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Samra Husremović, Berit H. Goodge, Matthew P. Erodici, Katherine Inzani, Alberto Mier, Stephanie M. Ribet, Karen C. Bustillo, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Colin Ophus, Sinéad M. Griffin, D. Kwabena Bediako

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[Encoding multistate charge order and chirality in endotaxial heterostructures](https://mdr.nims.go.jp/datasets/51c3fe42-b900-4899-981a-7cdeeaef8f8b)

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Encoding multistate charge order and chirality in endotaxial heterostructuresArticle https://doi.org/10.1038/s41467-023-41780-yEncoding multistate charge order andchirality in endotaxial heterostructuresSamra Husremović 1, Berit H. Goodge 1,2, Matthew P. Erodici1,Katherine Inzani 3, Alberto Mier1, Stephanie M. Ribet4,5,6, Karen C. Bustillo 4,Takashi Taniguchi 7, Kenji Watanabe 8, Colin Ophus 4,Sinéad M. Griffin 9,10 & D. Kwabena Bediako 1,11High-density phase change memory (PCM) storage is proposed for materialswith multiple intermediate resistance states, which have been observed in 1T-TaS2 due to charge density wave (CDW) phase transitions. However, themetastability responsible for this behavior makes the presence of multistateswitching unpredictable in TaS2 devices. Here, we demonstrate the fabricationof nanothick verti-lateral H-TaS2/1T-TaS2 heterostructures in which the num-ber of endotaxial metallic H-TaS2 monolayers dictates the number of resis-tance transitions in 1T-TaS2 lamellae near room temperature. Further, we alsoobserve optically active heterochirality in the CDW superlattice structure,which is modulated in concert with the resistivity steps, and we show howstrain engineering can be used to nucleate these polytype conversions. Thiswork positions the principle of endotaxial heterostructures as a promisingconceptual framework for reliable, non-volatile, and multi-level switching ofstructure, chirality, and resistance.Charge density wave (CDW)materials host correlated electronic statestypified by periodic lattice distortions and static modulations of con-duction electrons1. Non-volatilememoryand computing devices basedon the principle of phase change memory (PCM)2,3 may leverage theintrinsic resistivity changes associated with CDW phase transitions4–9.1T-TaS2, a van der Waals (vdW) layered solid, is a prototypical CDWmaterial in which the atomic lattice distorts in-plane to form 13-atomstar-shaped clusters10,11. The tiling of these clusters and the extent ofcommensuration with the underlying atomic lattice define the CDWphases and the electronic properties of 1T-TaS210–15. Notwithstandingthe in-plane nature of this CDW lattice distortion, interlayer couplingplays a key role in stabilizing intralayer charge order in 1T-TaS2.Accordingly, together with flake thickness16–18 and doping levels16,19,vertical heterostructuring is a powerful route for engineering CDWtransitions20–25. For example, whereas in pristine, bulk 1T-TaS2 thecommensurate (C) CDWphase only formsbelow about 180K11,12 (and isonly observed at much lower temperatures in exfoliated thin flakes15),electronically isolating monolayer 1T-TaS2 with thicker metallic slabsof H-TaS2 has been shown to stabilize the C-CDW state in monolayer1T-TaS2 at room temperature23,24. To this end, the recent synthesis ofendotaxial TaS2 offers new mechanisms for accessing modular CDWsystems23.In this work, we demonstrate an approach converse to precedingliterature—employing moderate thermal annealing to interdisperseReceived: 24 May 2023Accepted: 16 September 2023Check for updates1Department of Chemistry, University of California, Berkeley, CA 94720, USA. 2Max-Planck-Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, 01187Dresden, Germany. 3School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, UK. 4National Center for Electron Microscopy,Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. 5Department of Materials Science and Engineering, Northwestern University,Evanston, IL 60208, USA. 6International Institute of Nanotechnology, Northwestern University, Evanston, IL 60208, USA. 7Research Center for FunctionalMaterials, National Institute for Materials Science, Tsukuba 305-0044, Japan. 8International Center for Materials Nanoarchitectonics, National Institute forMaterials Science, Tsukuba 305-0044, Japan. 9Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. 10The Mole-cular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. 11Chemical Sciences Division, Lawrence Berkeley National Laboratory,Berkeley, CA 94720, USA. e-mail: bediako@berkeley.eduNature Communications |         (2023) 14:6031 11234567890():,;1234567890():,;http://orcid.org/0000-0002-4741-3780http://orcid.org/0000-0002-4741-3780http://orcid.org/0000-0002-4741-3780http://orcid.org/0000-0002-4741-3780http://orcid.org/0000-0002-4741-3780http://orcid.org/0000-0003-0948-7698http://orcid.org/0000-0003-0948-7698http://orcid.org/0000-0003-0948-7698http://orcid.org/0000-0003-0948-7698http://orcid.org/0000-0003-0948-7698http://orcid.org/0000-0002-3117-3188http://orcid.org/0000-0002-3117-3188http://orcid.org/0000-0002-3117-3188http://orcid.org/0000-0002-3117-3188http://orcid.org/0000-0002-3117-3188http://orcid.org/0000-0002-2096-6078http://orcid.org/0000-0002-2096-6078http://orcid.org/0000-0002-2096-6078http://orcid.org/0000-0002-2096-6078http://orcid.org/0000-0002-2096-6078http://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/0000-0003-3701-8119http://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/0000-0003-2348-8558http://orcid.org/0000-0003-2348-8558http://orcid.org/0000-0003-2348-8558http://orcid.org/0000-0003-2348-8558http://orcid.org/0000-0003-2348-8558http://orcid.org/0000-0002-9943-4866http://orcid.org/0000-0002-9943-4866http://orcid.org/0000-0002-9943-4866http://orcid.org/0000-0002-9943-4866http://orcid.org/0000-0002-9943-4866http://orcid.org/0000-0003-0064-9814http://orcid.org/0000-0003-0064-9814http://orcid.org/0000-0003-0064-9814http://orcid.org/0000-0003-0064-9814http://orcid.org/0000-0003-0064-9814http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41780-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41780-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41780-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41780-y&domain=pdfmailto:bediako@berkeley.edumonolayer H-TaS2 between few-layer 1T-TaS2 lamellae. In the resultingverti-lateral 1T-TaS2/H-TaS2 heterostructures, decoupled 1T-TaS2 frag-ments undergo independent transitions from the disordered incom-mensurate (IC) to ordered commensurate CDW phase above roomtemperature. These transitions are hallmarked by synchronous step-wise switching of chirality and resistance with high predictability; thenumber of steps is encodedby the quantity and arrangementofH-TaS2layers. Thus, the developed materials represent a distinctive frame-work for deterministic engineering of multistate resistance and chir-ality changes in 1T-TaS2. Additionally, we find that the nucleation of H-TaS2 polytype initiates at macrosocopic flake defects, a mechanisticinsight we harness to showcase the potential of strain engineering forthe rational design of verti-lateral TaS2 heterostructures. Moreover,modulating the H-TaS2 content tunes the proportion of heterochiralCDW superlattices, resulting in a range of optically detectable netchiralities. Therefore, our work provides an adaptable roadmap fordesignof versatile optoelectronicphasechangematerialswith reliable,multilevel and multifunctional switching.ResultsCommensuration in verti-lateral TaS2 heterostructuresExfoliated 1T-TaS2 crystals were annealed in high vacuum at 350 °Cfor 30mins and then rapidly cooled to room temperature (see“Methods" section), engendering changes in optical contrast, indi-cative of structural transformations (Fig. 1a). This thermally inducedphase evolution was characterized by selected area electron dif-fraction (SAED) of TaS2 flakes before and after annealing. Beforeannealing, SAED patterns of 1T-TaS2 flakes are consistent with theexpected nearly commensurate (NC)-CDW structure (Fig. 1b)11. Incontrast, SAED data from annealed samples (Fig. 1c) reveal the� �Fig. 1 | Polytype and charge densitywave (CDW) transformations inTaS2flakes.a Optical micrographs of a 1T-TaS2 flake, labeled S1, before and after thermalannealing on 90nm SiO2/Si substrate. Regions of interest are marked. Scale bars:15μm.b, c Room temperature selected area electron diffraction (SAED) patterns ofa representative 1T-TaS2 flake before (b) and after (c) thermal annealing. A repre-sentative set of first-order superlattice peaks is marked for each sample. Scale bars:2 nm−1. d Schematic of real space α and β CDW domains. Unit cells of α, β, and 1T-TaS2 are shaded in violet, pink and blue, respectively. Angle ϕ represents therotational misalignment between the unit cell of 1T-TaS2 and the unit cells of theCDW superlattices. Schematic diffraction patterns for α, β, and α + β patterns areshown at the bottom. e Linearly polarized Raman spectra in selected regions of S1after thermal annealing. Vertical dashed line represents the energy cutoff afterwhich the Raman intensity was scaled by a factor of 2. f Relationship between thered-channel optical contrast change upon annealing (ΔOCR) and the number ofH-TaS2 layers in distinct regions of S1 and S2 (a 1T-TaS2 sample) after annealing. Thisdata is overlaid with the thickness dependence of OCR for 2H-TaS2 on 90 nm SiO2/Si substrate (ref. 31). g–j Atomic-resolution differential-phase-contrast scanningtransmission electron microscopy (DPC-STEM) images along the ½1010� zone axisof: region R1 of S1 (g), area R2 of S1 (h), regions R3--R4 of S2 (i), and region R3 of S1(j) overlaidwith structures of 1T-TaS2 (ref. 63) andH-TaS2 (ref. 64).H-TaS2 layers arehighlighted andTa ions aligned along the c-axis are connectedwith pink lines. Scalebars in g–j are 1 nm.Article https://doi.org/10.1038/s41467-023-41780-yNature Communications |         (2023) 14:6031 2presence of twoffiffiffiffiffi13p×ffiffiffiffiffi13pheterochiral superlattices. The CDWenantiomorphs, α (L) and β (R), possess supercells that are rota-ted ± 13.9 degrees relative to the unit cell of 1T-TaS2 (Fig. 1d)11,26,27.Additionally, the SAED data of annealed 1T-TaS2 flakes are consistentwith a C-CDW phase at room temperature23,24. These ensemblechanges in extent of CDW commensuration in heat-treated flakeswere also evinced by linearly polarized Raman spectroscopy (Fig. 1eand Supplementary Figs. 15 and 16). Raman spectra obtained invisually distinct regions of annealed flake S1 (Fig. 1e) show astrong correlation between the red-channel optical contrast changeupon annealing (ΔOCR) and the sharpness of low-frequency(40–100 cm−1) Raman modes related to CDWs28–30. The CDW spec-tral peaks become increasingly well-defined from regions 3 to 1(R3–R1), a behavior that is tightly correlated with progressive ΔOCR.Furthermore, as ΔOCR becomes more negative, new Raman spectralfeatures emerge at 64 cm−1, 89 cm−1, 123 cm−1, and 230 cm−1. Themanifestation of new peaks and general sharpening of Raman fea-tures is consistent with Brillouin zone folding of 1T-TaS2 as itundergoes the transition from the nearly commensurate CDW (NC-CDW) to C-CDW28–30.To unveil the relationship betweenΔOCR, CDWcommensuration,and atomic lattice structure of these annealed 1T-TaS2 crystals, atomicresolution differential-phase-contrast scanning transmission electronmicroscopy (DPC-STEM) imaging and analysis (Fig. 1f–j) was per-formed on cross-sectional samples made from optically distinctregions of flakes S1 (Fig. 1a) and S2 (Supplementary Fig. 15b). Repre-sentative DPC-STEM micrographs, depicted in Fig. 1g–j, reveal thatthermal annealing induces a partial transition from the 1T (octahed-rally coordinated Ta) to the H (trigonal prismatic Ta) structure. The Hpolytype forms within the 1T-TaS2 matrix (i.e., endotaxially), over-whelmingly as monolayers, separating generally thicker fragments of1T-TaS2. At boundaries between regions with dissimilar ΔOCR, thenumber of H-TaS2 layers varies across a single 1T-TaS2 flake, con-structing lateral heterostructures with atomically sharp interfaces(Fig. 1i). Furthermore, these DPC-STEM data show how 1T-TaS2 slabsseparated by a H-TaS2 layer slip relative to each other, resulting in themisalignment of the Ta centers (vertical lines in Fig. 1g–j) in mixedpolymorph heterostructures.We find that optical contrast measurements are a powerful andconvenient tool for identifying polymorph composition, owing to thelinear relationship between ΔOCR upon annealing and the number ofH-TaS2 layers, determined from DPC-STEM (Fig. 1f). This relationshipmirrors, and stems from, the linear scaling between layer count andOCR for freestanding few-layerH-TaS231 (see Supplementary Note 2 fordetails). Therefore, crystal sections with a more negative ΔOCR (i.e.,appearing increasingly blue) contain a greater number of layers of theH polymorph. Taken together with the increased sharpness andnumber of CDW Raman modes (Fig. 1e), these data establish that theformation of monolayer H structures leads to increased order of 1T-TaS2 C-CDW domains, consistent with prior work with thicker H-TaS2slabs23,24 and bulk mixed polytype TaS2 phases12,26,32,33.The ensemble room-temperature ordering of CDW domains inTaS2 heterostructures with different polytype compositions wasfurther probed using SAED. Our findings support that samplescomprising ≥ 20% of H-TaS2 manifest an ordered C-CDW phase,characterized by sharp CDW reflections (Supplementary Fig. 4b–d).In contrast, the CDW reflections observed in samples with < 20% H-TaS2 appear less well-defined and exhibit peak splitting and angularblurring (Supplementary Fig. 4a). Accordingly, we infer that crystalscontaining less than 20% H-TaS2 content host a disordered C-CDWphase with likely coexistence of some NC-CDW domains. Notably,the chirality of CDW domains (Fig. 1d) could be exploited for next-generation switching devices, making the nano-scale structuralunderstanding of C-CDWs in TaS2 heterostructures integral for theirpotential applications.Diverse chirality in polytype heterostructuresThe heterochirality of CDW superlattices in H-TaS2/1T-TaS2 at roomtemperature was mapped with nano-scale resolution using four-dimensional scanning transmission electron microscopy (4D-STEM),establishing that the α and β enantiomorphs are stacked along the c-axis to form vertical CDW superstructures. In 4D-STEM, a convergedelectron probe is scanned across a sample in a 2D array, whilerecording 2D diffraction data at each probe position (Fig. 2a)34. Weobtained 4D-STEM datasets of a 20-layer flake, S3 (Fig. 2b), parallel tothe c-axis with ~ 5.5 nm spatial resolution in regions R2–R5. Theseregions exhibit progressively sharper Raman spectral features (Sup-plementary Figure 16) and larger H/T ratios from measurements ofΔOCR. For R2–R5, Bragg reflections associated with both commensu-rate α and β enantiomorphs are present in nanodiffraction patterns(Fig. 2c, d andSupplementaryFigure 7). Thus, theCDWenantiomorphsare coexistent ina ~ 5.5 nmarea, revealing their formation in theout-of-plane (∥c-axis) direction. We note that CDW superstructures can bevertically stacked in two configurations across the H-TaS2 interface:heterochiral (α–β) (Fig. 2e) andhomochiral (α–α) (Fig. 2f), eachhostinginequivalent CDWcluster interlayer stackings and charge distributions(Supplementary Figure 19)27. The interlayer arrangement of CDWclusters in polytype heterostructures exhibits notable distinctionscompared to both 1T-TaS2 flakes and homointerfaces. In pristine 1T-TaS2, CDW clusters can be perfectly eclipsed because their buildingblocks—Ta ions—are directly aligned in the out-of-plane direction35,36.In contrast, in polytype heterostructures, Ta ions in 1T-TaS2 slabsacrossH-TaS2 interfaces must be laterally offset (Fig. 1g–j). Thus, CDWclusters in neighboring 1T-TaS2 slabs must assume a staggeredarrangement, resulting in distinct CDW superlattice patterns (2e–f,Supplementary Figure 19).Next, integrated intensities of α and β diffraction spots wereevaluated at each probe position (see “Methods" section for details)37to reconstruct dark-field images associated with the difference insuperlattice ratios, defined as: (β − α)/(β + α) (Fig. 2g–j). The resultantenantiomorphic ratio maps reveal a minor extent of in-plane variationwithin each heterostructure (see histograms in Fig. 2 g–j), potentiallyarising from domain pinning defects. Nevertheless, 4D-STEM data andhigh-resolution TEM analysis (Supplementary Figure 5) consistentlypoint to coexisting, out-of-plane α and β superstructures regardless ofthe H/T composition. However, the polymorph composition appearsto influence the α/β proportion. For example, a less than 45% meandifference in ratio of diffraction pattern intensity from enantio-morphic phases was measured for R4 and R5 at room temperature(Fig. 2i, j). Conversely, a larger mean enantiomorphic disproportionexceeding 65% was obtained for R2 and R3 (Fig. 2g, h). This can beunderstood by considering that changing the polymorph compositionalters the size and number of 1T-TaS2 fragments hosting the two het-erochiral CDWs, thereby engendering changes in the overall chirality.A high enantiomorphic disproportion is therefore the most likely forless transformed samples with larger 1T-TaS2 fragments, which wouldthen dominate the overall chirality.The chirality of TaS2 heterostructures can also be assessed opti-cally, as enantiomorphic disproportion engenders Raman opticalactivity (ROA): a distinct Raman response to right- and left-circularlypolarized light (see Supplementary Note 9 for details)36,38. For 1T-TaS2displaying ROA, the integrated area ratio of Eg(I) and Eg(II) modesdiffers in the σ+σ− and σ−σ+ Raman polarization configurations (Fig. 3a),where σiσs (i, s = ±) are phonon helicities of the incident and scatteredlight38. Note, a stronger ROA signals a higher enantiomorphic dis-proportion and a larger overall chirality. Representative chirality-dependent optical measurements of sample S4 (Supplementary Fig-ure 18c) are shown in Fig. 3.We find that ROAdecreases from regionR1(x/n =3/20) to R3 (x/n =5/20), signaling decreasing overall chirality foran increasing H-TaS2 layer count (Fig. 3b–d and SupplementaryFig. 14). These results are consistent with our 4D-STEM findings; highlyArticle https://doi.org/10.1038/s41467-023-41780-yNature Communications |         (2023) 14:6031 3��� ����������������������� ��������������� ��� ��������������� ��� ������������������ ����������Fig. 2 | Mapping heterochiral CDW domains with four-dimensional scanningtransmission electronmicroscopy (4D-STEM). a Schematic illustrating 4D-STEMof annealed 1T-TaS2 samples. Three compositionally distinct flake regions arelabeled as r1, r2 and r3. The two heterochiral superlattices are marked as α and β.bOptical micrograph of a 20-layer annealed 1T-TaS2 sample S3. Regions of interestand their H-TaS2 proportion (x/n, where x = number of H-TaS2 layers and n = totalnumber of layers), calculated from optical contrast measurements, are labeled.Scale bar: 10μm. c, d The maximal diffraction patterns, displayed on a logarithmicscale, for S3--R3 (c) and S3--R5 (d). Scale bars: 5 nm−1. e, f Illustration of CDWsuperstructures for α,β (e) and α,α (f). Unit cells of the CDW superstructures areoutlined in black. g–j (β − α) / (β +α) virtual dark-field images and their histogramsfor R2--R5 regions of S3. Insets show the proposed sample composition and plau-sible chirality stacking based on the H-TaS2 content and 4D-STEM analysis of eachregion. We note that only the net chirality can be determined, and the exactstacking sequence of the chirality shown here is one of several possibilities as theprecise sequence cannot be obtained from plan-view 4D-STEM. All 4D-STEM datawas acquired at room temperature. Scale bars in g–j: 50 nm.   ��                    Fig. 3 | Optical detection of chirality in TaS2 heterostructures. a Schematic of apolarization-dependent Raman measurement. b, c Raman spectra in the circularcontrarotatingpolarization configurations (σ+σ− and σ−σ+) obtained for regionR1 (b)and region R3 (c) of a 20-layer sample S4. Lorentzian peak fits and the cumulativefits are displayed. d Stacked bar charts displaying the normalized area percentageof Eg(I) and Eg(II) modes measured in the two contrarotating Raman polarizationconfigurations (top: σ+σ−, bottom: σ−σ+) for R1–R3 of S4. Forb–d, x/n denotes theH-TaS2 proportion. Data was obtained at room temperature.Article https://doi.org/10.1038/s41467-023-41780-yNature Communications |         (2023) 14:6031 4transformed regions, on average, exhibit a weaker overall chiralitycompared to medium transformed regions (Fig. 2g–j). Notably, ourverti-lateral heterostructures exhibit a broad spectrum of possibleoverall chiralities, distinguishing them from 1T-TaS2 flakes/homo-interfaces and heavily transformed H-TaS2/1T-TaS2 heterostructures,which can onlymanifest a single enantiomorphic state23,36. Specifically,the former are homochiral, comprising fully of α or β36, while the latterhave been shown to be achiral, hosting an equal proportion of α andβ23. Accordingly, our verti-lateral heterostructures may enable chiralopto-electronic memory schemes through their wide array of chiralstates that can generate strong optical responses at roomtemperature.Multistate resistance and chirality switchingElectronic properties of these heterochiral endotaxial polytype het-erostructures were probed using variable-temperature transportmeasurements. In these studies, we monitored the temperature-dependent longitudinal resistance (Rxx) of mesoscopic devices fabri-cated fromS1 (Fig. 4a) and S4 (Supplementary Fig. 18c).Measurementsfrom compositionally distinct regions (Fig. 4b) were used to establishthe relationship between polytype composition and the IC-to-C CDWphase transition behavior. For all measured regions, transport below300 K is dominated by the metallic H-TaS2 layers (decreasing resis-tance with decreasing temperature), while transport above roomtemperature traces CDW transitions of 1T-TaS2 lamellae (Fig. 4c,d).These transport data were complemented with temperature-dependent 4D-STEM of representative heterostructures to providestructural insight (Fig. 4e–g). Above room temperature, 1T-TaS2transforms from the IC (more conductive) to the C (more insulating)CDW phase with a hysteresis between cooling and warming profiles(Fig. 4c–e)11. As a general observation, increasing H-TaS2 content leadsto narrowing of the thermal hysteresis (Fig. 4c), which indicates sta-bilization of the ordered C-CDW state. These observations lie inagreement with our confocal Raman measurements; consistentlysharper CDW Raman features are observed for samples with a higherH-TaS2 content (Fig. 1e and Supplementary Figs. 15 and 16).Interestingly, the formation ofH-TaS2 layers dictates the stepwiseevolution of resistance and chirality with temperature in these endo-taxial polytype heterostructures. Upon cooling, we observe a series ofstepped resistance increases (Fig. 4d), with the step count matchingthe number of 1T-TaS2 slabs determined from DPC-STEM images ofdevice cross-sections. Thus, the H-TaS2-separated 1T-TaS2 lamellaebehave as isolated crystals with distinct IC-C CDW transitions, likelydue to the electronic decoupling imposed by the metallic (H-TaS2)spacers23. For this reason, the number of H spacer layers determinis-tically encodes the number of resistance steps, and the profile (mag-nitude of resistivity change) of each step is governed by the variousthicknesses of the 1T-TaS2 segments; thicker 1T-TaS2 slabs exhibitsharper CDW transitions, as observed in freestanding 1T-TaS2crystals17,18. We note that resistance traces upon warming are notice-ably broadened relative to the respective cooling sweeps. This may beunderstood by considering that strength of defect pinning is con-tingent on the CDW phase15,17,28,39. Defects may exert stronger pinningeffects on the CDWdomains in the localized C-CDWstate compared tothe “melted" IC-CDW phase, leading to less well-defined transitionsupon warming. Nevertheless, the stepwise resistance transitions areFig. 4 | Multistate resistance and chirality switching in TaS2 heterostructures.a Optical micrograph of a mesoscopic device fabricated from annealed flake S1.Scale bar: 10μm. bDiagrams of sample composition for S1 and S4. For S1, diagramsare derived from atomic resolution DPC-STEM data, while for S4 the structure isproposed based on the ΔOCR-derived H-TaS2 content. Note, for S4, the H-TaS2layers are randomly placed in themodel. cTemperature-dependent resistanceof S1in regions R1–R3 and S4 in region R2. The marked x/n denotes the H-TaS2 pro-portion. d High-temperature section of c. Curves were vertically shifted for clarity.Inflection points in the cooling curve are marked by a circle. Scaling factors of theresistance curves are indicated on the right. Inset shows the resistancemodulationof S4--R2 in five thermal cycles. Temperature ramp rate in c, d was 1 K/min.e Representative temperature-dependent 4D-STEM diffraction patterns, displayedon a logarithmic scale, for a 20-layer heterostructurewithfiveH-TaS2 lamella. Insetsdisplay a zoomed-in view of a primary Bragg spotwith labeledCDW superstructurepeaks. Scale bars: 5 nm−1. f Normalized mean intensity of α, β and incommensurate(IC) diffraction peaks in 4D-STEM datasets obtained at different temperatures forthe heterostructure in e. g Temperature-dependent (α − β)/(α + β+IC) calculatedfrom f. For e–g, heating was performed in situ and the data were acquired uponcooling from 373 K at 1 K/min.Article https://doi.org/10.1038/s41467-023-41780-yNature Communications |         (2023) 14:6031 5highly reproducible in subsequent cooling cycles (Fig. 4d and Sup-plementary Figs. 17 and 18d). Moreover, in addition to the resistancesteps upon cooling, temperature-dependent 4D-STEM reveals step-wise appearance of the α (L) and β (R) C-CDW enantiomorphs in con-cert with vanishing of the achiral IC phase (Fig. 4e-g). Thus, the IC-CCDW transition in our endotaxial heterostructures is marked both bysimultaneous evolution of resistance and overall chirality (Fig. 4g),defined by the proportion of chiral superlattices: (α-β)/(α+β+IC). Thissynchronous switching sets the stage for optoelectronic devicescombining charge and chirality degrees of freedom.Polytype nucleation and designer heterostructuresLastly, having established the structure and multistate electronic/chiral switching in TaS2 endotaxial heterostructures, we turn to con-sidering the mechanism of nucleation of these polytype transforma-tions, finding them tobe facilitated bywrinkles and folds.Weobservedthat polymorph transitions in 1T-TaS2 flakes, evidenced by changes inΔOCR and sharpness of Raman spectral features associated with CDWmodes, generally emanate from wrinkles, tears, and folds in flakes(Fig. 5a–c and Supplementary Fig. 20). These microscale structuraldefects inevitably introduce differential stress, which can be accom-modated by strain (Fig. 5d)40–42, and this strain in turn can alter theenergetic barrier between polytypes43–46. Accordingly, one explanationfor the emanation of H-TaS2 at these features, is a strain-induceddecreased energetic barrier for the H–T transformation, facilitating innucleation of polytypic domains near stress points. In addition, dif-ferential stress in layered materials can also be accommodated byshear and slip between layers (Fig. 5e)42. This leads to the formation ofextended shear dislocations42, which as we observed in Fig. 1g–j,appear to be a prerequisite for the formation of 1T-TaS2/1H-TaS2/1T-TaS2 interfaces from 1T-TaS232. Specifically, in native 1T-TaS2, the Taions are directly aligned in the out-of-plane direction (Fig. 5f). How-ever, upon transformation of one layer to H-TaS2, crystallographicstacking with direct S–S overlap would be encountered (Fig. 5g). Wefind this configuration to be, on average, 8meVper Å2 higher in energyaccording to density functional theory calculations (see “Methods"section for calculation details). To eliminate this unfavorable interlayerinteraction, one of the 1T-TaS2 layers can slip across the trigonal�Fig. 5 | Nucleationof endotaxial polytype transformation. a,bOptical imageof a1T-TaS2flakebefore (a) and after (b) thermal annealing. Aflake fold ismarkedwith amagenta arrow. c Atomic ForceMicroscopy (AFM)map of b. d, eModels of 1T-TaS2bending at a fold or wrinkle that are accommodated by in-plane strain (d) orinterlayer shear and slip e. Models in d and e are adapted from ref. 42. f–h Stackingconfigurations of three TaS2 structures: interface of three 1T-TaS2 layers (f), 1T-TaS2/1H-TaS2/1T-TaS2 interface without layer sliding (g) and 1T-TaS2/1H-TaS2/1T-TaS2 interface with shifting of the topmost 1T-TaS2 layer (h). Violet dashed verticallines in f–h indicate the alignment of Ta ions between the three TaS2 layers. Blackdashed lines in (g) represent direct vertical overlap of sulfur ions between thetopmost andmiddle layers. i, jOptical micrograph (i) and illustration (j) of an hBN/1T-TaS2 heterostructure before annealing. k Optical micrograph of flake in i afterannealing. Yellow arrows indicate the direction of propagation of the blue H-TaS2domains. l AFM height profile of flake in i, k in the region marked with a magentaarrow.mMapofΔOCRafter annealingoverlaid on theopticalmicrograph (k). Flakeoutlines are added in i, k, and m. All scale bars are 5μm.Article https://doi.org/10.1038/s41467-023-41780-yNature Communications |         (2023) 14:6031 6prismatic interface (Fig. 5h), precisely as observed in Fig. 1g–j. Notethat interlayer slips are readily present at flake folds, wrinkles and tearsin 2D materials. Thus, polytype domains may form more readily inthose defect regions of 1T-TaS2. We surmise that polytype transitionsnucleate at macroscopic defect points due to the formation ofextended dislocations and/or decreasing of the 1T-H energy barrierdue to strain.We build upon these nanoscale insights to demonstrate thatmechanical/strain engineering of 1T-TaS2 may be used for rationaldesign of vertical/lateral TaS2 heterostructures. To this end, westacked a 14-layer 1T-TaS2 crystal onto a ~ 112 nm-thick hexagonalboron nitride (hBN) flake to deliberately impart local stress onto theregion of the 1T-TaS2 flake in the vicinity of hBN (Fig. 5i,j). Indeed, afterannealing, the H-TaS2 polytype formation, evidenced by ΔOCR, radi-ates away from the hBN/TaS2 interface (Fig. 5k–m). It is important tonote that coincident vertical/lateral heterostrucures are only formedupon annealing at moderate temperatures for short time periods, asextended or repeated heating leads to formation of predominantlyhomogeneous structures (Supplementary Fig. 21)23. Accordingly,intricate, multi-component device architectures could be realized bycombining substrate patterning with moderate thermal annealingconditions.DiscussionIn conclusion, we have demonstrated that highly tunable, verti-lateralpolytype heterostrucures of 1T-TaS2 andH-TaS2 can be synthesized bymoderate thermal annealing of nano-thick 1T-TaS2 flakes. Stress pointsin 1T-TaS2 are nucleation sites for the H-TaS2 domains, resulting inmulti-component flakes with coexisting vertical and lateral hetero-structures. The polytype composition of these heterostructures cannow be conveniently determined using the optical contrast metho-dology developed in this work, enhancing the accessibility for char-acterizing and studying complex TaS2 crystals. Further, we useelectron microscopy, Raman spectroscopy, and electronic transportstudies to showthat altering theH/1T ratio opensmanifoldpossibilitiesfor tailoring structural and electronic behavior of mixed polymorphcrystals. Interlayer coupling between 1T-TaS2 fragments is interruptedby H-TaS2 layers, and the increasing content of H-TaS2 correlates withgreater CDW commensuration, the appearance of optically detectableheterochiral CDW superlattices, and tunable chirality by modulatingthe α/β ratios. Furthermore, decoupled 1T-TaS2 fragments transitionfrom the IC-CDW to the C-CDW state independently at high tempera-tures and the resulting temperature-driven,multistate phase transitionis highly predictable: the number and size of resistance and steps isdefined by the count and placement of H-TaS2 layers within the poly-type heterostructure. Moreover, the changes in resistance areaccompanied by corresponding changes in chirality, resulting insimultaneous modifications of both optical and electrical properties.Given the precedent for fast switching in 1T-TaS2 usingelectrical5,7,15,27,47–50 and optical fields35,51, endotaxial H-TaS2/1T-TaS2heterostructures offer a rich framework as designer CDW materialsthat should exhibit multi-level switching between chiral CDW phases.The ability to predictably fabricate and control such well-definedphase change materials using low-energy external stimuli is a highlypromising roadmap toward next-generation computing and datastorage.MethodsMechanical exfoliation of 1T-TaS2The mechanical exfoliation of 1T-TaS2 (HQ Graphene) is done in an Arglovebox using an adhesive tape (Magic Scotch). The crystals areexfoliated onto 90nm SiO2/Si wafers, whose oxide layer is formed bydry chlorination followed by annealing in forming gas (Nova ElectronicMaterials). First, wafers are cut into ~1 × 1 cm pieces and cleaned for2mins in an oxygen plasma cleaner. The chips are then heated to200 °C on the glovebox hotplate while tessellating a sizeable(~3 × 3mm) 1T-TaS2 crystalwith the adhesive tape. Following this, chipsare takenoff thehotplate, andplaced shiny-side-uponto the tapewhilestill warm. The chips are then pressed for 10mins with finger pressure.Lastly, the tape is swiftly taken off the chips.Mechanical exfoliation of hexagonal boron nitrideThemechanical exfoliation of hBN (used as received fromT. Taniguchiand K. Watanabe) is performed in atomospheric conditions. First, a90 nm SiO2/Si wafer (Nova Electronic Materials) is cut into ~1 × 1 cmpieces and cleaned for 90mins in an ozone cleaner. Immediatelybefore the chip cleaning is complete, 3 hBN crystals (~ 1.5mm×1.5mm) are tessellatedwith an adhesive tape (Magic Scotch). Promptlyafter cleaning the chips, they are placed shiny-side-up onto the tapeand pressed for 10mins with finger pressure. After this, the tape isswiftly taken off the chips.Thermal annealing of 1T-TaS2 crystalsThe 1T-TaS2 flakes were annealed in high-vacuum (approximately 10−7Torr) by rapidly warming to 120 °C at 60 °C/min with a 5-minute hold.This is followedbyheating at 11.5 °C/min to 350 °Canda 30minholdat350 °C, before rapidly cooling to room temperature at 13.5 °C/min.Determination of layer count for TaS2 flakesFor flakes S1 and S2 that were studied by differential-phase-contrastscanning transmission electronmicroscopy (DPC-STEM)52, we countedthe number of layers in the atomic resolution data. For all other flakes,the number of layers was identified using optical contrast (OC) mea-surements, following the relationship between OC and thicknessestablished in ref. 53. The OC data was commonly obtained in con-junction with atomic force microscopy (AFM) to corroborate the OC-derived thickness.Preparation of samples for transmission electron microscopyFor c-axis imaging, we prepared our samples within an Ar gloveboxusing a custom-built transfer stage. This involved using a polymericstamp composed of a poly(bisphenol A carbonate) (PC) film covering apolydimethylsiloxane (PDMS) square on a glass slide. The PC/PDMSstampwas created by initially preparing a solution of PC in chloroformwith a concentration of 5 %w/w. The solution was then dispensed ontoa glass slide using a pipette and evenly distributed by placing itbetween two glass slides, which were promptly separated. Subse-quently, the slides were positioned with the PC side facing up on ahotplate set at 120 °C for 5mins, resulting in the formation of a rela-tively uniform PC film. This PC film was then precision-cut into smallsquares, ~2mm× 2mm in size, using a razor blade. Additionally,squares of PDMS, measuring approximately 4mm×4mm, were pre-pared and affixed to glass slides. To complete the stamp, a PC squarewas centered within the PDMS square. Finally, the stamp was placedwith the polymer side facing up on a hotplate set at 120 °C for 2mins.Next, the PC/PDMS stamp is used to pick up 1T-TaS2 flakes. To this end,1T-TaS2 flakes of interest were covered in PC for 3mins at 160 °C,followed by rapid cooling to room temperature. Then, flakes adheredto the PC/PDMS stampwereplaced onto a 200nm silicon nitride holeyTEMgrid (Norcada) bymelting the PCpolymer at 160 °C. The TEMgridunderwent a 5-minute cleaning process with O2 plasma immediatelybefore stacking to enhance flake adhesion. After stacking, the PC filmwas dissolved in chloroform for 20mins under ambient atmosphere,washed in isopropanol and dried with flowing N2.For imaging along the crystallographic ab-plane, cross-sectionalTEM samples were prepared by standard the standard focused ionbeam (FIB) lift-out procedure using Thermo Fisher Scientific Helios G4and Scios 2 FIB-SEM systems. A 200nm coating of Pt was depositedover the region of interest using an electron beam at 5 kV and 1.6 nA.This was followed by a deposition of 2.5 μ m Pt using a gallium-ionArticle https://doi.org/10.1038/s41467-023-41780-yNature Communications |         (2023) 14:6031 7beam at 8 kV and 0.12 nA. The initial lift-out was performed with a30 kV Ga beam and 3 nA probe current, followed by a 1 nA current forthe lift-out cleaning. Next, the samplewasmilledwith 30 kV and0.5 nAuntil reaching ~ 1μm thickness, followed by 16 kV and 0.23 nA thinningto 0.5μm. Next, a 5 kV beam, operated between 77-48 pA, was used tothin the sample to electron transparency. Lastly, final polishing wasdone at 2 kV and 43 pA.Nanofabrication of mesoscopic devices from TaS2heterostructuresAll nanofabrication steps were performed in the Marvell Nanofabri-cation Laboratory. In a typical procedure, electron beam lithography(100 kV Crestec CABL-UH Series Electron Beam Lithography System)was used to define electrical contacts. PMMA (polymethyl methacry-late) e-Beam resist was used for this purpose (950 PMMA A6, Micro-Chem). After lithography, reactive ion etching (RIE) with a mixture of70 sccm CHF3 and 10 sccm O2 (Semigroup RIE Etcher) was used toremove top TaS2 layers and expose a fresh surface immediately beforeevaporating Cr/Pt (1 nm/100nm) (NRC thermal evaporator). Afterovernight metal lift-off in acetone, electron-beam lithography wasused to define a Hall bar-shaped etchmask. Etching of the Hall bar wasaccomplishedby reactive ion etchingwith 70 sccmSHF6 and8.75 sccmO2 (Semigroup RIE Etcher). After the SHF6/O2 treatment, samples werecleaned for 20 seconds in a 40 sccm O2 plasma and consecutively thePMMA resist was dissolved in acetone for 20–30mins.Transmission electron microscopySelected area electron diffraction (SAED) patterns were obtained witha 40μm diameter aperture aperture (defining a selected diameterof ~ 720 nm on the sample) using FEI TitanX TEM operated at60–80 kV.Four-dimensional scanning transmission electron microscopy(4D-STEM) was performed on FEI TitanX (80 keV, 0.3 mrad indicatedconvergence semi-angle) with the Gatan 652 Heating holder for in-situheating experiments. The 4D-STEM data was analyzed with the py4D-STEM Python package37. First, peak detection in py4DSTEM was usedto identify the primary Bragg peaks and construct the reciprocal vec-tors of the host lattice. Next, CDW reciprocal vectors were calculatedfrom symmetry relations to the primary Bragg vectors. Subsequently,we constructed virtual apertures that mask the entirety of the dif-fraction space except for the CDW (α, β or IC) satellite peak regions(Supplementary Fig. 6a, b). These CDW virtual apertures were thenapplied to the 4D-STEM diffraction data to integrate the CDW inten-sities at each probe position. Note, we only integrated over the CDWsatellite peaks around the second and third-order primary Bragg peaksto minimize the diffuse scattering contribution. Further, we alsodefined a background (bg) virtual aperture to measure the diffusescattering background for each diffraction pattern (SupplementaryFig. 6a, b). This background was subtracted from the integrated CDWintensities at each probe position for a more accurate calculation ofenantiomorphic disproportion. Lastly, for the in-situ heating data, weconstructed small virtual apertures that exclude overlap regionsbetween the IC and the α/β peaks (Supplementary Fig. 6b).Differential phase contrast (DPC) STEM images52 were collectedon a Thermo Fisher Scientific Spectra 300 X-CFEG operating at 300 kVwith a probe convergence angle of 21.4mrad. The inner and outercollection angles of the quadrant detector were 15 and 54 mradrespectively. DPC-STEM images were reconstructed from the compo-nent images output by each quadrant using the py4DSTEM package37.Raman spectroscopyUltra-low frequency (ULF) Raman spectra (Horiba Multiline LabRamEvolution) of TaS2 heterostructures were obtained using a 633nmlaser excitation with the corresponding ULF notch filters at a power of50–80μW with 10 s acquisition times and 3 accumulations.Circularly polarized Raman spectroscopy was performed inbackscattering configuration along the ZZ direction. A 100 x objective(N.A. = 0.80) was used for focusing the incident beamonto the sampleand for collecting the scattered light. The Raman laser spot sizewas ~ 1μm. Circularly polarized light was achieved by using two linearpolarizers (LP1 and LP2) and a λ/4 waveplate (Supplementary Fig. 12).Electron transport measurementsTransport measurements were performed using standard lock-in tech-niques. Briefly, a 1μA alternating current (17.777 Hz) was appliedbetween the source and drain contacts while sweeping the temperaturein the PPMS DynaCool system. Concurrently, the longitudinal (Vxx)voltage wasmeasured with the SR830 lock-in amplifier. All phases were≤ 5, and the resistances were determined from Ohm’s law. All datadisplayed in this work displays the four-probe resistance except for themeasurement for S1-R1, which was taken in the 3-probe configuration.Density functional theory calculationsDensity Functional Theory (DFT) calculationswere carried out using theVienna Ab initio Simulation Package (VASP)54–57 with projector aug-mentedwave (PAW)pseudopotentials58,59 includingTa 5pd, 6s, andS3spelectrons as valence. The plane-wave energy cutoff was set to 400eVand the k-point grids were Gamma-centered with a k-point spacing of0.3Å−1 for the 1T phase and 0.2 Å−1 for the 1H phase, which gave anenergy convergenceof 1meVper atom.The convergence criteria for theelectronic self-consistent loop was set to 10−7 eV. Structural optimiza-tions were done using the PBEsol60 exchange-correlation functionaluntil the residual forces on the ions were less than 0.001 eVÅ−1.The energy gain for the interlayer slip observed byDPC-STEMwasdetermined by DFT calculations on mixed phase structures. A shiftbetween 1H and 1T layers of (2a/3, b/3), where a and b are the 1H latticeparameters,was introduced to eliminate direct S-Soverlap. This shift iscomparable to the offset between layers in the 6R-TaS2 phase. In a6-layer 1H/1T-α/1T-α stack, the energy gain with interlayer slip was8meVÅ−2.Data availabilityRaw datasets used to generate figures in the main text are publiclyavailable on Zenodo61. Additional data is available from the corre-sponding author upon request.Code availabilityExemplary code used for 4D-STEMdata processing is publicly availableon Zenodo62.References1. Gruner, G. Density Waves In Solids (CRC press, 2018).2. Lankhorst, M. H., Ketelaars, B. W. & Wolters, R. A. Low-cost andnanoscale non-volatile memory concept for future silicon chips.Nat. Mater. 4, 347–352 (2005).3. Wuttig, M. & Yamada, N. Phase-change materials for rewriteabledata storage. Nat. Mater. 6, 824–832 (2007).4. Stojchevska, L. et al. 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This material is based upon work supportedby the Air Force Office of Scientific Research under AFOSR Award No.FA9550-20-1-0007. B.H.G. was supported by the University of CaliforniaPresidential Postdoctoral Fellowship (PPFP) and the Schmidt ScienceFellows, in partnership with the Rhodes Trust. Work at the MolecularFoundry, LBNL was supported by the Office of Science, Office of BasicEnergy Sciences, the U.S. Department of Energy under Contract no. DE-AC02-05CH11231. Confocal Raman spectroscopy was supported by aDefenseUniversityResearch Instrumentation Programgrant through theOffice of Naval Research under award no. N00014-20-1-2599 (D.K.B.).Electron microscopy was, in part, supported by the Platform for theAccelerated Realization, Analysis, and Discovery of Interface Materials(PARADIM) under NSF Cooperative Agreement no. DMR-2039380. Thiswork made use of the Cornell Center for Materials Research (CCMR)Shared Facilities, which are supported through theNSFMRSECProgram(no. DMR- 1719875). The Thermo Fisher Spectra 300 X-CFEG wasacquired with support from PARADIM, an NSF MIP (DMR-2039380) andCornell University. Other instrumentation used in this work was sup-ported by grants from the Canadian Institute for Advanced Research(CIFAR-Azrieli Global Scholar, Award no. GS21-011), the Gordon andBetty Moore Foundation EPiQS Initiative (Award no. 10637), the W.M.Keck Foundation (Award no. 993922), and the 3M Foundation throughthe 3M Non-Tenured Faculty Award (no. 67507585). K.W. and T.T.acknowledge support from JSPS KAKENHI (Grant Numbers 19H05790,20H00354, and 21H05233). S.M.R acknowledges support from theSCGSR program, the IIN Ryan Fellowship, and the 3M NorthwesternGraduate Research Fellowship. S.H. acknowledges support from theBlavatnik Innovation Fellowship. K.I. acknowledges support from theEPSRC (EP/W028131/1).Author contributionsS.H. and D.K.B. conceived the study. S.H. and A.M. fabricated the sam-ples. S.H., B.H.G., M.P.E., and K.C.B. performed the experiments. K.I. andS.M.G. carried out the DFT computations. S.H., S.M.R., and C.O. devel-oped the code for the virtual apertures. T.T. and K.W. provided the hBNcrystals. S.H. and D.K.B. wrote the manuscript with input from all co-authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-41780-y.Correspondence and requests for materials should be addressed to D.Kwabena Bediako.Peer review information Nature Communications thanks Suk HyunSung, and the other, anonymous, reviewer(s) for their contribution to thepeer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023Article https://doi.org/10.1038/s41467-023-41780-yNature Communications |         (2023) 14:6031 10https://doi.org/10.5281/zenodo.8201515https://doi.org/10.5281/zenodo.8201515https://doi.org/10.5281/zenodo.8216192https://doi.org/10.5281/zenodo.8216192https://doi.org/10.1038/s41467-023-41780-yhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Encoding multistate charge order and chirality in endotaxial heterostructures Results Commensuration in verti-lateral TaS2 heterostructures Diverse chirality in polytype heterostructures Multistate resistance and chirality switching Polytype nucleation and designer heterostructures Discussion Methods Mechanical exfoliation of 1T-TaS2 Mechanical exfoliation of hexagonal boron nitride Thermal annealing of 1T-TaS2 crystals Determination of layer count for TaS2 flakes Preparation of samples for transmission electron microscopy Nanofabrication of mesoscopic devices from TaS2 heterostructures Transmission electron microscopy Raman spectroscopy Electron transport measurements Density functional theory calculations Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information