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[Le Zhang](https://orcid.org/0000-0001-8211-9715), [Jing Ding](https://orcid.org/0009-0009-7678-7675), Hanxiao Xiang, Naitian Liu, [Wenqiang Zhou](https://orcid.org/0009-0004-2862-3776), Linfeng Wu, [Na Xin](https://orcid.org/0000-0002-9293-3056), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Shuigang Xu](https://orcid.org/0000-0002-0589-5291)

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[Electronic ferroelectricity in monolayer graphene moiré superlattices](https://mdr.nims.go.jp/datasets/9d89189e-b855-49f9-9023-a1185d4bb8e2)

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Electronic ferroelectricity in monolayer graphene moiré superlatticesArticle https://doi.org/10.1038/s41467-024-55281-zElectronic ferroelectricity in monolayergraphene moiré superlatticesLe Zhang 1,2, Jing Ding 1,2, Hanxiao Xiang1,2, Naitian Liu1,2,Wenqiang Zhou 1,2,Linfeng Wu1,2, Na Xin 3 , Kenji Watanabe 4, Takashi Taniguchi 5 &Shuigang Xu 1,2Extending ferroelectric materials to two-dimensional limit provides versatileapplications for the development of next-generation nonvolatile devices.Conventional ferroelectricity requires materials consisting of at least twoconstituent elements associated with polar crystalline structures. Monolayergraphene as an elementary two-dimensional material unlikely exhibits ferro-electric order due to its highly centrosymmetric hexagonal lattices. Here, wereport the observations of electronic ferroelectricity in monolayer grapheneby introducing asymmetric moiré superlattice at the graphene/h-BN interface,in which the electric polarization stems from electron-hole dipoles. Thepolarization switching is probed through the measurements of itinerant Hallcarrier density up to room temperature, manifesting as standard polarization-electric field hysteresis loops. We find ferroelectricity in graphene moiré sys-tems exhibits generally similar characteristics in monolayer, bilayer, and tri-layer graphene, which indicates layer polarization is not essential to observethe ferroelectricity. Furthermore, we demonstrate the applications of thisferroelectric moiré structures inmulti-state nonvolatile data storage with highretention and the emulation of versatile synaptic behaviors. Our work not onlyprovides insights into the fundamental understanding of ferroelectricity, butalso demonstrates the potential of graphene for high-speed and multi-statenonvolatile memory applications.Ferroelectric materials possess electrically switchable spontaneouspolarizations, which offer fascinating applications for nonvolatilememories, electric sensors, radio frequency, beyond Boltzmann tyr-anny transistors, and synaptic devices1–4. In conventional ferroelectricmaterials, the spontaneous electric polarization is formed by thespatial separation of the cation and anion, which is switchable by anexternal electric field (E) via small lattice displacements inside a unitcell. Recently, the emergence of two-dimensional ferroelectricity notonly provides the opportunity for realizing the miniaturization andmultifunction of nonvolatile devices but also opens the door to thediscovery of novel ferroelectricity5–9. The reduced dimensionality anddesignable interlayer stacking in two-dimensional ferroelectric mate-rials enablemany unconventional properties different from traditionalthree-dimensional counterparts10–15. Among various two-dimensionalferroelectricity, the interfacial ferroelectricity is particularly intriguingbecause it arises from stacking non-polar constituents and exhibitshigh tunability and room-temperature functionality16–23. Up to now,there are mainly two kinds of interfacial ferroelectricity discovered inReceived: 11 September 2024Accepted: 6 December 2024Check for updates1Key Laboratory for QuantumMaterials of Zhejiang Province, Department of Physics, School of Science,Westlake University, 18 Shilongshan Road, Hangzhou310024 Zhejiang Province, China. 2Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou 310024 ZhejiangProvince, China. 3Department of Chemistry, Zhejiang University, Hangzhou 310058, China. 4Research Center for Electronic and Optical Materials, NationalInstitute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 5Research Center for Materials Nanoarchitectonics, National Institute for MaterialsScience, 1-1 Namiki, Tsukuba 305-0044, Japan. e-mail: na.xin@zju.edu.cn; xushuigang@westlake.edu.cnNature Communications |        (2024) 15:10905 11234567890():,;1234567890():,;http://orcid.org/0000-0001-8211-9715http://orcid.org/0000-0001-8211-9715http://orcid.org/0000-0001-8211-9715http://orcid.org/0000-0001-8211-9715http://orcid.org/0000-0001-8211-9715http://orcid.org/0009-0009-7678-7675http://orcid.org/0009-0009-7678-7675http://orcid.org/0009-0009-7678-7675http://orcid.org/0009-0009-7678-7675http://orcid.org/0009-0009-7678-7675http://orcid.org/0009-0004-2862-3776http://orcid.org/0009-0004-2862-3776http://orcid.org/0009-0004-2862-3776http://orcid.org/0009-0004-2862-3776http://orcid.org/0009-0004-2862-3776http://orcid.org/0000-0002-9293-3056http://orcid.org/0000-0002-9293-3056http://orcid.org/0000-0002-9293-3056http://orcid.org/0000-0002-9293-3056http://orcid.org/0000-0002-9293-3056http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-0589-5291http://orcid.org/0000-0002-0589-5291http://orcid.org/0000-0002-0589-5291http://orcid.org/0000-0002-0589-5291http://orcid.org/0000-0002-0589-5291http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55281-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55281-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55281-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55281-z&domain=pdfmailto:na.xin@zju.edu.cnmailto:xushuigang@westlake.edu.cnwww.nature.com/naturecommunicationstwo-dimensional materials: one is the sliding ferroelectricity, wherethe out-of-plane electric polarization can be switched by in-planeinterlayer sliding benefiting from the weak interlayer van der Waalsforce17–24; the other is the unconventional ferroelectricity observed inBernal-stacked bilayer graphene/h-BN moiré superlattice. In contrastto lattice-driven polarization, the ferroelectricity in bilayer graphene isbelieved to arise from spontaneous electronic polarization4,16,25,26,which provides promising applications in ultrafast switchable mem-ories, multiple state storage, and low-power neuromorphic devices4,27.Nevertheless, the two-dimensional materials exhibiting electronicferroelectricity remain extremely rare, limited to bilayer graphenestructures with specific alignment with h-BN16,25,26,28,29.The origin of unconventional ferroelectricity in bilayer grapheneis still elusive. Previous understanding suggested it is highly related tolayer-polarized flatmoiré bands and tunable quadratic bands of bilayergraphene, as evidencedby the accompanying layer-specific anomalousscreening effect16,25,26,30. The switchable electronic states are presumedto arise from layer polarization of charges and interlayer chargetransfer between the top and bottom layers. This interlayer chargetransfer model is based on the strong electron-electron interactions inthe moiré band.Here we report the observations of unexpected electronic fer-roelectricity in monolayer graphene moiré superlattices, where thelayer polarization is essentially absent and linear Dirac band weakensthe electron-electron interactions, in contrast to bilayer graphenesystems. However, we find that in monolayer graphene, the ferroe-lectricity, as well as gate-specific anomalous screening (GSAS) effect,basically resembles that in bilayer graphene. The ferroelectricity inmonolayer graphene manifests as the standard polarization-electricfield (P2D � E) hysteresis loops and atypical multiple-state switching.Our results argue that layer polarization is not an essential factor forthe observation of electronic ferroelectricity in graphene/h-BNsuperlattices. The underlying mechanism of electronic dynamics inthese systems is unveiled by performing a series of P2D � E loopmeasurements. Our observations establish graphene as the thinnestferroelectric material known to exist, enriching the fascinating prop-erties of this wonder material. Furthermore, our discovery will pro-mote the applications of graphene in multi-nonvolatile switchabledevices with ultrahigh mobility.ResultsFerroelectric hysteresisOur high-quality monolayer graphene devices were made from h-BNencapsulated structures with dual-gate configuration as depicted inFig. 1a, which allows us to independently tune externally injected totalcarrier density ntotal and the out-of-plane displacement field D. Tocreate the moiré superlattices, we intentionally aligned the straightedges of graphene with those of both top and bottomh-BN during theassembly process. Raman spectra and second harmonic generationidentified the single alignment configuration, namely, graphene crys-tallographically aligned with the top h-BN and misaligned with thebottom h-BN by 30° (see Methods and Supplementary Fig. 1). Thesingle alignment can be further confirmed from the electronic trans-port behavior as shown in Fig. 1b, which exhibits typical grapheneFig. 1 | Ferroelectric hysteresis in monolayer graphene superlattices.a Schematic of our device with asymmetric moiré interfaces and dual-gate struc-ture. The redwavy line illustrates themoiré potential at top interface trappingholes(green balls) injected by the top gate (V t), which are bound by itinerant electrons(red balls) injected by the bottom gate (Vb). The vertical arrow defines the positiveelectric field. Bottom panel shows conductive atomic force microscopy image ofgraphene/h-BN moiré superlattices. The scale bar is 50nm. b, c Four-terminallongitudinal resistance Rxx as a function of V t at fixed Vb =0 for monolayergraphene (b) and bilayer graphene (c)moiré superlattices. The arrows illustrate thesweep direction.d Rxx as a function ofV t by sweepingV t in various ranges ( V t����max)while fixing Vb =0. e Rxx as a function of Vb by sweeping Vb in various ranges( Vb����max) while fixing V t = 0. The curves in (d) and (e) are vertically shifted forclarity. The forward and backward sweeps are shown in solid and dashed lines,respectively. The inset in (e) plots the difference of charge-neutrality pointsbetween forward and backward sweeps as a function of Vb����max.Article https://doi.org/10.1038/s41467-024-55281-zNature Communications |        (2024) 15:10905 2www.nature.com/naturecommunicationsmoiré superlattices hallmark with two satellite peaks at second Diracpoint (SDP) besides the main Dirac peak at charge-neutrality point(CNP). The twist angle between graphene and top h-BN is calculated tobe 0.68°, resulting in a moiré wavelength of about 12.4 nm (see Sup-plementary Note 2).To unveil the layer-dependent ferroelectricity in graphene moirésuperlattices,we fabricated a device comprising regions ofmonolayer,bilayer, and trilayer graphene, which allows us to in-situ compare theirtransport behaviors. The layer number of each region can be easilydistinguished from the optical contrast and further confirmed byRaman spectra (see Supplementary Fig. 1). Figure 1b, c show thetransport behaviors measured from monolayer and bilayer graphenemoiré superlattices, respectively. Compared with bilayer graphenemoiré superlattice, the monolayer counterpart exhibits prominentelectron-hole asymmetry with hole-side SDP reaching the same orderas CNP and weak electron-side SDP, which is consistent with thosereported in literatures31–35. More characteristics of monolayer gra-phene can be identified from the nearly D-independent CNP (seeSupplementary Fig. 2). In the main text, we mainly present the datafrom monolayer graphene device (Device D1-1), leaving the data fromother devices including bilayer, trilayer and twistedbilayer graphene inSupplementary Information. All the data were taken at the base tem-perature T =2:2 K unless otherwise specified.Figure 1d, e show the transfer characteristics of monolayer gra-phene device given by sweeping either the top gate (V t) or bottomgate (Vb) forward and backward, while keeping the other gate at zero.For Vb sweeps, the forward and backward curves overlap within smallgate-sweep ranges ( Vb����max ≤ 19 V). However, when Vb����max>19 V, four-terminal longitudinal resistance Rxx exhibits remarkable hysteresis,which can be easily identified by tracking the positions of CNP andSDP. We can exclude the extrinsic origins of this hysteresis (see Sup-plementary Note 3). Although both V t and Vb sweeps show hysteresis,they exhibit different responses across various sweeping ranges.Exceeding a critical Vb����max, the amplitudes of hysteretic loops mea-sured by the shift of CNP (ΔVb) increase with the increasing Vb����max asshown in the inset of Fig. 1e, while ΔV t are almost unchanged in V tsweep as shown in Fig. 1d. The distinct gate tunability reflects theasymmetric moiré potential at the two interfaces of graphene.Gate-specific anomalous screeningIt’s worth noting that in Fig. 1d, hole-side SDP does not appear asexpected when V t����max ≤ 14 V even if the sweep range exceeds the fullfilling of moiré band (corresponding ΔV 0t = 9:7 V in this device). Tofurther investigate this anomaly, we measured the dual-gate maps ofRxx shown in Fig. 2, which strongly depend on the scan directions ofboth top and bottom gates. For example, when comparing the V tforward (Fig. 2a) with backward (Fig. 2b) maps, remarkable hysteresiscan be observed by tracing the positions of CNP and SDPs. The sub-traction between the forward and backwardmaps is plotted in Fig. 2c.Three sets of hysteretic loops consisting of red and blue peaks areassociated with CNP and two SDPs.Besides the hysteresis behavior, another prominent feature inFig. 2a is the nearly horizontal lines, manifesting as Rxx anomalouslyindependent of V t. In normal dual-gate maps of graphene devices, theresistance peaks associated with CNP and SDPs trace as straight diag-onal lineswhose slopes aredeterminedby the capacitances of twogatedielectrics, suggesting that both gates can effectively inject carriersand tune the Fermi energy. If the dual-gatemaps are converted to ntotal- D maps, the diagonal lines turn into vertical lines (see Methods).However, in our device, within some regions (for instance,�20V<Vt<� 5V for hole-side SDP in Fig. 2a), the position of SDPabruptly freezes, as if V t has been screened and does not work any-more. We denote this phenomenon as GSAS. In this device, V t is thespecific gate, stemming from moiré superlattice at the top interface(see Supplementary Note 2). The appearances ofGSAS regions dependon the scandirection of fast-scangate as shown in Fig. 2a, b. As the fast-scan gate is changed from V t to Vb as shown in Fig. 2e, f, the GSASregions tend to shrink but still exist. Moreover, the slopes of thediagonal line are different before and after GSAS occurs. For instance,if tracing the electron-side SDP in Fig. 2f, the slope of diagonal line isFig. 2 | Gate-specific anomalous screeningand scan-dependent hysteresis.Dual-gate maps of Rxx by scanning V t forward (a) and backward (b) at each fixed Vb.c The difference between Rxx in (a) and (b). d The corresponding ntotal � D plot of(c). Dual-gatemaps ofRxx by scanningVb forward (e) andbackward (f) at eachfixedV t. g The difference between Rxx in (e) and (f). h The corresponding ntotal � D plotof (g). In (a–c, e–g), the fast-scan axis and slow-scan axis are plotted in horizontalaxis and vertical axis, respectively. The solid arrows illustrate the fast-scan direc-tion, and the dashed arrows mark the slow-scan direction.Article https://doi.org/10.1038/s41467-024-55281-zNature Communications |        (2024) 15:10905 3www.nature.com/naturecommunicationsnormal when the slow-scan gate (V t) is swept from 25 to 12 V. Acrossthe region of 12 V>Vt>7 V, electron-side SDP appears as a vertical lineindicating V t is screened.When V t<7 V, trajectory of electron-side SDPbecomes a diagonal line but with a smaller slope compared with initialstates (V t>12 V), indicating that Vb is partially screened in this region.The CNP and hole-side SDP show similar evolution trend, althoughoccur at slightly different regions. The GSAS can be identified moreclearly as we plot the corresponding ntotal - Dmaps in Fig. 2d, h, wherestraight lines represent the normal gating effect and oblique linesindicate screening effect. More detailed results show that GSAS alsodepends on the scan range of fast-scan gate (see SupplementaryFigs. 9 and 10), but independent of the scan direction of slow-scangate(see Supplementary Fig. 11).Polarization-electric field hysteresis loopsThe presence of GSAS indicates the anomalous external field tunabilityof charge carrier density in this system. To unveil this, we resort to theHall measurements. The Hall resistance Rxy directly probes the itiner-ant charge density given by nH = � B=eRxy, where B is external mag-netic field, and e is the electron charge. Figure 3a shows the differenceof Hall density (ΔnH) between forward and backward sweeps as afunction of ntotal and E, in which the fast-scan axis is E, achieved bysimultaneously sweeping V t and Vb with a fixed relation (see Meth-ods). In normal dual-gate devices, scanning E will not change nH(=ntotal) when fixing ntotal. Specifically, at ntotal = 0, we should achievenH =0. However, in our device, as shown in Fig. 3b,c, though ntotal isfixed at zero, prominent nonzero polarization P2D = enHddipole / nH(see Methods) can be achieved and is strongly dependent on the scanhistory of E. Similar behavior of tunable ΔnH by scanning E at ntotal ≠ 0can be observed as shown in Fig. 3a. We believe this feature sharescommon origin as GSAS, which we will discuss later.Figure 3b shows a typical P2D � E hysteresis loop. Obviously, twodistinct states of nonzero remanent polarization (Pr) with oppositesigns can be achieved at E =0 after a history of applying E. The signs ofthe two states can be reversed by applying a large E with the oppositedirection. More generally, the polarization at finite E is dependent notonly on the current E but also on its applied history, yielding a hys-teretic loop. From Fig. 3c, d, we find no obvious hysteresis within thesweep range Ej jmax<28 mVnm−1. This feature is a typical ferroelectriccharacteristic that switching polarization necessitates E exceeding acritical value. With increasing the sweep range of Ej jmax>28 mVnm−1,the hysteresis loops and the corresponding Pr dramatically increase,resulting in a largememorywindowwith twononvolatile states. All theabove features, including both spontaneous polarization and itsswitchable characteristic, unambiguously confirm the observations offerroelectricity in our system. When Ej jmax is increased to � 73mVnm−1, Pr approaches the saturation polarization (Ps). Furtherincreasing Ej jmax does not changePr anymore.However, thewindowofhysteresis loops continuously enlarges without showing any sign ofsaturation with increasing Ej jmax. Figure 3d summarizes the Pr and Psas a function of Ej jmax, showing a step-like increase in Pr and Ps.Mechanism of electronic ferroelectricityLikewise, the measurements of P2D � E hysteresis loops provide usessential information to understand the mechanism of the observedferroelectricity in our system. Herein, the hysteresis loops are dividedinto eight processes in a half cycle as shown in Fig. 3e. The other halfcycle has similar processes. Normally, when we fix total carrier densityE (mV nm-1)0 200-200 -100 100E (mV nm-1)0-100 100P2D  (pC m-1)00.8-0.8aE (mV nm-1)0-100 100n total  (1012 cm-2)02-2�nH (1012 cm-2) -5 5 b2PrScan range (mV nm-1)± 18± 37± 68± 103± 137± 166± 53|E |max (mV nm-1)0 200100Pr  (pC m-1)0dPs   (pC m-1)0.700.7P2D  (pC m-1)00.8-0.8c2Psholeelectronⅰⅱⅲⅳⅴⅵⅶⅷeⅰⅱ ⅲⅳⅴⅵⅶⅷlocalizedVtitinerantVbFig. 3 | Polarization-electric field (P2D -E) hysteresis loops. a The difference ofHall carrier density nH between the forward and backward sweeps of externalelectric field E at each fixed carrier density ntotal. b Two-dimensional polarizationP2D as a functionof Emeasuredby sweeping E sequentially in thedirectiondenotedby the arrows at fixed ntotal = 0. c Scan-range dependent P2D � E hysteresis loopsmeasured by the same method as that in (b). The remanent polarization Pr andsaturation polarization Ps are extracted according to the marks in the plots.d Summary of Pr and Ps as a function of scan range Ej jmax. e Schematic of chargepolarization and saturation at each process marked in (b). The red wavy linesillustrate the moiré potential. The green (red) ball denotes hole (electron). Thearrows illustrate the injection (or extraction) process of charge carriers at top andbottom interfaces controlled by V t and Vb, respectively. The black wavy lines inProcess iii and viii denote the recombination of electrons and holes. Process i, iv, v,and vi are GSAS regions. Process ii, iii, vii, and viii are the normal dual-gatingregions. All the data in (b) and (c) weremeasured at fixed ntotal = 0. The sharp peaksnear P2D =0 in (b, c) are due to the measured Rxy ! 0 when passing through CNP.Article https://doi.org/10.1038/s41467-024-55281-zNature Communications |        (2024) 15:10905 4www.nature.com/naturecommunicationsntotal = 0 and scan the electric field E, the hole density injected by V t isequal to the electron density injected by Vb. Thus, wewill get zeroHallcarrier density nH =ntotal = 0. However, in our devices, the holesinjected by V t (green balls in Fig. 3e) are trapped by top moirépotential, which become localized and don’t contribute to channelconductance. This situation is analogous to the case where the holesinjected by V t are zero.Meanwhile, the electrons can be injected by Vb(red balls in Fig. 3e) normally and become detectable by Hall mea-surement. Therefore, the net carrier density nH is nonzero.In Process i shown in Fig. 3b, e, localized holes and itinerantelectrons are continuously injected by V t and Vb, respectively. nH isgradually increased, resulting in a nonzero polarization. The electron-hole dipolemoments are formedby the localized holes at top interfaceand itinerant electrons at bottom interface. It’s worth noting that thebound of localized hole and itinerant electron pairs is dynamic,resembling the formation of Cooper pairs in superconductivity. Onreaching Process ii, the density of the injected holes by V t approachesthe half-filling of the moiré band. Further increasing E will triggerProcess iii. In this process, the saturated moiré band cannot trap theadditionally injected holes by V t anymore. Instead, they recombinewith the electrons injected by Vb. Therefore, nH is saturated, and thedual-gating effect becomes valid. In Process iv, E is decreased, namely,holes and electrons are extracted by V t and Vb, respectively. Theremaining itinerant electrons (i.e., nH) continuously decrease till zero,arriving at Process v. Further decreasing E will inject localized elec-trons at top interface and itinerant holes at the bottom interface, asshown in Process vi. The direction of electron-hole dipole moment(i.e., polarization) is reversed, relative to Process i-iv. In the subsequentProcess vii-viii, nH saturates again, similar to Process ii-iii but withopposite values.Besides the standard hysteresis loop, we also observed severalunique switching behaviors which can support the mechanismaforementioned.Firstly, conventional ferroelectric insulators always show ananticlockwise hysteretic P2D � E loop because the bound charges onlyoccur at the interface17,20. However, ferroelectric semiconductors ormetals, due to the presence of mobile carriers, can exhibit partialpolarization switching, resulting in clockwise hysteresis36. In our sys-tem, thedirectionof hysteretic loopsprogresses in a clockwisemanneras shown in Fig. 3b and c, due to itinerant charges in graphene effec-tively reducing the penetration depth of electric fields. This featureindicates the electric dipoles and itinerant carriers are in the samechannel in our system.Secondly, the measured saturation itinerant density nsH �1:5 × 1012 cm−2 is independent of Ej jmax and layer number (see Sup-plementary Fig. 16), but highly relative to moiré period. In our device,the observation of SDP facilitates the determination of the full-fillingcarrier density (nFull = 3:0× 1012 cm−2) of a moiré band. We found thatthe saturation occurs at half-filling of the moiré band, as we havensH � 0:5nFull. Increasing temperature will thermally active the loca-lized carriers, causing them to become itinerant ones. Therefore, weobserved the decrease in nsH (or Ps) with increasing temperature, asshown in Fig. 4. The temperature-dependent nsH follows the thermalactivation fitting as shown in Supplementary Fig. 8a.Thirdly, above the threshold ( Ej jmax>73 mVnm−1), as shown inFig. 3b, c the Pr is approximately identical to the Ps, indicating theexistence of single domain in our sample. The uniform polarizationand smooth switching in our system suggest that the ferroelectricityarises more likely from electronic dynamics, rather than sliding fer-roelectricity assisted by domain motions. The slope of the curveFig. 4 | Temperature-dependent ferroelectricity and nonvolatile switching.P2D � E hysteresis loops measured at various temperature for two representativesEj jmax = 80 mVnm−1 (a) and 36mVnm−1 (b). The traces in (a, b) are measured fromT = 2.2 K to T = 300K with an interval of 20K. c Temperature dependent Pr at tworepresentatives Ej jmax = 36 mVnm−1 and 80mVnm−1. Additionally, we observed Psdecreased with the increasing of temperature for both (a, b) and the windows ofP2D � E hysteresis loops were broadened at elevated temperature. d nH measuredas a function of timeunder repetitive E pulses alternating between two equal valuesin amplitude but opposite sign. The upper panel shows repeated cycles of appliedE. e Programmablemeasurement of nH in response to a series of E pulses. E pulseswere programmed to be alternate positive and negative values with graduallyincreasing amplitudes. The bottom panel is the corresponding nH as a function oftime. All the nH in (d, e) are measured from Rxy at B=0:1 T without anti-symmetricprocessing. Therefore, there is slightly difference between positive and negative nHdue to the unperfect Hall bar geometry. All the data aremeasured at fixed ntotal = 0.Article https://doi.org/10.1038/s41467-024-55281-zNature Communications |        (2024) 15:10905 5www.nature.com/naturecommunicationstracing from Process iv-v-vi-vii remains unchanged, regardless of var-iations in Ej jmax (see Fig. 3c), temperature (see Fig. 4a, b), or layernumber (see Supplementary Fig. 16), as it’s only relative to the gatingcapacity of Vb. The polarization switching is not due to the domainmotion as that in conventional ferroelectricity or sliding ferroelec-tricity, but arising from the process of injecting and exctracting loca-lized carriers assisted by GSAS as shown in Process iv-v-vi-vii.Fourthly, when Ej jmax<73 mVnm−1, Process ii is absent, because ofthe insufficient supply of localized carriers in Process i, resulting innrH <nsH. This is also the origin of the nonmonotonic dependence of Pron temperature for Ej jmax = 36 mVnm−1 as shown in Fig. 4b, c, becauseit needs to keep the slope of the GSAS curves unchanged whiledecreasing nsH with increasing temperature. Within the region ofnrH<nsH, quasi-continuous remanent polarizations, which are stableeven after E is removed, endows the device with the functionality ofmulti-state data storage and multifunctional synapse emulation.Layer independence of electronic ferroelectricityThe GSAS and ferroelectricity observed in monolayer graphene moirésuperlattice resemble that in bilayer counterpart16,26. Based on previousunderstanding, layer-polarized flat moiré bands and interlayer chargetransfer are essential roles in the emergence of ferroelectricity in gra-phene moiré systems. To explicitly unveil layer-dependent ferroelec-tricity, we intentionally designed a control device, which allows us to in-situ compare the emerging ferroelectricity in monolayer, bilayer, andtrilayer graphene moiré structures. It’s found that all of these threesystems exhibit ferroelectric behavior and have some characteristics incommon (see Supplementary Figs. 16–19). Firstly, the ferroelectrichysteresis coexists with GSAS. Secondly, the GSAS depends on the gatesweep range and is believed to arise from the asymmetric moirésuperlattice. Thirdly, the window of hysteresis loops continuouslyenlargeswithout saturationwith the increasing Ej jmax as shown inFig. 3cand Supplementary Fig. 16b, which is an atypical behavior distinct fromconventional ferroelectricity. Above a critical Ej jmax, they have the samesaturation Hall carrier density nsH, which is independent of layer num-ber, but highly relative to half-filling density of a moiré band (see Sup-plementary Fig. 16). Our results suggest the electronic ferroelectricityobserved here is independent of graphene layer number and the fineband structure of graphene (see in Supplementary Figs. 16–19). How-ever, we believe the semimetal characteristics of graphene plays acrucial role since the formation of electron-hole dipoles hinges on thefacile excitation of electron-hole pairs by gates.Robust ferroelectricity for nonvolatile memory devicesWe further study the temperature dependence of electronic ferroe-lectricity and demonstrate proof-of-concept devices, providing pro-mising applications of monolayer graphene ferroelectricity in multi-state data storage. As shown in Fig. 4a, c, Pr decreases with increasingtemperature at Ej jmax = 80 mVnm−1, which is opposite to otherextrinsicmechanisms such as charge trapping and external adsorbates(see more discussions in Supplementary Note 3), but consistent withthe typical ferroelectric behavior. Specially, Pr exhibits nonmonotonicdependence on temperature at Ej jmax = 36 mVnm−1 shown in Fig. 4b, cas a unique feature of electronic ferroelectricity. Moreover, we foundthat the ferroelectric hysteresis loops and spontaneous polarizationcan persist even at room temperature as shown in Fig. 4a–c. Therobustness of our electronic ferroelectricity can be further demon-strated by switching the polarization states using a small E pulse in anonvolatile way as shown in Fig. 4d. We also check the stability of thenonvolatile switch by keeping the polarization states for an extendedperiod, which remains almost the same for more than 12 h (see Sup-plementary Fig. 20).Apart from two-state switch resembling that in conventional fer-roelectric materials, the multiple spontaneous polarization states canbe achieved here. It’s noted that the multi-state switch in our system isnot arising from domain configurations as that in conventional ferro-electric memristors37. Instead, the tunable Pr is achieved by the con-tinuous injection of localized holes (electrons) by the specific gate (V t,in this specific device) and electrons (holes) by the other gate. Thisunique feature endows us to utilize it to realize unconventionalapplications. As shown in Fig. 4e, positive and negative pulses of E aresequentially applied with gradual increase in the amplitudes. Underpulses of small Ej j<60mVnm−1, nH���� increases quasi-continuously withincreasing Ej j. Each polarization state is stable over time even after E isremoved and switchable by changing sign of E pulse. This typicalnonvolatile memory state can be widely applied to data storage.Beyond the simple two-state (0 and 1 in digital circuits) storage, ourdevice can function as multiple-state storage.Synapse emulationOur ferroelectric devices exhibit diverse electrical characteristics,enabling us to emulate multifunctional synaptic activities such assynaptic plasticity including short-term plasticity (STP), long-termpotentiation (LTP), and long-term depression (LTD). By programmingthemagnitude and sign of E pulses as shown in Fig. 5a, the nonvolatileand quasi-continuous change of nH���� can emulate the synaptic plasti-city, which is the key component of artificial synaptic devices forneuromorphic computing. In neuroscience, the long-term synapticplasticity represents the ability of synapses to strengthen (LTP) orweaken (LTD) over time in response to increases or decreases in theirFig. 5 | Multifunctional synaptic devices. a Schematic of a biological synapse.b The emulation of long-term plasticity in synaptic devices by utilizing nonvolatilemultiple states in our device. nH���� serves as the synaptic weights, which can con-tinuously increase and decrease under a series of input stimuli (here is E), emu-lating the long-term potentiation and long-term depression, respectively. c Theemulation of short-term plasticity. nH���� evolves as a function of time under repe-titive stimuli of E. The inset shows one cycle of applied E.Article https://doi.org/10.1038/s41467-024-55281-zNature Communications |        (2024) 15:10905 6www.nature.com/naturecommunicationsactivity and is widely considered as a primary mechanism for learningand memory. Analogously, in our system, by writing E pulses, thedevice shows potentiation and depression of nH���� (emulating synapticweight), which is reminiscent of LTP and LTD in synapse transistors,respectively.More excitingly, we notice that nH���� experiences spontaneousdecay in a short time at large E >60 mVnm−1, as shown in Fig. 5b. Tobetter understand the behavior under large electric field, we investi-gated how nH���� emulating the synaptic weight evolves upon applica-tion of a train of E pulses. Upon excitation of a high E pulse, nH����immediately increases to a high value and gradually relaxes until theapplication of next pulse as shown in Fig. 5c. This feature can be usedto emulate STP for processing temporal information. This process ishighly reproducible and can work for over 20 cycles without anydegradation in performance as demonstrated in Fig. 5c. The under-lying mechanism is still to be understood but may be attributed to thesaturation of moiré traps.DiscussionOur findings of electronic ferroelectricity in monolayer graphene notonly enrich its fruitful properties in this wonder material but also offernew opportunities for exploring novel physics.When interplayingwithother properties in graphene such as ferromagnetism, topology, andsuperconductivity, intriguing properties including unconventionalmultiferroics and topological ferroelectrics may emerge. From theperspective of applications, nonvolatile memory and synaptic devicesbased on monolayer graphene possess unique advantages in terms ofhigh mobility, high stability, and multifunctionality. Moreover, ourgraphene ferroelectric devices approach to 2D limit, compatible withpost-Moore’s Law era devices. As aforementioned, the main ferro-electric features in monolayer graphene moiré superlattices can sur-vive up to room temperature, further facilitating their applications.The already well-developed growth of scalable monolayer graphenesuperlattices can beused to construct the novel ferroelectric devices38.The h-BN required for the construction of moiré superlattices alsoserves as the dielectric material, which simplifies the design of ferro-electric devices.MethodsDevice fabricationAll the devices weremade using standard dry-transfer method. In brief,graphene and h-BN flakes were mechanically exfoliated on the 285 nmSiO2/Si substrates. In particular, the graphene flake of Device D1 con-tains consecutive mono-/bi-/tri-layer parts, which were identified bytheir optical contrast (Supplementary Fig. 1). The top h-BN, graphene,and bottom h-BN flakes were layer-by-layer assembled using a poly(bi-sphenol A carbonate)/polydimethylsiloxane (PC/PDMS) stamp. Gra-pheneflakewas intentionally alignedwith both top andbottomh-BNbyutilizing their straight and longedges. The alignmentbetweengrapheneand h-BN can be determined by transport measurement, while therelative angle between top andbottomh-BNwas determined by secondharmonic generation (SHG) measurements. The h-BN/graphene/h-BNheterostructure was finally released on a plasma-cleaned SiO2/Si sub-strate which served as back gates. The contact regions were patternedby electron beam lithography (EBL) and etched as trenches by CHF3/O2plasma. Metallic contacts (5 nmCr/60nmAu) were deposited into thetrenches. The metallic top gate was made by a second EBL and e-beamevaporation. The final Hall bar geometry was defined by another roundof EBL and plasma etching. The list of devices, including the ferroelec-tricity behaviors and the stagger angles between top and bottom h-BN,are summarized in Supplementary Table 1.Optical measurementsRaman measurements were performed at room temperature using aconfocal Raman spectrometer (Witec Alpha 300RAS with UHTS300 spectrometer) equipped with a 532 nm excitation laser. The laserspot size was about 1μm. The second harmonic generation (SHG)measurements were conducted in the same setup with incident lightwavelength of 1064 nm and a fixed excitation power of 20mW.Conductive atomic force microscopy measurementsThe sample for conductive atomic force microscopy (c-AFM) mea-surements was made by sequentially picking up h-BN and graphenewith PC/PDMS stamp. The stack was then flipped on a fresh PDMS.After dissolving PC with n-methyl-2-pyrrolidone (NMP), the stack wasreleased on a new SiO2/Si substrate. The c-AFM measurements wereperformed on Asylum Research Jupiter XR at room temperature.Transport measurementsThe devices were wire-bonded on the LCC-44 chip carriers (Kyocera)and measured in a 4 K closed cycle refrigerator system (Janis SHI-4-2)cooled down by a Sumitomo F-20L cold head. The base temperaturewas 2.2 K, recorded by a calibrated sensor mounted near the sampleand controlled by a Lake Shore temperature controller. All the mea-surements presented in the manuscript, such as dual gate mappingsand P2D � E loops, except the temperature-dependentmeasurements,were carried out at this base temperature. The longitudinal and Hallresistances weremeasured by lock-in amplifier (SR-830) with constantexcitation current of 100 nA. The top and bottom gates were appliedby source meters (Keithley 2450).Our dual-gate structure allows us to convert V t � Vb mapsto ntotal � D maps. The total gate-induced carrier densityis ntotal = ðCbVb +CtV tÞ=e, and the displacement field isD= ðCbVb � CtV tÞ=2ε0, where Ct and Cb are the capacitance per areaof top and bottom gate measured by Hall effect, respectively, e isthe elementary charge, and ε0 is the vacuumpermittivity. The four-terminal longitudinal resistance Rxx maps were acquired at zeromagnetic fields unless otherwise specified.To convert D to E, we note that Vb was applied on SiO2 andbottom h-BN. Therefore, the voltage across the bottom h-BN isVbBN =VbεSiO2dbBNεBNdSiO2+ εSiO2dbBN, where dbBN and dSiO2are the thickness of bot-tom h-BN and SiO2, respectively39, εSiO2= 4:3 and εBN = 3:8 are thedielectric constant of h-BN and SiO2, respectively, calibrated by capa-citancemeasurements throughHall effect at normal gating region. Theelectric field across graphene is E = ðVbBN=dbBN � V t=dtBN Þ=2 =D=εBN ,where dtBN is the thickness of top h-BN.nH and P2D �E loops measurementsThe itinerant carrier density nH is determined from Hall effect bymeasuring Hall resistanceRxy under small magnetic field ofB= ±0:1 T.Rxy is anti-symmetrized by Rxy = ðR0:1Txy � R�0:1Txy Þ=2 to remove residualvalues induced by unperfect sample geometry. The Hall (itinerant)carrier density is calculated to be nH = � B=eRxy. To measure Fig. 3a,we simultaneously swept Vb and V t with a specific relation by fixingntotal = ðCbVb +CtV tÞ=e as a constant value, and measured nH. In thisway, we can realize the sweeps of E atfixed ntotal, namely, E as fast-scanaxis and ntotal as slow-scan axis. The ΔnH is the difference of nHbetween forward and backward sweeps of E.In order to measure P2D � E loops, we always fixed ntotal = 0. Bysweeping E forward and backward in a given rang of Ej jmax, weacquired the response of nH. The 2D polarization P2D followsP2D = enHddipole17,20, where ddipole is the size of dipole moment, i.e., thethickness of graphene. For monolayer graphene, ddipole = 0:26 nm40,while for bilayer graphene, ddipole is doubled as that of monolayergraphene. To comparewith other ferroelectrics, we can convert P2D toP3D = P2Dddipole= enH. At Ej jmax = 80mV/nm, the measured saturation itin-erant density is nsH � 1:5 × 1012 cm−2, yields 2D saturation polarizationP2D =0:63pC=m, which is corresponding to P3D = 0.24μC/cm2.Article https://doi.org/10.1038/s41467-024-55281-zNature Communications |        (2024) 15:10905 7www.nature.com/naturecommunicationsThis value is in the same order as those in other 2D ferroelectrics, suchas bilayer graphene superlattices16,25, twisted h-BN17, 3R-MoS220, whilemuch smaller than those in other traditional ferroelectrics probablybecause of its 2D nature.Reporting summaryFurther information on research design is available in the NaturePortfolio Reporting Summary linked to this article.Data availabilityRelevant data supporting the findings of this study are available fromthe corresponding authors upon request. Source data are providedwith this paper.References1. Valasek, J. Piezo-electric and allied phenomena in Rochelle salt.Phys. Rev. 17, 475–481 (1921).2. Khan, A. 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The electronic thickness of graphene. Sci. Adv. 6,eaay8409 (2020).AcknowledgementsThis work was funded by National Natural Science Foundation of China(Grant No. 12274354), the Zhejiang Provincial Natural Science Founda-tion of China (Grant No. LR24A040003; XHD23A2001), and WestlakeEducation Foundation atWestlake University. We thank Chao Zhang andZhen Yang from the Instrumentation and Service Center for PhysicalSciences (ISCPS) at Westlake University for technical support in dataacquisition. We also thank Westlake Center for Micro/Nano Fabricationand the Instrumentation and Service Centers for Molecular Science forfacility support. L.Z. acknowledges to the Zhejiang Province SelectedFunding for Postdoctoral Research Projects (ZJ2023077). K.W. and T.T.acknowledge support from the JSPS KAKENHI (Grant Numbers21H05233 and 23H02052) and World Premier International ResearchCenter Initiative (WPI), MEXT, Japan.Author contributionsS.X. and N.X. conceived the idea and supervised the project. N.X. andL.Z. fabricated the devices. L.Z. performed the transport measurementswith the assistance of J.D., W.Z., N.L., and L.W. H.X. performed AFMmeasurements. L.Z., W.Z., and H.X. performed Raman and SHG mea-surements. K.W. andT.T. grewh-BNcrystals. L.Z., N.X., andS.X. analyzedthe data and wrote the paper. All the authors contributed to thediscussions.Competing interestsThe authors declare no competing interests.Article https://doi.org/10.1038/s41467-024-55281-zNature Communications |        (2024) 15:10905 8https://arxiv.org/abs/2306.03922https://arxiv.org/abs/2306.03922www.nature.com/naturecommunicationsAdditional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-55281-z.Correspondence and requests for materials should be addressed toNa Xin or Shuigang Xu.Peer review information Nature Communications thanks MartinoAldrigo and theother anonymous reviewer(s) for their contribution to thepeer review of this work. A peer review file is available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jur-isdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons licence, and indicate ifchanges were made. The images or other third party material in thisarticle are included in the article’s Creative Commons licence, unlessindicated otherwise in a credit line to the material. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-55281-zNature Communications |        (2024) 15:10905 9https://doi.org/10.1038/s41467-024-55281-zhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunications Electronic ferroelectricity in monolayer graphene moiré superlattices Results Ferroelectric hysteresis Gate-specific anomalous screening Polarization-electric field hysteresis loops Mechanism of electronic ferroelectricity Layer independence of electronic ferroelectricity Robust ferroelectricity for nonvolatile memory devices Synapse emulation Discussion Methods Device fabrication Optical measurements Conductive atomic force microscopy measurements Transport measurements nH and P2D - E−E loops measurements Reporting summary Data availability References Acknowledgements Author contributions Competing interests Additional information