACCESSLayer-selective spin-orbit coupling and strongcorrelation in bilayer grapheneTo cite this article: Anna M Seiler et al 2025 2D Mater. 12 035009 View the article online for updates and enhancements.You may also likeStrain activation of localized states inWSe2Ouzhan Yücel, Denis Yagodkin, Jan NKirchhof et al.-Tunable interfacial electronic propertiesand contact types in 2D AuS/m-TMDheterostructuresYuheng Zhang, Lei Gao, Yufei Xue et al.-Multiscale computational modelingtechniques in study and design of 2Dmaterials: recent advances, challenges,and opportunitiesMohsen Asle Zaeem, Siby Thomas,Sepideh Kavousi et al.-This content was downloaded from IP address 144.213.253.16 on 04/06/2025 at 03:18https://doi.org/10.1088/2053-1583/add74a/article/10.1088/2053-1583/add414/article/10.1088/2053-1583/add414/article/10.1088/2053-1583/add7ce/article/10.1088/2053-1583/add7ce/article/10.1088/2053-1583/add7ce/article/10.1088/2053-1583/ad63b6/article/10.1088/2053-1583/ad63b6/article/10.1088/2053-1583/ad63b6/article/10.1088/2053-1583/ad63b62D Mater. 12 (2025) 035009 https://doi.org/10.1088/2053-1583/add74aOPEN ACCESSRECEIVED30 January 2025REVISED24 April 2025ACCEPTED FOR PUBLICATION12 May 2025PUBLISHED28 May 2025Original content fromthis work may be usedunder the terms of theCreative CommonsAttribution 4.0 licence.Any further distributionof this work mustmaintain attribution tothe author(s) and the titleof the work, journalcitation and DOI.PAPERLayer-selective spin-orbit coupling and strong correlation in bilayergrapheneAnna M Seiler1, Yaroslav Zhumagulov2, Klaus Zollner2, Chiho Yoon3, David Urbaniak1,Fabian R Geisenhof4, Kenji Watanabe5, Takashi Taniguchi6, Jaroslav Fabian2, Fan Zhang3and R Thomas Weitz1,∗1 1st Physical Institute, Faculty of Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany2 Institute for Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany3 Department of Physics, University of Texas at Dallas, Richardson, TX 75080, United States of America4 Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, 80539Munich, Germany5 Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan6 Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan∗ Author to whom any correspondence should be addressed.E-mail: thomas.weitz@uni-goettingen.deKeywords: bilayer graphene, spin-orbit coupling, correlationsSupplementary material for this article is available onlineAbstractSpin-orbit coupling (SOC) and electron-electron interaction can mutually influence each otherand give rise to a plethora of intriguing phenomena in condensed matter systems. In pristinebilayer graphene (BLG), which has weak SOC, intrinsic Lifshitz transitions and concomitantvan-Hove singularities lead to the emergence of many-body correlated phases. Layer-selective SOCcan be proximity induced by adding a layer of tungsten diselenide (WSe2) on its one side. Byapplying an electric displacement field, the system can be tuned across a spectrum whereinelectronic correlation, SOC, or a combination of both dominates. Our investigations reveal anintricate phase diagram of proximity-induced SOC-selective BLG. Not only does this phasediagram include those correlated phases reminiscent of SOC-free doped BLG, but it also hostsunique SOC-induced states allowing a compelling measurement of valley g-factor and a correlatedinsulator at charge neutrality, thereby showcasing the remarkable tunability of the interplaybetween interaction and SOC in WSe2 enriched BLG.1. MainVarious distinct strongly interacting states often com-pete for the ground state of a disorder-free two-dimensional (2D) electron system under electron–electron interactions. Recently, the seemingly well-explored family of few-layer graphene has gainedrevived interest [1–10]. For example, in the simplestAB-stacked bilayer graphene (BLG), a plethora ofmany-body states has been revealed [2, 4, 5, 10]. Here,electric displacement field-controlled inversion sym-metry breaking further flattens the bands yet makingthe low-density saddle points experimentally access-ible. Consequently, Stoner ferromagnetic states [2,4, 5, 10], correlated (semi-) insulating and metal-lic states [4, 5], and superconducting states [2] havebeen identified close to the field-controlled van-Hovesingularities. The detailed nature and mechanismsof these states are under active investigations. Forexample, it has been shown that proximity-inducedspin-orbit coupling (SOC) of Ising (valley-Zeeman)type allows the observation of superconducting statesin a much broader parameter space [11, 12], lead-ing to the question of whether SOC is responsiblefor suppressing interacting states that compete withsuperconductivity [13], or whether superconductiv-ity is enhanced by SOC [12]. To date which effect(e.g. SOC,Coulomb interaction, saddle points) favorswhich ground state has still been an open questionboth from the theoretical [13] and experimental [11,12] sides.While previous investigations have focused on theimpact of proximity-induced SOC on the supercon-ductivity of BLG [11, 12], impacts of such a SOC on© 2025 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/2053-1583/add74ahttps://crossmark.crossref.org/dialog/?doi=10.1088/2053-1583/add74a&domain=pdf&date_stamp=2025-5-28https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://orcid.org/0000-0002-9883-9220https://orcid.org/0000-0002-6239-3271https://orcid.org/0009-0006-4561-1704https://orcid.org/0000-0002-3623-1906https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0001-5404-7355mailto:thomas.weitz@uni-goettingen.dehttp://doi.org/10.1088/2053-1583/add74a2D Mater. 12 (2025) 035009 A M Seiler et althe rest of its correlated phase diagram remains unex-plored. Here, we systematically disentangle the intric-ate interplay between electronic correlations and SOCin spin-orbit proximitized BLG, aiming to elucidatethe entire phase diagram. To this end we prioritize thecompetition between SOC and Coulomb interactionin their impacts on those BLG ground states enrichedby the displacement field-controlled saddle points yetoutside of the superconducting regime.A typical device scheme is shown in figure 1(a),where a monolayer of WSe2 is placed below a BLGflake. The BLG/WSe2 heterostructures are contactedby two-terminal graphite flakes and encapsulated inhexagonal boron nitride (hBN). Additional graph-ite top and bottom gates are incorporated to provideelectrostatic control and to ensure a high device qual-ity. Optical microscope images of the two encapsu-lated devices investigated in this study are displayedin figure 1(b) and supplementary figure S1.The dual-gate structure enables independent tun-ing of the charge carrier density (n) and the electricdisplacement field (D). In such a device configura-tion, Ising SOC (valley-Zeeman type) [14] is expectedto only be introduced to the bottom graphene layer[12, 15, 16], which can be confirmed by our bandstructure calculations (figure 1(c)). The proximity-induced SOC results in out-of-plane spin-valley lock-ing of the Ising SOC (valley-Zeeman type), and rel-atively large (meV) spin-splitting of the low-energybands of BLG at the K and K’ points with no over-all layer asymmetry [16]. Note that the influence ofRashba SOCon the low-energy band structure ismin-imal (see supplementary figure S2). As a result, it isneglected in the present study. At D > 0 and n > 0(orD< 0 and n< 0), electronic states near the Fermienergy are polarized to the layer adjacent to the WSe2[12, 15, 16], exhibiting the proximity spin-orbit phys-ics. Conversely, the energy bands forD> 0 and n< 0(or D < 0 and n > 0) are only weakly affected bythe presence ofWSe2 (figure 1(c)). ThisD-dependentspin-valley-locked, spin-split band structure has adirect consequence for the charge transport at smalln and D as shown in figure 1(d), where the occu-pation of the high-energy spin-split conduction andvalence bands, as marked with arrows, are featuredby increased dG/dn with conductance G (see supple-mentary figure S3 for a complete phase diagram ofboth devices investigated for the present study) [15].While these transitions are more clearly resolved inthe derivative map shown in figure 1(d), they are alsopresent—albeit less prominently—in the raw con-ductance data (see, for example, figure 3(e) whichwillbe discussed later). The strength of the Ising SOC λIcan be determined directly by mapping the magneticfield dependence of particular Landau-Levels (LL),e.g. the ν = 3 state, to be λI = (1 ± 0.1) meV (seemethods and supplementary figure S4), which is con-sistent with previous results [11, 12, 15, 17, 18] andDFT calculations [14, 16].2. Correlated phases in the vicinity oftunable van-Hove singularitiesWe start our analysis in the conduction band at largeD fields, where, in the absence of SOC, a cascadeof correlated phases was found as low-temperatureground states (figures 1–3) [5]. Since BLG is onlyproximitized on one side by WSe2, we can investigatethe presence and absence of SOC in the same sample,by selectively addressing the layer-polarized energylevels. We first re-investigate the conduction bandwithout SOC (D<0, n>0) in both non-proximitizedBLG (figures 2(a)–(c)) and in proximitized BLGwhenelectron transport is taking place in the top layerwhere the effects of SOC are weak (figures 2(d)–(f)).Consistent with previous works [5, 10], three phasescan be identified at large |D| close to the band edge:a spin- and valley-polarized (quasi-) insulating phase(1x), a spin-polarized (quasi-) insulating phase (2x),and a fully spin- and valley-degenerate metallic phase(4x) (figures 2(a)–(f)). The (quasi-) insulating char-acter of the 1x and 2x phases was discussed in [5]. Thelabels ‘1x,’ ‘2x,’ and ‘4x’ reflect the different spin andvalley degeneracies of the system which are determ-ined by examining the behavior of the phase bound-aries with respect to the applied out-of-plane and in-plane magnetic field (B⊥ and B∥) [5, 10]. Applying afinite B∥ (figures 2(c) and (f)), which only couples tothe spin degree of freedom, does not shift the phaseboundary between the 1x and 2x phases, indicatingsimilar spin polarizations of both phases. By contrast,the phase boundary between the 2x and 4x phasesshifts towards higher electron densities, indicatingspin polarizations in the 1x and 2x phases but not inthe 4x phase. Applying B⊥, which couples to the val-ley and out-of-plane spin degrees of freedom via theorbital and spin Zeeman effects, affects both phaseboundaries (figures 2(b) and (e)), indicating a changein valley polarization between the 1x and 2x phases,i.e. we can identify the 1x phase to be valley polar-izedwhile the 2x and 4x phases are valley unpolarized.This method allows to identify the degeneracies evenat B⊥ = 0 where no quantum Hall oscillations arepresent. Remarkably, these characteristics are consist-ent in both non-proximitized BLG (figures 2(a)–(c))and in proximitized BLG when electron transport istaking place in the top layer where the effects of SOCare weak (figures 2(d)–(f)).A drastically different phase diagram appears inthe same parameter space (|D| and n) but for the22D Mater. 12 (2025) 035009 A M Seiler et alFigure 1. Phase diagram of bilayer graphene exhibiting layer-selective proximity-induced SOC. (a) Device schematic of anencapsulated bilayer graphene flake located on top of a WSe2 flake. (b) Optical microscope image of Device I. Graphite flakesserving as gates (contacts) are outlined in purple (grey), hBN flakes are outlined in orange, the WSe2 flake is outlined in green,and the BLG flake is outlined in blue (the same color code as in (a)). (c) Low-energy band structures of bilayer graphene near theK-point of the Brillouin zone for electric potentials V =−2 meV (top) and V = 2 meV (bottom), calculated from a model thatincludes an Ising SOC of λI = 1.07 meV on the bottom layer. Green bands are spin polarized up, orange bands are spin polarizeddown. (d) Derivative of the two-terminal conductance G (dG/dn) as a function of charge carrier density n and electricdisplacement field Dmeasured in Device I with B⊥ = B∥ = 0 T at a temperature T = 10 mK. Changes in the conductanceassociated with proximity-induced spin-orbit coupling (SOC) are highlighted: the arrows indicate changes in G associated withthe band splitting due to proximity-induced SOC (see figures 2(g) and 3(e) for more better visibility); the circle marks thecorrelated insulating state at D= n= B⊥ = 0, shown in more detail in figure 4. The labels i–iv mark the four quadrants in then-D plane and correspond to the energy bands shown in (c).WSe2 proximitized conduction band (D > 0, n > 0,figures 2(g)–(i)). Consistent with other works [19–21], we do observe signatures of a spin/ valley polar-ized phase, which we attribute to the SOC-inducedsplitting of the originally four-fold degenerate bandinto two sets of two-fold degenerate spin-valley-locked bands. While the transition between the twosets of SOC-split bands shown in figure 1(d) extendsto large D (figure 2(g)), in the investigated rangeup to 0.8 V nm, no additional conductance fea-tures indicating additional spin or valley polariza-tion appear at D > 0 and B = 0, unlike on the non-WSe2-proximitized side. It appears that in the pres-ence of SOC, the formation of interaction-driven spinand/or valley polarized Stoner phases near the con-duction band edge of D field-gapped BLG is sup-pressed. This picture is also consistent with the mag-netic field data. Applying B⊥ induces a valley split-ting in the low-energy spin-valley-locked band dueto the valley-Zeeman effect. This splitting shifts tohigher energies with increasing B⊥ and manifests asa peak in dG/dn that is marked with a dashed linein figure 2(h) and is shifting to higher n for increas-ing B⊥. At a critical magnetic field BC (supplement-ary figure S5), the upper band of the low-energy spin-valley-locked band (K valley, spin down and the lowerband of the high-energy spin-valley locked band (K’valley, spin down) intersect. These bands share thesame spin but have opposite valley indices. This cross-ing point allows us to determine theD-dependent val-ley g-factor, which quantifies the strength of the valleymagnetic moment [22]. Using λI =12 µB gVBC withBohr magneton µB and BC = 1.9 T, we find gV to be22 at D = 0.7 Vnm−1, which aligns well with previ-ous results obtained in BLGquantumdots [23–25]. Inthe B∥ map up to 2 T we do not observe any changeof the phase boundaries, since in this regime the spinZeeman energy Ez ≪ λI [16].All our observations point to the weakeningor absence of Stoner ferromagnetic phases whenthe electrons are polarized to the layer adjacent toWSe2. Theoretically, the Ising SOC of out-of-planespin quantization, together with the WSe2-enhancedscreening effect, is expected to disfavor those correl-ated phases with in-plane spin orientations as previ-ously identified in the absence of SOC [4, 5]. We notethat WSe2 does have a larger dielectric constant thanhBN [26]. Given that monolayer WSe2 is used in ourdevices, the short-range part of Coulomb interactionis more significantly screened than the long-rangeCoulomb tail. Nevertheless,—even though the effectwill likely be small—the WSe2-enhanced screening32D Mater. 12 (2025) 035009 A M Seiler et alFigure 2. Phase diagrams of electron-doped bilayer graphene without and with layer-selective proximity-induced SOC. (a) dG/dnas a function of n and negative Dmeasured in a BLG heterostructure without proximate WSe2 layer (Device III) withB⊥ = B∥ = 0 T. The 1x, 2x and 4x degenerate phases are labeled. (b), (c) dG/dn as a function of n and B⊥ (b) and B∥ (c) forD=−0.7 V nm−1 (b) and D=−0.6 V nm−1 (c). Phase boundaries are highlighted by dashed lines. (d) dG/dn as a function of nand negative Dmeasured in a BLG—WSe2 heterostructure (Device I) with B⊥ = B∥ = 0 T. Electron transport is taking place inthe top layer where the effects of SOC are weak. (e), (f) dG/dn as a function of n and B⊥ (e) and B∥ (f) for D=−0.65 V nm−1.Electron transport is taking place in the top layer where the effects of SOC are weak. Phase boundaries are highlighted by dashedlines. (g) dG/dn as a function of n and positive Dmeasured in a BLG—WSe2 heterostructure (Device I) with B⊥ = B∥ = 0 T.Electron transport is taking place in the bottom layer where the effects of SOC are strong. (h), (i) dG/dn as a function of n and B⊥(h) and B∥ (i) for D=−0.65 V nm−1. Electron transport is taking place in the bottom layer where the effects of SOC are strong.Phase boundaries are highlighted by dashed lines. No changes in the phase boundaries can be observed as a function of B∥ (then-B∥ map is dominated by vertical lines). The data presented in panels (a)–(c) was obtained using Device III, the data in panels(d)–(i) was obtained using Device I. All measurements were performed at a temperature of T = 10 mK.may disfavor Stoner and more elaborate correl-ated phases [27–29]. The suppression of the Stonerphases on the WSe2 polarized layer might be furtherenhanced by greater disorder at the WSe2/BLG inter-face compared to the BLG/hBN interface (see meth-ods for details on the sample fabrication).The picture becomes more complex on the hole-doped side of BLG, where trigonal warping is morepronounced [30] and Lifshitz transitions with con-comitant van-Hove singularities give rise to a cas-cade of correlated insulating and metallic phases ofboth Stoner and non-Stoner types [4]. These phaseswere initially observed in pristine BLG (see alsofigures 3(a), (b)) and can also be identified similarlyin the BLG/WSe2 devices for D> 0 and n< 0, wherecharge transport occurs in the layer non-adjacent to42D Mater. 12 (2025) 035009 A M Seiler et alFigure 3. Phase diagrams of hole-doped bilayer graphene without and with layer-selective proximity-induced SOC. (a)Conductance G (top panel) and derivative of the conductance dG/dn (bottom panel) as a function of the charge carrier density nand electric displacement field |D| measured in a BLG heterostructure without proximate WSe2 layer (Device III) withB⊥ = B∥ = 0 T. Electron transport is taking place in the top layer where the effects of SOC are weak. Phase boundaries arehighlighted by dashed lines. The 1x, 2x and 4x degenerate phases are labeled. Interaction-induced phases are labeled according toSeiler et al [4]. Where phases I and IV correspond to correlated metals of non-Stoner type and phases II and III correspond tocorrelated insulating phases consistent with a Wigner-Hall crystal (phase II) and a trivial Wigner crystal (phase III). (b) G (toppanel) and dG/dn (bottom panel) as a function of n and B⊥ at |D|= 0.6 Vnm−1. (c) G as a function of n and positive Dmeasured in a BLG—WSe2 heterostructure (Device II) with B⊥ = B∥ = 0 T. Electron transport is taking place in the top layerwhere the effects of SOC are weak. Phase boundaries are highlighted by dashed lines. The interaction-induced phases are labeled.(d) G as a function of n and B⊥ at D= 0.6 Vnm−1. (e) G (top panel) and dG/dn (bottom panel) as a function of n and negative Dwith B⊥ = B∥ = 0 T. Electron transport is taking place in the bottom layer where the effects of SOC are strong. Phase boundariesare highlighted by arrows. The interaction induced phases I–IV are not present. (f) Top panel: dG/dn as a function of n and B⊥for D=−0.5 V nm−1. Phase boundaries are highlighted by arrows. Quantum Hall states arising from the second energy band aretraced by dashed lines for negative B⊥. Bottom panel: schematic of the different phases induced by SOC. The one-fold, two-fold,and four-fold degenerate phases are labeled as 1x, 2x, and 4x, respectively. Additional phases in the low-density regime of the 2xand 4x degenerate bands are shaded in gray. Furthermore, an insulating phase emerges near the band edge. The data presented inpanels (a), (b) was obtained using Device III, the data in panels (c)–(f) was obtained using Device II. All measurements wereperformed at a temperature of T = 10 mK.52D Mater. 12 (2025) 035009 A M Seiler et alWSe2 (figures 3(c) and (d)). However, the proximity-induced Ising SOC is present for D < 0 and n < 0when charge transport occurs in the layer adjacentto WSe2, and evidently it disfavors these correlatedphases (see figures 3(e) and (f) for the data fromDevice II and supplementary figure S6 for data fromDevice I). Notably, our findings reveal multiple dis-tinctive features in the density derivative of the con-ductance, as indicated by arrows in figures 3(e) and(f), which is in sharp contrast to our observationsat low D fields (figure 1(d)), at electron doping(figures 2(e) and (f)), and in previous literature [13].The first feature at lowest n near the bandedge separates low and high conductance regimes(red arrows in figures 3(e) and (f)). In the low-conductance regime, the conductance sharplyincreases with increasing applied current IBias (sup-plementary figures S7(a) and (b)), indicating insulat-ing behavior, possibly arising from disorder [31, 32],Wigner crystallization [33], or more exotic phenom-ena, e.g. induced by exchange interaction betweenthe trigonal warping induced mini valleys [34–36].A detailed analysis of this regime, however, extendsbeyond the scope of this present study. This regimeis markedly different from that when WSe2 is absent,where a metallic phase had been observed at thevalence band edge [4].Another marked difference is in the higher dens-ity regime, where a cascade of correlated metallic andinsulating phases were found [4] in the absence ofSOC, whereas in the presence of SOC no clear signs ofphysics beyond SOC can be identified. These featurescan be associated with the SOC-induced band split-ting and the occupation of the second energy band(green arrow in figures 3(e) and (f)), exhibiting B∥-and B⊥-dependences similar to those observed at theelectron doped case with induced SOC (supplement-ary figures S8 and 3(f)).Additional phase boundaries (blue and grayarrows in figures 3(e) and (f)) emergewithin the spin-valley-locked bands, with the corresponding phasesshaded gray in the lower panel of figure 3(f) [11,12]. Since trigonal warping is more pronounced inthe valence band [30], these boundaries may sep-arate regions with a different Fermi surface topolo-gies, i.e. where the Fermi surface transitions frombeing three-fold degenerate to one-fold degenerate.Alternatively, they may mark the transition from apartially isospin-polarized to a fully isospin-polarizedregime. This interpretation is supported by theappearance of an additional fan with Landau levelsthat curve in the n-B⊥ space (see e.g. dashed linesin figure 3(f)) and has been attributed to a partiallyisospin-polarized regime with small minority Fermipockets [1, 2].With the exception of the phase at lowest n, theprevalence of mainly SOC-driven states is also sup-ported by the absence of non-linear dI/dV featureand the lack of strong temperature dependence (sup-plementary figures S7(a)–(c)). Finally, we note theabsence of any indication of superconductivity nearthese potential phase boundaries [11, 12]. This maybe attributed to constraints imposed by the applic-ation of higher D-fields due to elevated gate cur-rents and the use of thicker hBN dielectrics in therange of 37 nm to 62 nm compared to two previousstudies [11, 12].3. Transport inWSe2 proximitized BLG atoverall charge neutralityWhile at largeD fields and finite doping the correlatedphases are strongly suppressed when charge carriersare layer-polarized to the WSe2-BLG interface, thesituation is different at charge neutrality when there isno layer polarization (D= n= 0). The ground state ofundoped BLG has been intensively addressed by mul-tiple works [7, 37–41]; the strength of Coulomb inter-action plays a critical role. In the limit of strong inter-action, as experimentally realized in suspended BLG,an insulating layer antiferromagnetic (LAF) state hasbeen identified as the ground state [7, 37–41]. In theLAF state, two spin species spontaneously polarizeto opposite layers [22]. On the other hand, in hBNencapsulated BLG, interaction is weaker due to thelarger dielectric constant ∈ r and closer distance ofscreeningmetal gates (about 150 nm in the suspendedsamples and typically below 60 nm in hBN encapsu-lated samples), and the LAF state has not been found.Thus, one may wonder whether the ground state isstill correlated or non-interacting given the inducedSOC but the weakened Coulomb interaction.From our multi-scale theoretical investigation ofthe single-particle bands (figures 4(f) and (g)), con-sistent with previous reports, a SOC-split but overallgapless band structure is present. An interesting ques-tion now is whether the induced Ising SOC and themore screened interaction lead to a correlated insu-lating state like in the freestanding case or disfavorcorrelated states as in the case of large D fields dis-cussed above. Figure 4 shows our experimental obser-vations, and a region of suppressed conductance isevident at charge neutrality. This region is unstableagainst the application of doping or aD field of eithersign. These suggestmost likely the topologically trivialLAF state as in the freestanding case [7, 37–41], andwith increasing B⊥ the LAF state evolves into a can-ted antiferromagnetic (CAF) state (figure 4(c)) [42–44]. Furthermore, this state is not strongly affectedby the application of a B∥ field (figure 4(d)), con-sistent with two previous studies [41, 44]. In addi-tion, we observe insulating behavior, i.e. decreasingresistance with increasing temperature or increas-ing current (figure 4(e) and supplementary figureS9). The insulating state is stable below 5 K, and weextract an energy gap of 0.4 meV using Arrhenius62D Mater. 12 (2025) 035009 A M Seiler et alFigure 4. Correlated insulating state at D= n= B⊥ = 0 and multi-scale modeling. (a) Two-terminal conductance G in arbitraryunits (arb. units) as a function of D and n at zero magnetic field Bmeasured in a BLG—WSe2 heterostructure (Device I) at asample temperature of T = 10 mK. Line traces are shown for D= 0 and n= 0, respectively. (b) Non-interacting band structuresof bilayer graphene on top of WSe2 at different interlayer electric potentials. Green bands are spin polarized up, orange bands arespin polarized down. No band gap is open at V = 0. (c) G as a function of D and an out-of-plane magnetic field B⊥ at n= 0 andT = 10 mK. The layer antiferromagnetic (LAF), canted antiferromagnetic (CAF) and layer polarized (LP) states are labeled. (d) Gas a function of D and an in-plane magnetic field B∥ at n= 0, B⊥ = 0 and T = 10 mK. (e) Two-terminal resistance R as afunction of D for different temperatures. The inset shows the size of the activation gap∆, as determined via Arrhenius fits, as afunction of D. (f) Inverse density of states at Fermi level as a function of D for different temperatures calculated from aHartree-Fock theory for BLG/WSe2 heterostructure at zero level of doping. (g) Trend of the dependence of the correlated gap(direct gap) on the amplitude of the onsite Coulomb interaction U = U0 = 1.3 U1 for BLG and proximitized BLG/WSe2 systems.(h) Trend of the dependence of the long-range Coulomb interaction induced spontaneous gap (indirect gap) on the SOC strengthλI and the dielectric constant ε. The data presented in panels (a), (c)–(e)) was obtained using Device I.fits (see inset of figure 4(e) and supplementary figureS10). The respective stability of the LAF state in theD, B⊥, B∥ space is consistent with the observationsmade in freestanding graphene, i.e. both states areonly stable at low D and become suppressed at finiteD ≈ ±0.015 V nm−1 (figure 4(a) and supplement-ary figure S11(a)) and gradually evolve into a CAF atfinite B⊥ without apparent changes in the conduct-ance (figure 4(c) and supplementary figure S11(b)).Also the extracted activation gaps are of similar order(see supplementary figure S11(c) for a direct com-parison of the gaps). These experimental observa-tions also align with our self-consistent Hartree–Fock calculations addressing both short- and long-range interactions (see methods for details): open-ing a spontaneous gap in a BLG/WSe2 heterostructurerequires a smaller Coulomb interaction (figures 4(f)and (g)), and the larger the induced SOC the stronger72D Mater. 12 (2025) 035009 A M Seiler et althe spontaneous indirect gap opening (figure 4(h)).We thus believe that a larger activation gap can beachieved when maximizing the SOC, e.g. by minim-izing the twist angle between BLG and WSe2 [45, 46]or by replacing the WSe2 with WS2 [46].It is worth noting that SOC would introducesingle-particle gaps in WSe2/BLG heterostructures incase they are spin-polarized (figure 4(b)). In this case,the gap would, however, not symmetrically close atfinite values of D. Furthermore, the extracted energygap is approximately one order of magnitude lar-ger than these spin gaps (supplementary figure S17).Lastly, our observations are not only at odds with thesingle-particle band structure of our WSe2/BLG het-erostructure but also at odds with a previous study ofWSe2/BLG/WSe2 structures [15, 47], where symmet-rically induced Ising SOC results in a single-particleKane-Mele SOC gap that is suppressed by the applic-ation of a B∥ field [15, 47].4. ConclusionsIn summary, asymmetrically introducing WSe2 tohBN-encapsulated BLG devices provides a uniqueplatform for the distinct exploration of correlatedphases and SOC-induced states, respectively, in thepresence of large D fields, depending on the signsof n and D. Whereas a cascade of correlated phasesemerges, like those devices without WSe2, when thecharge carriers are polarized on the WSe2-remotelayer of BLG, clear signatures of SOC dominant bandsplitting have been identified allowing the furthermeasurement of a strong valley g-factor, as if theinteraction is nearly absent, when the charge carriersare polarized on theWSe2-proximate layer of BLG. Atzero D field for which the BLG is not layer-polarized,surprisingly, the interaction strength in BLG appearsto be enhanced by the induced SOC, giving rise toa correlated insulating state with both theoreticallyand experimentally anticipated features under B⊥,B∥, and D fields. Our results have established a richphase diagram of BLG, paving the way for explor-ing the interplay between geometry, interaction, andSOC in strongly correlated electrons.Data availability statementAll data supporting the messages of the manuscript isdisplayed in the manuscript. The raw data is availablefrom the authors upon request. The data that supportthe findings of this study are available upon reason-able request from the authors.AcknowledgmentsWe thank Michele Masseroni, Thomas Ihn, andKlaus Ensslin for fruitful discussions. R T W andA M S acknowledge funding from the DeutscheForschungsgemeinschaft (DFG, German ResearchFoundation) under the SFB 1073 project B10. R TW acknowledges partial funding from the SPP2244from the Deutsche Forschungsgemeinschaft (DFG,German Research Foundataion). K W and T Tacknowledge support from the JSPS KAKENHI(Grant Nos. 20H00354, 21H05233 and 23H02052)and World Premier International Research CenterInitiative (WPI), MEXT, Japan. K Z, Y Z and J F weresupported by the Deutsche Forschungsgemeinschaft(DFG, German Research Foundation) SFB 1277(Project No. 314695032), SPP 2244 (Project No.443416183), the European Union Horizon 2020Research and Innovation Program under ContractNo. 881603 (Graphene Flagship) and FLAGERA pro-ject 2DSOTECH. The theoretical work done at UTDallas was supported by NSF under Grants Nos.DMR-1945351, DMR-2105139, and DMR-2324033.We acknowledge the Texas Advanced ComputingCenter (TACC) for providing resources that have con-tributed to the research results reported in this work.Note from the authorsWhile analyzing the data we became aware of sim-ilar results presented in a manuscript by Masseroniet al [48]. It is remarkable that very similar data wasobtained by two different groups, using a differentTMD on bilayer graphene (WSe2 in Göttingen andMoS2 in Zurich).Author contributionsA.M.S. fabricated Device I and II with help of D.U.and conducted the measurements and data analysis.F.R.G fabricated and measured Device III. K.W. andT.T. grew the hexagonal boron nitride crystals. Y.Z,K.Z, C.Y., J.F. and F.Z. contributed to the theoreticalpart. All authors discussed and interpreted the data.R.T.W. supervised the experiments and the analysis.The manuscript was prepared by A.M.S., Y.Z., K.Z.,J.F., F.Z. and R.T.W. with input from all authors.Conflict of interestAuthors declare no competing interests.ORCID iDsAnna M Seiler https://orcid.org/0000-0002-9883-9220Klaus Zollner https://orcid.org/0000-0002-6239-3271David Urbaniak https://orcid.org/0009-0006-4561-1704Fabian R Geisenhof https://orcid.org/0000-0002-3623-1906Kenji Watanabe https://orcid.org/0000-0003-3701-8119R Thomas Weitz https://orcid.org/0000-0001-5404-73558https://orcid.org/0000-0002-9883-9220https://orcid.org/0000-0002-9883-9220https://orcid.org/0000-0002-9883-9220https://orcid.org/0000-0002-6239-3271https://orcid.org/0000-0002-6239-3271https://orcid.org/0000-0002-6239-3271https://orcid.org/0009-0006-4561-1704https://orcid.org/0009-0006-4561-1704https://orcid.org/0009-0006-4561-1704https://orcid.org/0000-0002-3623-1906https://orcid.org/0000-0002-3623-1906https://orcid.org/0000-0002-3623-1906https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0001-5404-7355https://orcid.org/0000-0001-5404-7355https://orcid.org/0000-0001-5404-73552D Mater. 12 (2025) 035009 A M Seiler et alReferences[1] Zhou H et al 2021 Half and quarter metals in rhombohedraltrilayer graphene Nature 598 429–33[2] Zhou H, Holleis L, Saito Y, Cohen L, Huynh W,Patterson C L, Yang F, Taniguchi T, Watanabe K andYoung A F 2022 Isospin magnetism and spin-polarizedsuperconductivity in Bernal bilayer graphene Science375 774–8[3] Zhou H, Xie T, Taniguchi T, Watanabe K and Young A F2021 Superconductivity in rhombohedral trilayer grapheneNature 598 434–8[4] Seiler A M, Geisenhof F R, Winterer F, Watanabe K,Taniguchi T, Xie T, Zhang F and Weitz R T 2022 Quantumcascade of correlated phases in trigonally warped bilayergraphene Nature 608 298–302[5] Seiler A M, Statz M, Weimer I, Jacobsen N, Watanabe K,Taniguchi T, Dong Z, Levitov L S and Weitz R T 2024Interaction-driven quasi-insulating ground states of gappedelectron-doped bilayer graphene Phys. Rev. Lett. 133 66301[6] Winterer F, Geisenhof F R, Fernandez N, Seiler A M, Zhang Fand Weitz R T 2024 Ferroelectric and spontaneous quantumHall states in intrinsic rhombohedral trilayer graphene Nat.Phys. 20 422–7[7] Geisenhof F R, Winterer F, Seiler A M, Lenz J, Xu T, Zhang Fand Weitz T R 2021 Quantum anomalous Hall octet drivenby orbital magnetism in bilayer graphene Nature 598 53–58[8] Han T, Lu Z, Scuri G, Sung J, Wang J, Han T, Watanabe K,Taniguchi T, Park H and Ju L 2023 Correlated insulator andChern insulators in pentalayer rhombohedral-stackedgraphene Nat. Nanotechnol. 91 181–7[9] Han T et al 2023 Orbital multiferroicity in pentalayerrhombohedral graphene Nature 623 41–47[10] de La Barrera S C, Aronson S, Zheng Z, Watanabe K,Taniguchi T, Ma Q, Jarillo-Herrero P and Ashoori R 2022Cascade of isospin phase transitions in Bernal-stackedbilayer graphene at zero magnetic field Nat. Phys. 18 771–5[11] Holleis L, Patterson C L, Zhang Y, Yoo H M, Zhou H,Taniguchi T, Watanabe K, Nadj-Perge S and Young A F 2023Ising superconductivity and nematicity in bernal bilayergraphene with strong spin orbit coupling (arXiv:2303.00742)[12] Zhang Y, Polski R, Thomson A, Lantagne-Hurtubise É,Lewandowski C, Zhou H, Watanabe K, Taniguchi T, Alicea Jand Nadj-Perge S 2023 Enhanced superconductivity inspin–orbit proximitized bilayer graphene Nature613 268–73[13] Xie M and Das Sarma S 2023 Flavor symmetry breaking inspin-orbit coupled bilayer graphene Phys. Rev. B107 L201119[14] Gmitra M and Fabian J 2015 Graphene on transition-metaldichalcogenides: a platform for proximity spin-orbit physicsand optospintronics Phys. Rev. B 92 155403[15] Island J O et al 2019 Spin-orbit-driven band inversion inbilayer graphene by the van der Waals proximity effectNature 571 85–89[16] Gmitra M and Fabian J 2017 Proximity effects in Bilayergraphene on monolayer WSe{2}: field-effect spin valleylocking, spin-orbit valve, and spin transistor Phys. Rev. Lett.119 146401[17] Wang D, Che S, Cao G, Lyu R, Watanabe K, Taniguchi T,Lau C N and Bockrath M 2019 Quantum Hall effectmeasurement of spin-orbit coupling strengths in ultracleanbilayer graphene/WSe2 heterostructures Nano Lett.19 7028–34[18] Wang Z, Ki D-K, Chen H, Berger H, MacDonald A H andMorpurgo A F 2015 Strong interface-induced spin-orbitinteraction in graphene on WS2 Nat. Commun. 6 8339[19] Patterson C L et al 2024 Superconductivity and spin cantingin spin-orbit proximitized rhombohedral trilayer graphene(arxiv:2408.10190)[20] Li C et al 2024 Tunable superconductivity in electron- andhole-doped Bernal bilayer graphene Nature 631 300–6[21] Koh J M, Thomson A, Alicea J and Lantagne-Hurtubise É2024 Symmetry-broken metallic orders inspin-orbit-coupled Bernal bilayer graphene Phys. Rev. B 110245118[22] Zhang F, Jung J, Fiete G A, Niu Q and MacDonald A H 2011Spontaneous quantum Hall states in chirally stackedfew-layer graphene systems Phys. Rev. Lett. 106 156801[23] Banszerus L, Möller S, Steiner C, Icking E, Trellenkamp S,Lentz F, Watanabe K, Taniguchi T, Volk C and Stampfer C2021 Spin-valley coupling in single-electron bilayergraphene quantum dots Nat. Commun. 12 5250[24] Möller S, Banszerus L, Knothe A, Valerius L, Hecker K,Icking E, Watanabe K, Taniguchi T, Volk C and Stampfer C2023 Impact of competing energy scales on the shell-fillingsequence in elliptic bilayer graphene quantum dots Phys.Rev. B 108 125128[25] Lee Y et al 2020 Tunable valley splitting due to topologicalorbital magnetic moment in bilayer graphene quantumpoint contacts Phys. Rev. Lett. 124 126802[26] Laturia A, van de Put M L and Vandenberghe W G 2018Dielectric properties of hexagonal boron nitride andtransition metal dichalcogenides: from monolayer to bulknpj 2D Mater. Appl. 2 6[27] Fatemi V and Ruhman J 2018 Synthesizing Coulombicsuperconductivity in van der Waals bilayers Phys. Rev. B98 94517[28] Stepanov P, Das I, Lu X, Fahimniya A, Watanabe K,Taniguchi T, Koppens F H L, Lischner J, Levitov L andEfetov D K 2020 Untying the insulating and superconductingorders in magic-angle graphene Nature 583 375–8[29] Chuang Y-W, Li J, Fu H, Watanabe K, Taniguchi T and Zhu J2019 Landau levels of bilayer graphene in a WSe2/bilayergraphene van der Waals heterostructure Phys. Rev. B100 195402[30] Seiler A M, Jacobsen N, Statz M, Fernandez N, Falorsi F,Watanabe K, Taniguchi T, Dong Z, Levitov L S and Weitz R T2024 Probing the tunable multi-cone band structure inBernal bilayer graphene Nat. Commun. 15 3133[31] Icking E et al 2022 Transport spectroscopy of ultracleantunable band gaps in bilayer graphene Adv. Electron. Mater.8 2200510[32] Li J, Tan L Z, Zou K, Stabile A A, Seiwell D J, Watanabe K,Taniguchi T, Louie S G and Zhu J 2016 Effective mass inbilayer graphene at low carrier densities: the role of potentialdisorder and electron-electron interaction Phys. Rev. B94 161406[33] Joy S and Skinner B 2023 Wigner crystallization in Bernalbilayer graphene (arXiv: 2310.07751)[34] Dong Z, Davydova M, Ogunnaike O and Levitov L 2023Isospin- and momentum-polarized orders in bilayergraphene Phys. Rev. B 107 075108[35] Lin J-X, Wang Y, Zhang N J, Watanabe K, Taniguchi T, Fu Land Li J I A 2023 Spontaneous momentum polarization anddiodicity in Bernal bilayer graphene (arXiv: 2302.04261)[36] Cheung P, Bao Z and Zhang F 2018 Flavor symmetry andferroelectric nematics in transition metal dichalcogenides(arxiv:1805.06493)[37] Freitag F, Trbovic J, Weiss M and Schönenberger C 2012Spontaneously gapped ground state in suspended bilayergraphene Phys. Rev. Lett. 108 76602[38] Geisenhof F R, Winterer F, Seiler A M, Lenz J, Zhang F andWeitz R T 2022 Impact of electric field disorder onbroken-symmetry states in ultraclean bilayer graphene NanoLett. 22 7378–85[39] Velasco J et al 2012 Transport spectroscopy ofsymmetry-broken insulating states in bilayer graphene Nat.Nanotechnol. 7 156–60[40] Weitz R T, Allen M T, Feldman B E, Martin J and Yacoby A2010 Broken-symmetry states in doubly gated suspendedbilayer graphene Science 330 812–6[41] Veligura A, van Elferen H J, Tombros N, Maan J C, Zeitler Uand van Wees B J 2012 Transport gap in suspended bilayergraphene at zero magnetic field Phys. Rev. B 85 1554129https://doi.org/10.1038/s41586-021-03938-whttps://doi.org/10.1038/s41586-021-03938-whttps://doi.org/10.1126/science.abm8386https://doi.org/10.1126/science.abm8386https://doi.org/10.1038/s41586-021-03926-0https://doi.org/10.1038/s41586-021-03926-0https://doi.org/10.1038/s41586-022-04937-1https://doi.org/10.1038/s41586-022-04937-1https://doi.org/10.1103/PhysRevLett.133.066301https://doi.org/10.1103/PhysRevLett.133.066301https://doi.org/10.1038/s41567-023-02327-6https://doi.org/10.1038/s41567-023-02327-6https://doi.org/10.1038/s41586-021-03849-whttps://doi.org/10.1038/s41586-021-03849-whttps://doi.org/10.1038/s41565-023-01520-1https://doi.org/10.1038/s41565-023-01520-1https://doi.org/10.1038/s41586-023-06572-whttps://doi.org/10.1038/s41586-023-06572-whttps://doi.org/10.1038/s41567-022-01616-whttps://doi.org/10.1038/s41567-022-01616-whttps://arxiv.org/abs/2303.00742https://doi.org/10.1038/s41586-022-05446-xhttps://doi.org/10.1038/s41586-022-05446-xhttps://doi.org/10.1103/PhysRevB.107.L201119https://doi.org/10.1103/PhysRevB.107.L201119https://doi.org/10.1103/PhysRevB.92.155403https://doi.org/10.1103/PhysRevB.92.155403https://doi.org/10.1038/s41586-019-1304-2https://doi.org/10.1038/s41586-019-1304-2https://doi.org/10.1103/PhysRevLett.119.146401https://doi.org/10.1103/PhysRevLett.119.146401https://doi.org/10.1021/acs.nanolett.9b02445https://doi.org/10.1021/acs.nanolett.9b02445https://doi.org/10.1038/ncomms9339https://doi.org/10.1038/ncomms9339https://arxiv.org/abs/2408.10190https://doi.org/10.1038/s41586-024-07584-whttps://doi.org/10.1038/s41586-024-07584-whttps://doi.org/10.1103/PhysRevB.110.245118https://doi.org/10.1103/PhysRevB.110.245118https://doi.org/10.1103/PhysRevLett.106.156801https://doi.org/10.1103/PhysRevLett.106.156801https://doi.org/10.1038/s41467-021-25498-3https://doi.org/10.1038/s41467-021-25498-3https://doi.org/10.1103/PhysRevB.108.125128https://doi.org/10.1103/PhysRevB.108.125128https://doi.org/10.1103/PhysRevLett.124.126802https://doi.org/10.1103/PhysRevLett.124.126802https://doi.org/10.1038/s41699-018-0050-xhttps://doi.org/10.1038/s41699-018-0050-xhttps://doi.org/10.1103/PhysRevB.98.094517https://doi.org/10.1103/PhysRevB.98.094517https://doi.org/10.1038/s41586-020-2459-6https://doi.org/10.1038/s41586-020-2459-6https://doi.org/10.1103/PhysRevB.100.195402https://doi.org/10.1103/PhysRevB.100.195402https://doi.org/10.1038/s41467-024-47342-0https://doi.org/10.1038/s41467-024-47342-0https://doi.org/10.1002/aelm.202200510https://doi.org/10.1002/aelm.202200510https://doi.org/10.1103/PhysRevB.94.161406https://doi.org/10.1103/PhysRevB.94.161406https://arxiv.org/abs/%25202310.07751https://doi.org/10.1103/PhysRevB.107.075108https://doi.org/10.1103/PhysRevB.107.075108https://arxiv.org/abs/%25202302.04261https://arxiv.org/abs/1805.06493https://doi.org/10.1103/PhysRevLett.108.076602https://doi.org/10.1103/PhysRevLett.108.076602https://doi.org/10.1021/acs.nanolett.2c02119https://doi.org/10.1021/acs.nanolett.2c02119https://doi.org/10.1038/nnano.2011.251https://doi.org/10.1038/nnano.2011.251https://doi.org/10.1126/science.1194988https://doi.org/10.1126/science.1194988https://doi.org/10.1103/PhysRevB.85.155412https://doi.org/10.1103/PhysRevB.85.1554122D Mater. 12 (2025) 035009 A M Seiler et al[42] Maher P, Dean C R, Young A F, Taniguchi T, Watanabe K,Shepard K L, Hone J and Kim P 2013 Evidence for a spinphase transition at charge neutrality in bilayer graphene Nat.Phys. 9 154–8[43] Kharitonov M 2012 Canted antiferromagnetic phase of theν=0 quantum Hall state in bilayer graphene Phys. Rev. Lett.109 46803[44] Zhang F and MacDonald A H 2012 Distinguishingspontaneous quantum Hall states in bilayer graphene Phys.Rev. Lett. 108 186804[45] Zhang Y et al 2024 Twist-programmable superconductivityin spin-orbit coupled bilayer graphene (arxiv:2408.10335)[46] Li Y and Koshino M 2019 Twist-angle dependence of theproximity spin-orbit coupling in graphene ontransition-metal dichalcogenides Phys. Rev. B 99 75438[47] Kedves M et al 2023 Stabilizing the inverted phase of aWSe2/BLG/WSe2 heterostructure via hydrostatic pressureNano Lett. 23 9508–14[48] Masseroni M et al 2024 Spin-orbit proximity in MoS2/bilayergraphene heterostructures Nat. Commun. 15 925110https://doi.org/10.1038/nphys2528https://doi.org/10.1038/nphys2528https://doi.org/10.1103/PhysRevLett.109.046803https://doi.org/10.1103/PhysRevLett.109.046803https://doi.org/10.1103/PhysRevLett.108.186804https://doi.org/10.1103/PhysRevLett.108.186804https://arxiv.org/abs/2408.10335https://doi.org/10.1103/PhysRevB.99.075438https://doi.org/10.1103/PhysRevB.99.075438https://doi.org/10.1021/acs.nanolett.3c03029https://doi.org/10.1021/acs.nanolett.3c03029https://doi.org/10.1038/s41467-024-53324-zhttps://doi.org/10.1038/s41467-024-53324-z Layer-selective spin-orbit coupling and strong correlation in bilayer graphene 1. Main 2. Correlated phases in the vicinity of tunable van-Hove singularities 3. Transport in WSe2 proximitized BLG at overall charge neutrality 4. Conclusions References