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Qingxin Li, Yiwei Chen, LingNan Wei, Hong Chen, Yan Huang, Yujian Zhu, Wang Zhu, Dongdong An, Junwei Song, Qikang Gan, Qi Zhang, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Xiaoyang Shi, Kostya S. Novoselov, Rui Wang, Geliang Yu, Lei Wang

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[Strongly coupled magneto-exciton condensates in large-angle twisted double bilayer graphene](https://mdr.nims.go.jp/datasets/4c6cc3a5-8195-4c15-8abb-293c06928aae)

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Strongly coupled magneto-exciton condensates in large-angle twisted double bilayer grapheneArticle https://doi.org/10.1038/s41467-024-49406-7Strongly coupled magneto-excitoncondensates in large-angle twisted doublebilayer grapheneQingxin Li1,6, YiweiChen1,6, LingNanWei1,6,HongChen1,6, YanHuang1, YujianZhu1,Wang Zhu1, Dongdong An1, Junwei Song1, Qikang Gan1, Qi Zhang1,Kenji Watanabe 2, Takashi Taniguchi 3, Xiaoyang Shi4 ,Kostya S. Novoselov 5, Rui Wang1 , Geliang Yu 1 & Lei Wang 1Excitons, pairs of electrons and holes, undergo a Bose-Einstein condensationat low temperatures. An important platform to study excitons is double-layertwo-dimensional electron gases, with two parallel planes of electrons andholes separated by a thin insulating layer. Lowering this separation (d)strengthens the exciton binding energy, however, leads to the undesiredinterlayer tunneling, resulting in annihilation of excitons. Here, we report theobservation of a sequences of robust exciton condensates (ECs) in doublebilayer graphene twisted to ~ 10° with no insulating mid-layer. The largemomentum mismatch between two graphene layers suppresses interlayertunneling, reaching a d ~ 0.334 nm.Measuring the bulk and edge transport, wefind incompressible states corresponding to ECs when both layers are in half-filledN = 0, 1 Landau levels (LLs). Theoretical calculations suggest that the low-energy charged excitation of ECs can be meron-antimeron or particle-holepair, which relies on both LL index and carrier type. Our results establish anovel platform with extreme coupling strength for studying quantumbosonic phase.An EC is a Bose-Einstein condensate formed when a large number ofelectron-hole pairs occupy the ground state with macroscopic phasecoherence1. In bulkmaterials, condensed excitons can be generated byoptical pumping but with short lifetimes2. In small-bandgap semi-conductors and semimetals, ECs are predicted to live for longer timewhereby exciton binding energy exceeds the charge gap3. But thestructural character of spontaneous symmetry breaking in these solid-state systems may hamper the possibility to realize superfluidity4,5.Double-layer system subject to finite magnetic field is shown asimpressive platform for exciton condensation6,7. As the recombinationis blocked by midlayer insulator, electron-like carriers in a partiallyfilled LL in one layer couple with hole-like carriers in the other, forminginterlayer magneto-excitons, which then experience a Bose-Einsteincondensation to a coherent superfluid ground state8–11.The energy of the magneto-excitons is determined by the ratio ofintralayer and the interlayer Coulomb interaction: Eintra/Einter ~ d/lB,where lB =ffiffiffiffiffiffiffiffiffiffi_=eBpis the magnetic length, ℏ is the reduced Planckconstant, e is the electron charge, and B is magnetic field. An attractivecharacteristic of such quantum hall bilayer structure is that d/lB can betuned by B and d, providing an opportunity to adjust the electron-holeReceived: 20 December 2023Accepted: 31 May 2024Check for updates1National Laboratory of Solid-StateMicrostructures, School of Physics, NanjingUniversity, Nanjing 210093,China. 2ResearchCenter for Electronic andOpticalMaterials, National Institute forMaterials Science, 1-1 Namiki, Tsukuba305-0044, Japan. 3ResearchCenter forMaterials Nanoarchitectonics, National Institutefor Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 4Environmental and Sustainable Engineering, College of Engineering and Applied Science,University at Albany, Albany, NY 12222, USA. 5Institute for Functional Intelligent Materials, National University of Singapore, Building S9, 4 Science Drive 2,Singapore 117544, Singapore. 6These authors contributed equally: Qingxin Li, Yiwei Chen, LingNan Wei, Hong Chen. e-mail: xshi7@albany.edu;rwang89@nju.edu.cn; yugeliang@nju.edu.cn; leiwang@nju.edu.cnNature Communications |         (2024) 15:5065 11234567890():,;1234567890():,;http://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/0000-0003-4972-5371http://orcid.org/0000-0003-4972-5371http://orcid.org/0000-0003-4972-5371http://orcid.org/0000-0003-4972-5371http://orcid.org/0000-0003-4972-5371http://orcid.org/0000-0002-0169-7781http://orcid.org/0000-0002-0169-7781http://orcid.org/0000-0002-0169-7781http://orcid.org/0000-0002-0169-7781http://orcid.org/0000-0002-0169-7781http://orcid.org/0000-0002-1919-9107http://orcid.org/0000-0002-1919-9107http://orcid.org/0000-0002-1919-9107http://orcid.org/0000-0002-1919-9107http://orcid.org/0000-0002-1919-9107http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-49406-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-49406-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-49406-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-49406-7&domain=pdfmailto:xshi7@albany.edumailto:rwang89@nju.edu.cnmailto:yugeliang@nju.edu.cnmailto:leiwang@nju.edu.cncoupling strength and the average distance between excitons. In thisway, it facilitates exploring quantum condensate phase changes inbosonic system, e.g., the crossover of weak-coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a strong-coupling Bose-Einstein condensa-tion pairing12 and the transition of superfluid coherent phase totranslational symmetry breaking supersolid coherent phase13. How-ever, the intriguing region with extremely strong coupling, whichneeds tiny d/lB remains elusive due to the difficulty in achievingextremely small d without raising interlayer tunneling.Recently, progress on reducing the d down to subnanometer hasbeen made in natural bilayer WSe2, where interlayer tunneling wasavoided by the intrinsic spin-valley structure14. However, the unipolarnature of such semiconductor system limits the observation ofmagneto-excitons only on the hole side. Another candidate reachingsucha smalld is the large-angle twistedgraphene system,where a largemomentum mismatch between different sheets suppresses the inter-layer tunneling15, making it possible to realize ECs in the strong cou-pling limit with layerswidely covering both the electron andhole sides.Although recent studies have shown some plausible traces of ECs insuch twisted bilayers by observing quantumHall states(QHSs) at someincomplete odd-integer total fillings limited on one carrier side16,17, dueto contact quality issues and disorders16, the sequence of ECs is yet tobe observed.Here, we reported the observation of a complete sequence of ECsemerging at both electron and hole fillings with extremely strongcoupling strength in high-quality large twisted angle twisted doublebilayer graphene(TDBG) devices (Fig. 1a). At finite magnetic field, theinterlayer tunneling gap due to spatial wave functions overlap in twobilayers can be negligible(10−10meV) based on our numerical calcula-tion(see Supplementary Note 3). By measuring the bulk and edgetransport properties, we unambiguously identified these robust ECswhich appear at the half-filled N = 0 and N = 1 LL. Thermally activatedmeasurements combined with theoretical models indicate that thelow-energy charged excitation of ECs is topologically nontrivial spin-texture in N = 0 LL18, whereas for N = 1 LL, it changes from such spin-texture on the hole side to particle-hole pair on the electron side.ResultsWe fabricated high-quality TDBG devices with ‘cut and pick-up’transfer method19,20 by picking up and twisting two pieces of bilayergraphene, cut from a single flake, to an angle about 10∘. (see in Meth-ods). Depicted in Fig. 1b, the structure of the device, which containstop and bottom graphite gates with voltages VT and VB, allows us toindependently tune carrier density: n = (CBVB +CTVT)/e, and displace-ment field: D = (CBVB −CTVT)/2, where CT(CB) is top(bottom) gatecapacitance and e is the elementary charge. Figure 1c shows thelongitudinal resistance Rxx as a function of n and D in the absence of amagnetic field. A high resistance state appearing around zero values ofn and D suggests the presence of crystal fields15, which occurs due tothe imbalanceof electronoccupancybetween the outer two layers andinner ones. Upon increasing the displacement field, the high resistancestate evolves into two splitting resistive traces, dividing the diagramfor D >0 into five regions (Fig. 1d), which correspond to the differentcarrier population configurations in the two bilayers. In region I and V,both bilayers are simultaneously populated by either holes or elec-trons, respectively; in region II and IV, one of the bilayers is gappedwhile the other is filled; in region III, the two bilayers are populated byopposite carrier types, and the system contains a mixture of holes andelectrons. This layer-selective population behavior evidences the twobilayers in our large-angle TDBG are decoupled, allowing the top andbottom gates to control them separately21,22.(Supplementary Note 1).Next, we investigate the behavior of the system under magneticfields. Figure 1f plots the Rxx versus the D and total filling factor νtot atB = 14 T, where νtot = νT + νB, and νT, νB are the LL filling fractions of theabdfEKcexcitonbottom bilayertop bilayer 100 1 0 0 1 1N-2-3-4 -1 1 2 3 4νD(V/nm)n (x 1012 cm-2)D(V/nm)νtotgE (meV)D (V/nm)-8 -4 0 4 8-0.6-0.300.30.6102104T=1.5KRxx(Ω)B=0TeT=1.5KB=14T101104Rxx(Ω)+ TD=0+ B+ T - T- T+ + --+ B- B- BLayer polarizationBNGraphiteBNGraphite -40040-100 0 100D(V/nm)E(meV)4x48x8-10 0 10 20-20-0.6-0.4-0.200.20.40.6e-h+htop+hbottom etop+ebottomhbottomebottomhtopetophbottom+etophtop+ebottomFig. 1 | Large-angle TDBG Landau level structure and decoupled carrier popu-lation. a Illustration of magneto-excitons in TDBG. The interlayer tunneling issuppressed by large momentum mismatch, and at finite magnetic field, stronginteraction induces electron-like carriers in a half-filledLL in one layer couplingwithhole-like carriers in the other, forming interlayermagneto-excitons. b Schematic ofthe TDBG device structure. c–d Longitudinal resistance Rxx of TDBG at B = 0 T andT = 1.5 K, versus n and D. The map exhibits the different population of chargecarriers in two bilayers and the ‘layer-targeted’ population divides the diagram intodifferent regions highlighted in d. e Calculated LL spectra as a function of energyE and D at B = 14 T. Inset: Zooming-in on the LL crossings in the 8 × 8 matrix (top)(accidental degeneracy for N = 0 and 1) and a typical 4 × 4(bottom) matrix (for N ≥2), respectively. f Longitudinal resistanceRxxof TDBGatB = 14T andT= 1.5 K, versusνtot and D. White dashed line marks the four QHSs stabilized by the spin and valleydegeneracy lifting at D = 0 V/nm in non-zero LL. g Schematic illustration of LLcrossings driven by displacement field under a constant magnetic field. ‘T’: topbilayer; ‘B’: bottom bilayer.Article https://doi.org/10.1038/s41467-024-49406-7Nature Communications |         (2024) 15:5065 2top and bottom bilayer respectively. In bilayer graphene(BLG), thezero-energy LL(ZLL) has eight-fold degeneracy (spin, valley, and acci-dental orbital degeneracy N = 1, N = 0), and higher LLs have four-folddegeneracy23. As for our system consisting of two decoupled bilayergraphene layers, LLs have an extra two-fold degeneracy correspondingto ‘top layer’ and ‘bottom layer’ regulated by D. At B =14 T, thesedegeneracies are fully lifted, showing a sequence of QHSs at all integerfillings as resistance minima lines paralleling to the n = 0 line. Strik-ingly, we observed some repeated ‘4 × 4’ matrices (for ∣νtot ∣>8) and aunique ‘8 × 8’ matrix (for − 8 < νtot < 8). These matrices can be qualita-tively understood using the single-particle picture of LL crossings asillustrated in Fig. 1e and g. In a ‘4 × 4’ matrix, along the white dashedline (Fig. 1f) at D = 0, four QHSs at even total fillings stabilized by thespin and valley degeneracy lifting. As ∣D∣ increases, the layer degen-eracy is lifted and each of these four LLs splits into two, subsequentlyintersect with their neighbors, forming a series of crossing points(marked by yellow circles in Fig. 1g). At these crossing points, thedouble bilayer system is gapless since both bilayers are in partiallyfilled LLs (more details in Supplementary Note 2).Now we move on to look into the ‘8 × 8’ matrix centered at thecharge neutrality point. In Fig. 2a we plot longitudinal conductance σxxversusD and νtot for − 9 < νtot < 9. A clear ‘8 × 8’ structural patternwith aforming mechanism analogous to the ‘4 × 4’ matrices is displayed,which corresponds to crossings of the quantum Hall octet from twodecoupled bilayers(schematically illustrated in Fig. 2c). Unexpectedly,focusing on D =0V/nm, we notice a series of exceptional crossingpoints at νtot = − 7, − 3, − 1, 1, 3 and 5(red dotted circles in Fig. 2a and c)manifesting as anomalous states with quantized Hall conductivity andvanishing longitudinal conductivity, which is drastic contrast to thefinite conductivity in those normal LL crossings.(see SupplementaryFig. 4). Besides, for D ≠0, a few similar anomalous states also developwith the reduced longitudinal conductivity marked by orange dottedcircles in Fig. 2a. These anomalous states are inadequate to beunderstood from the single-particle LL crossings picture, where thesystem should show a finite conductivity as both bilayer LLs arehalf-filled.In order to investigate the origin of the vanishing of σxx at thesecrossing points, we further measure the bulk transport properties ofthese anomalous states using the configuration shown in Fig. 2b inset24.Figure 2bmaps the bulk resistance Rxx−Bulk as a function of νtot andD onthe same ‘8 × 8’ matrix. Along D = 0 V/nm, each anomalous statemanifests a high Rxx−Bulk peak, while other LL crossings show Rxx−Bulkdips. Based on these two different patterns of Rxx−Bulk at the crossingpoints, we group them into three categories as shown in Fig. 2d, e, f. Inthe top panels, the center of these Rxx−Bulk(νtot,D) maps corresponds toboth bilayers are half-filled and we take linecuts at the crossing pointsa bd e fcνB-3-2-10123νT3210-1-2-3104 105Rxx-Bulk(Ω)10-6 10-4σxx(e2/h)D(V/nm)-8 -4 0 4 8-0.3-0.2-0.100.10.20.3D(V/nm)-8 -4 0 4 8νtotT=1.5KB=14TT=1.5KB=14T-5 -3 3 5-7 -1 1 7D(1,2)(0,3)(2,1)(3,0)(-2,-1)(-3,0)(-1,-2)(0,-3)~AVxxVxx~A-0.3-0.2-0.100.10.20.3104 105Rxx-Bulk(Ω)1.5 2 2.5 3 3.5 4 4.54.550.40.25.50D(mV/nm)log(Rxx)(Ω)σ xx(e2 /h)(-1/2,7/2)Bulk Edge -140-120-100104.5 105Rxx-Bulk(Ω)1.5 2 2.5 3 3.5 4 4.540200-20-404.64.80.10.05D(mV/nm)log(Rxx)(Ω)σ xx(e2 /h)(3/2,3/2)Bulk Edge 40200-20-404.34.40.150.05D(mV/nm)log(Rxx)(Ω)σ xx(e2 /h)5.5 6 6.5 7 7.5 8 8.5(7/2,7/2)Bulk Edge 104.2 104.5Rxx-Bulk(Ω)νtot νtotνtot νtot νtotFig. 2 | ECs in the zero-energy Landau level matrix. a, b The longitudinal con-ductance σxx (a) and bulk resistance Rxx−Bulk (b) versus D and νtot at B = 14 T and T =1.5 K for − 9 < νtot < 9. Dotted red circles(a) and orange circlesmark the LL crossingsmanifesting as anomalous conductivity minimum states at D = 0 and D ≠0,respectively. The insets show themeasurement configurations. TomeasureRxx−Bulk,two contacts are grounded to make sure the signal comes from the bulk instead ofedge resistance of the sample. c, Schematic LL diagram for − 8 < νtot < 8. These LLcrossings originate from the cross of zero-energy LLs octet of two decoupledbilayerswhich aremarkedby different colours. Yellow shadesmark two typical IQHregions with the filling factor marked as (νT,νB). d–f Top panel displays enlargeimages of Rxx−Bulk versus νtot and D at B = 14 T around the three categories LLcrossings illustrated in maintext. In each bottom panel, the black curve is the bulkresistance linecut along the red dashed line in the top panel, while the blue curve isthe longitudinal conductance linecut in a. The yellow, red, and orange arrows pointto normal LL crossings, ECs, and less-developed ECs, respectively.Article https://doi.org/10.1038/s41467-024-49406-7Nature Communications |         (2024) 15:5065 3showing Rxx−Bulk vs. νtot in the bottom panels. For normal crossingpoints (Fig. 2d), the resistance dip in Rxx−Bulk linecut manifests that thesystem is compressible at these states. This confirms the single-particleLL crossings picture, meanwhile, also indicates the tunneling is negli-gible between two bilayers otherwise a LL anti-crossing gap would beinduced by tunneling25,26. On the contrary, for the anomalous crossingpoints alongD = 0 (Fig. 2e), the prominent resistive peak demonstratesthe state is incompressible, which is beyond the picture of single-particle LL crossing. Given that the tunneling is negligible here, thisphenomenon implies the emergence of a correlation energy gap due tomany-body interactions. When both bilayers are half-filled, interlayerinteractions prompt electrons in one bilayer and holes in the other toform magneto-excitons10,11 and condense into an incompressiblesuperfluid: exciton condensate. Besides, it’s worth pointing out that thecrossing points for D ≠0 (Fig. 2f) show comparatively weaker bulk-resistance peak compared to those alongD = 0. This is presumably dueto the imbalanced occupancy of LL orbitals of top and bottombilayers13,27 or slight spatial wave functions overlap in two bilayersinduced by finite D.To characterize the ECs, we examined the excitation energy gapat all odd-integer filling for − 8 < νtot < 8 with thermal activationmeasurements. Figure 3a shows the temperature dependence of bulkresistance (Rxx−Bulk) as a function of νtot atD = 0 V/nm forB = 14 T. TheEC gap (Δ) shows an unexpected hierarchy and manifests as a non-monotonic behavior with νtot (Fig. 3c). Remarkably, all ECs appearin − 4 < νtot≤4 hold obviously larger gap value than those appear inother odd-integer fillings. In BLG, orbital character of the ZLL hasbeenmappedout as the functionof filling factors and electric fields27,and the holes or electrons are fully polarized in a single orbitalcomponent (N = 0 or 1) covering the whole of accessible parameterspace. Based on this picture, we displayed the distribution of orbitalindex of these two decoupled bilayers with filling factors understrong magnetic field in Fig. 3b. Near D ≈0, LLs of both bilayers withunambiguous orbital index cross with each other, giving rise to thefilling sequence of orbital index throughout − 8 ≤ νtot≤ 8 as: − 4 < νtot≤0, 4 ≤ νtot ≤ 8 corresponds toN = 1 LL and − 8 ≤ νtot < − 4, 0 ≤ νtot < 4 arein accord with N = 0 LL. As a result, we find that the EC robustness istightly associated with LL index and carrier type(electron-holeasymmetry), specifically, ECs appearing within the N = 1 orbital ofhole side aremore stable than those within theN = 0 orbital, whereasit is opposite on the electron side.The orbital wavefunction plays an important role for formation ofcorrelated states. For example, in BLG, compared to the conventionalN =0 orbital with sharper composite-fermion interactions, the N = 1orbital has softer interactionswhich are beneficial for pairing due to anadditional node in the single-particle wavefunction28, and that lead tothe observation of the even-denominator fractional QHSs exclusivelywithin LL N = 1, not N =0.29–32. For our system consisting of twodecoupled bilayers, different orbitals may host distinct low-energyexcitations, which affects the robustness of ECs. This influence can bebetter understood by taking pseudospin magnetism picture intoconsideration in which pseudospin up (down) corresponds to anelectron or a hole in the upper(lower) bilayer, and spontaneous-interlayer-coherence broken symmetry occurs as easy-plane pseudo-ferromagnetism18. In this case, considering the finite interlayer spacingd, topologically stable charged vortices known as meron canemerge.18,33 Then the merons and anti-merons pairing, leads to thetopologically nontrivial spin configurations known as skyrmions.Theoretical works have suggested that the energy of this excitationincreases with orbital index n34. The meron-antimeron spin-texture isnot the sole low-energy excitation in the double-layer system. Withincreasing of LL orbital index, conventional particle-hole pairs mayhost lower energy due to shorter-ranged interactions causedby excessive screening, and overtakes meron-antimeron pairs. Arecent study suggests that in p-type bilayer WSe2 the spin-texturecharged excitation onlyoccurs in LLsn ≤ 214, while higher Landau levelshost the particle-hole excitation whose energy decreases with orbitalindex n.In our TDBG system, theoretical calculations suggest that the low-energy charged excitation of ECs is not only related to LL index butalso associated with carrier doping type. Figure 3d shows the theore-tical calculation of the Δ −N(LL index) dependence of these two dif-ferent charged excitations. It reveals that the spin-texture chargedexcitations for ECs are favoured in the lower LLs on both electron andhole sides, and switch to particle-hole type at higher LL index. How-ever, the transition points between two types of charged excitationsare different on the electron and hole sides, with the EC-gapmaximumoccurring between N = 1 and N = 2 for hole side and near N = 0 forelectron side. This discrepancy can be well understood by consideringthe different screening strength between the hole and electron sides.Being in ZLL of TDBG at D =0, with the total filling increasing, carrierspopulate QHSs with different spin-valley flavour from νtot = − 8 to 8sequentially. At the same time, increasing particle density strengthensthe screening, driving a shorter-ranged interaction. This, in turn,reduces the excitation energy of particle-hole pair originating fromexchange interactions, whereas leaving the spin-texture excitationenergy unaffected. This theoretical result well agrees with ourobserved EC-gap trend. On the hole side, ECs in N = 1 and N = 0hold spin-texture excitations, thereby excitation energies mono-tonically increase with the LL index. Meanwhile, on the electron side,ECs in N = 1 with reduced particle-hole pair excitation energy, havesmaller gaps compared to the ECs in N = 0 with spin-textureexcitations.The evolution of the bulk resistance with D provides furtherinsight into the identification of the two types of charged excitation.Figure 3e plots the bulk resistance as a function of D for ECs at νtot=1and 5, corresponding to spin-texture and particle-hole excitation type,respectively. The red curve regions around D =0 mark EC regime, andthe system transition into integer quantum hall(IQH) phase(greycurve) with the increasing of D. Previous numerical study find that theexcitation energy of meron-antimeron pairs show a sharp increase ingap with layer imbalance, while particle-hole excitation energy isindependent of the layer imbalance until the zeeman energy exceedsthe EC gap35. In our system, layer imbalance is regulated by D. In thisscenario, we find a sharp Rxx−Bulk decrease with D in red curve regionfor νtot = 1 whereas at νtot = 5, Rxx−Bulk hold a mild response withD (Fig. 3e). This suggests that ECs on electron side in N = 0 LL host thespin-texture charged excitation while ECs in N = 1 LL have a particle-hole excitation(At νtot= 1 in N = 0 LL, red curve corresponding tomeron-antimeron-type ECs with lager slope than gray curve corre-sponding to IQH, and At νtot= 1 in N = 1 LL, red curve corresponding toparticle-hole-type ECs with smaller slope than gray curve corre-sponding to IQH.). On the other hand, on the hole side, ECs in bothN =0 and 1 exhibit sharp Rxx−Bulk changes, corresponding a spin-texturecharged excitation(Supplementary Fig. 8). This result is consistentwith our theoretical calculation that the low-energy charged excitationof ECs is different on electron and hole sides.Finally, to fully identify the nature of ECs, we demonstrate theevolution of ECs withmagnetic field. Figure 4a shows B dependence ofRxx−Bulk for all the ECs at D = 0 V/nm. The Rxx−Bulk of all ECs decreaseswith diminishing of B indicating that our system is in strong couplingregime. In this regime, the main effect of increasing the magnetic fieldis to raise the excitons density(∝ B), rather than increasing thed/lB(/ffiffiffiBp) to soften the exciton pairing strength, which is preferred inweak coupling system12. We further find that all ECs gaps are positivelycorrelatedwithmagneticfield andwellfit byΔ= Ec/Ec(14T) (reddashedline in Fig. 4b) which is in line with our numerical calculations (Sup-plementary Note 4). Both of the particle-hole and the spin-textureexcitation energies are related to stiffness (ρs ~ 1/lB), causing the exci-tation energy is proportional to the Coulomb energy (Ec = e2/lB)Article https://doi.org/10.1038/s41467-024-49406-7Nature Communications |         (2024) 15:5065 4(Supplementary Note 4). Furthermore, it is worth noting that the N = 1orbital in BLG differs from conventional n = 1 orbital. In BLG, N = 1orbital contains a combination of both conventional LL orbital n = 0and n = 1 wavefunctions distributed on different atomic sites of BLG,with the relative weight of n = 0 wavefunction increasing with B31,32.Hence, under higher magnetic fields beyond our experiments (aboutB > 25 T)31,32, the extensive participation of n = 0 wavefunction in BLGN = 1 orbital renders ECs in decoupledbilayers prone to hold excitationenergy deviating from the trend of Ec.DiscussionIn summary, we have experimentally observed remarkable magneto-excitons and their EC phase in ZLL region of large-angle twisted TDBG.Interlayer tunneling is suppressed by large momentummismatch, andwe demonstrate the ECs in the strong coupling limit with sub-nanometer atomic separation between the two bilayers. The differentcarrier screening strengths in electron and hole sides lead to distinctstability of ECs in both carrier types, and the evolution of ECs with LLindex unveiled a change of the low-energy charged excitation fromFig. 3 | Energy gap of ECs and the low-energy charged excitations.a Temperature dependence of Rxx−Bulk as a function of νtot atD = 0 V/nm and B = 14T. Red dotted lines mark the ECs corresponding to both bilayers are half-filled.b Evolution of orbital occupancy(N =0, N = 1) with total filling factors in decoupledTDBG. c Excitation energy gaps of ECs at B = 14T andD = 0 V/nm. Purple rectanglescorrespond to ECswith the spin-texture charged excitation and the green rectanglecorresponds to EC with the particle-hole charged excitation. d Theoretical calcu-lations of energy gap for two types of excitations on hole and electron sides, at d/lB= 0.1 andD = 0 V/nm. Owing to the distinct electron and hole environments, we usethe parameter ‘w’ to quantify the strength of screening effects. Since the screeningeffect of carriers is weak when filling the zero-energy Landau level starting fromhole side, we take wh =0.1. Conversely, the screening effect is already significantwhen carriers fill the electron side, so we take the average screening effect for theelectron side aswe = 1.2. The spin-texture excitation energy increases with LL indexwhile particle-hole excitation energy decreases with LL index. Their crossing pointsfor hole and electron sides appear at different positions of LL index due to thescreening strength increasingwith totalfilling. Thefilledmarkers represent the low-energy excitations of ECs. e Rxx−Bulk as a function of D for the ECs at νtot= 1, 5, whichcorrespond to N =0 and 1 LL, respectively. Red curve regions mark ECs and greycurves correspond to IQH regime. At νtot= 1 in N = 0 LL, red curve corresponding tomeron-antimeron-type ECs with lager slope than gray curve corresponding to IQH,and At νtot= 1 in N = 1 LL, red curve corresponding to particle-hole-type ECs withsmaller slope thangray curve corresponding to IQH. (The rate of change of the bulkresistance with the displacement field near D =0 (the magnitude of the slope)determines the phase boundaries of different phases).Article https://doi.org/10.1038/s41467-024-49406-7Nature Communications |         (2024) 15:5065 5meron-antimeron pair to particle-hole pair on different carrier dopingtypes. The variations in pairing behavior concerning magnetic field,doping, and temperature are summarized in Fig. 4c.Using electrostaticgating, thus we achieved unprecedentedlymodulating the topology oflow-energy charged excitation of ECs, providing further opportunitieson application of skyrmion-type devices in magnetic data storage andtopological quantum computing. Moreover, the signature of incom-pressible states in finite displacement field may lead to an unconven-tional route to explore non-equilibriumECs36 ormulti-polar excitonic37physics.MethodsSample fabrication and measurement setupThe three devices (device A ~ C) in our textwere all fabricated using the‘cut-and-stack’ technique19. The raw materials for the preparation ofeach device, hexagonal boron nitride(hBN)(about 30nm), graphiteand bilayer graphene are obtained frommechanically exfoliation ontoSi/SiO2 substrate. Their thickness and quality were then identified byoptical microscopy and atomic force microscopy. Before stacking, wefirst cut the bilayer graphene into two pieces using atomic forcemicroscopy. Then we used hBN, grphite and precut bilayer graphenepieces to assembled the graphite/BN/TDBG/BN/grphite stackusingdrypick-up technique with a stamp consisting of polypropylene carbo-nate(PPC) film and polydimethylsiloxane(PDMS). Using graphite as thegate above and below the TDBG reduces the disorder and defectsintroduced during evaporation compared to metal gates. The stack isthen annealed under high vacuum at 400 °C for 25 minutes. Next wedefined the geometry of the topgate and hall bar by CHF3/O2 etching.Finally, electrode contact was evaporated with Cr/Pd/Au (1/15/100nm)metal by e-beam evaporation.Transport measurements were carried out in cryogenic super-conductingmagnets with base temperature of 1.5 K. The four-terminalresistance were measured using low-frequency lock-in techniques at17.777Hz with a current excitation of 20 nA.Data availabilityThe data that support the findings of this study are available from thecorresponding authors upon request.References1. Blatt, J. M., Böer, K. & Brandt, W. Bose-Einstein condensation ofexcitons. Phys. Rev. 126, 1691 (1962).2. Snoke, D. Spontaneous bose coherence of excitons and polaritons.Science 298, 1368–1372 (2002).3. Halperin, B. & Rice, T. 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Lett.132, 196202 (2024).AcknowledgementsL.W. acknowledges the National Key Projects for Research andDevelopment of China (Grant Nos. 2022YFA120470,2021YFA1400400), National Natural Science Foundation of China(Grant No. 12074173), Natural Science Foundation of Jiangsu Province(Grant No. BK20220066) and Program for Innovative Talents andEntrepreneur in Jiangsu(Grant No.JSSCTD202101). K.W. and T.T.acknowledge support from the JSPS KAKENHI (Grant Numbers20H00354 and 23H02052) and A3 Foresight by JSPS. K.S.N. isgrateful to the Ministry of Education, Singapore (Research Centre ofExcellence award to the Institute for Functional Intelligent Materials,I-FIM, project No. EDUNC-33-18-279-V12) and to the Royal Society (UK,grant number RSRP R 190000) for support. G.Y. acknowledges theNational Natural Science Foundation of China (Grant No. 11974169)and the Natural Science Foundation of Jiangsu Province (Grant No.BK20220066).Author contributionsL.W. and Q.L. conceived the experiment. Q.L., Y.C., L.N.W., H.Y., Z.Y.,Z.W., A.D., J.S., Q.G. and Q.Z. fabricated the samples. Q.L., Y.C., L.W.,K.S.N. and G.Y. performed transport measurement and data analysis.R.W., H.C. and S.X. performed theoretical calculations. K.W. and T.T.supplied hBN crystals. Q.L., Y.C., H.C. and L.W. wrote the manuscriptwith input from all co-authors.Competing interestsThe authors declare no competing interest.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-49406-7.Correspondence and requests for materials should be addressed toXiaoyang Shi, Rui Wang, Geliang Yu or Lei Wang.Peer review information Nature Communications thanks Kateryna Pis-tunova, and theother, anonymous, reviewers for their contribution to thepeer review of this work. 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If material is notincluded in the article’s Creative Commons licence and your intendeduse is not permitted by statutory regulation or exceeds the permitteduse, you will need to obtain permission directly from the copyrightholder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-49406-7Nature Communications |         (2024) 15:5065 8http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Strongly coupled magneto-exciton condensates in large-angle twisted double bilayer graphene Results Discussion Methods Sample fabrication and measurement�setup Data availability References Acknowledgements Author contributions Competing interests Additional information