Introduction

Some exotic crystals spontaneously reorganize their valence electrons into periodic structures known as charge density waves (CDWs). In essence, two crystals emerge—the underlying atomic lattice and the emergent charge lattice. Just like atomic crystals, a charge density wave has defects: dislocations, disclinations, and elastic deformation1,2,3. Furthermore, the charge density wave can undergo phase transitions wherein the charge lattice unit cell changes shape and size. All of this CDW reshaping and topological restructuring occurs even when the underlying atomic lattice remains unchanged.

In low dimensions, these quantum phase transitions are promising candidates for novel devices4,5,6,7, efficient ultrafast non-volatile switching8,9,10, and suggest elusive chiral superconductivity11,12,13. Unfortunately, 2D CDWs are inherently unstable and accessing low-dimensional CDWs remains a challenge14,15,16. Even worse, at elevated temperatures where devices typically operate, disruption of charge density waves is all but guaranteed due to ever-present disorder17,18,19. A long-range ordered incommensurate CDW has yet to be reported.

Here we stabilize ordered incommensurate charge density waves (oIC-CDW) at elevated temperatures (TIC = 350 K) in two dimensions by endotaxial synthesis of TaS2 polytype heterostructures. The estimated hundred-fold amplitude enhancement of the in-plane charge density wave has an increased coherence length comparable to the underlying atomic crystal. The enhanced order of the oIC-CDW increases electronic resistivity. This substantial enhancement of charge order is achieved through encapsulation of an isolated octahedral TaS2 CDW layer within a matrix of prismatic TaS2 metallic layers via 2D endotaxial synthesis.

Realizing the ordered incommensurate CDW reveals CDWs have hexatic structure at high-temperature—that is, long-range translational symmetry is limited by proliferation of topological defects (i.e., dislocations and disclinations) in CDWs. We show at high temperatures, the CDWs in TaS2 continuously melt as additional dislocations and disclinations form in the charge lattice. This hexatic CDW melting process was not previously observable since the incommensurate CDW normally emerges as a highly-disordered, melted state. By restoring in-plane order through 2D endotaxy, we can reversibly melt and unmelt CDWs in TaS2. Based on these results, we access new regimes of the CDW phase diagram for octahedrally coordinated TaS2 in temperature vs. disorder space. Similar vestigial ordering (i.e., hexaticity) was predicted by Nie, Tarjus and Kivelson18; however, with 2D endotaxy we can now tune down the disorder in the CDW phase diagram.

Results

The ordered incommensurate charge density wave

The ordered incommensurate CDW (oIC) reported herein (Fig. 1a–d) is strikingly distinct from the well-known incommensurate (IC) CDW (Fig. 1e–h) found in 1T-TaS2 or 1T-TaSe2. Here, the oIC phase is a truly two-dimensional (2D) CDW with long-range positional and orientational order that couples strongly with the underlying crystal lattice (Fig. 1a). The oIC-CDW, illustrated in Fig. 1b, is a crystalline charge-lattice with well-defined, sharp peaks in Fourier space (Fig. 1b-inset). This CDW charge lattice (aCDW = 11.87 nm) exists within an underlying atomic lattice illustrated in Fig. 1c.

Fig. 1: Long-range ordered incommensurate charge density waves.
figure 1

a Schematic representation of ordered IC-CDW. The CDW is two-dimensional with little disorder. b Ordered IC-CDW illustrated as a crystalline charge-density lattice. Here, white spots represent charge centers. Inset) Fourier transform of the charge lattice shows well-defined peaks. c Associated periodic lattice distortions (PLDs) move tantalum nuclei (black spots) along the charge density gradient. Inset) Simulated diffraction shows sharp superlattice peaks decorating Bragg peaks. d Schematic representation of ordered IC-CDW in endotaxial polytype heterostructure. Mono- or few layers of endotaxially protected Oc-TaS2 hosts 2D ordered IC-CDWs. e Schematic representation of hexatic IC-CDW. The CDW phase is quasi-2D with non-trivial interlayer interactions, and hexatically disordered. f Charge density distribution is comparable to hexatically disordered crystal lattice. Inset) Structure factor reveals azimuthally diffused peaks—characteristics of hexatic phases. g Associated lattice distortion of IC-CDW with (inset) Fourier transform showing azimuthally blurred superlattice peaks while maintaining sharp Bragg peaks. h Schematic representation of hexatic IC-CDW in bulk 1T-TaS2 where every layer hosts disordered IC-CDW.

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Electron–lattice interaction is an essential aspect of CDWs, and associated soft-phonon modes manifest as static periodic lattice distortions (PLDs) that reduce crystal symmetry and lower the electronic energy20,21. For TaS2, the CDW pulls atoms toward the nearest charge maximum to form periodic clusters of atoms (Fig. 1c, see also Supplementary Fig. 1). Notably for incommensurate charge ordering, each cluster is distinct since the atomic lattice is not commensurate with the CDW22. While these lattice distortions are small (<10 pm), selected area electron diffraction (SAED) is sensitive to subtle picoscale distortions and making it a popular choice for characterization of CDW/PLDs23. CDW/PLDs diffract incident swift electrons into distinct superlattice peaks decorating each Bragg peak2,24,25,26. In reciprocal space, the CDW charge lattice (Fig. 1b-inset) and the measurable atomic superlattice peaks (Fig. 1c-inset) have corresponding spacing, symmetry, and intensity.

Diffracted superlattice peaks provide a direct measure of the CDW lattice and contain rich information on their order-disorder. Specifically, diffraction represents an ensemble average of the structure over the selected area, and disorder manifests as diffused diffraction peaks27,28. Disorder of CDWs smears superlattice peaks but leaves the principal Bragg peaks unaffected (Fig. 1g-inset). For oIC-CDWs, the charge lattice is ordered with limited defects, thus diffraction shows both sharp superlattice and Bragg peaks (Fig. 1c-inset). In contrast, the well-known IC-CDW in 1T-TaS2 possesses significant disorder of its charge distribution. Across decades, the IC phase in 1T-TaS2 is reported with a ring-like, azimuthally diffuse diffraction around each Bragg peak24,29,30,31, yet the origin of the diffused superlattice peaks is hardly discussed32,33.

Here, we present the well-known IC-CDW in bulk 1T-TaS2 as a hexatically disordered charge lattice containing dislocations and disclinations (Fig. 1f). In-situ SAED of 1T-TaS2 taken at 408 K (Fig. 2a) shows azimuthally blurred first order superlattice peaks (marked brown). Averaging all six third-order Bragg peaks (inset, Γ3) better highlights this point. Notably, hexatic phases are known to have six-fold rotationally symmetric, azimuthally diffused peaks34. The experimental diffraction of IC-CDWs are consistent with a hexatic charge distribution (Fig. 1f)28,33,34,35 and corresponding azimuthally diffuse structure factor (Fig. 1f, g-inset). The IC-CDWs are three-dimensional (or quasi-2D) with non-negligible out-of-plane interactions (Fig. 1e–h).

Fig. 2: Endotaxial polytype heterostructure of TaS2.
figure 2

a In bulk TaS2, an IC-CDW phase emerges above 350 K, with azimuthally diffused superlattice peaks characteristic of hexatic disorder. b oIC-CDW in endotaxial polytype heterostructure has enhanced long-range order and amplitude. Superlattice peaks are well-defined, sharper and brighter. c Evolution of IC-CDW during the endotaxial synthesis. Atomic resolution cross-sectional HAADF-STEM of (d) bulk and (e) heat-treated TaSxSe2-x confirms polytypic transformation. After treatment, Pr layers encapsulate monolayers of Oc layers. Scale bar is 2 nm. A selenium-doped sample was imaged to enhance chalcogen visibility. f Resistivity vs. temperature measurement of bulk (brown) and thermally-treated (red) TaS2 shows an increase in resistivity. In pristine sample, IC-CDW gives way to nearly commensurate (NC-) CDW around 350 K. In polytype heterostructure, twinned commensurate (tC-) CDW emerges at a similar temperature range.

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In contrast, the oIC-CDW shows drastically sharper and stronger superlattice peaks measured by in-situ SAED at 408 K (Fig. 2b). Sharpening is especially highlighted in averaged third-order Bragg peaks (Γ3, See Supplementary Fig. 2). The measured superlattice peaks of oIC-CDW are sharper both in azimuthal (by ~60%) and radial (by ~50%) directions when compared to the IC-CDW. Notably, the superlattice peak widths of the oIC phase is comparable to the peak widths of the principal Bragg peaks. Therefore, the oIC is a spatially coherent electronic crystal.

The oIC-CDW, a 2D charge-ordered state, is enhanced by at least one-hundred fold over previously reported bulk IC-CDWs. SAED uses a transmitted beam that measures the embedded oIC-CDWs and the metallic matrix. Diffracted superlattice peaks in oIC-CDWs have an integrated intensity over ten times stronger despite that the number of charge-ordered TaS2 layers has been reduced to less than 10% of the material. Thus, endotaxial engineering improves not only the long-range order but also the charge order amplitude of the IC-CDW.

Endotaxial polytype heterostructure of TaS2

The oIC-CDW phase reported herein is stabilized by synthesizing endotaxial polytype heterostructures of TaS2, where oIC-CDWs reside in monolayers of octahedrally coordinated (Oc-) TaS2 embedded within prismatic (Pr-) TaS2 matrix and one-to-one atomic registry (Fig. 2e). oIC phase occurs in isolated monolayers of Oc-TaS2, but multiple instances of monolayer Oc-TaS2 may be embedded in Pr-TaS2 matrix—especially in thicker specimens (See Supplementary Fig. 3). Endotaxial polytype heterostructures are synthesized by heating 1T-TaS2 at ~720 K for 15–30 min in an inert environment. Notably, 1T-TaS2 is metastable and goes through Oc-to-Pr endotaxial layer-by-layer polytype transformation upon heating (≳620 K, See Supplementary Video). As the layer-by-layer polytype transitions are uncorrelated, the final system is not well described by bulk polytype symmetry groups—including the periodic 4-layer unit cell called 4Hb. In-situ SAEDs (Fig. 2c i–iv) were acquired at 20 s intervals at 408 K through the high-temperature conversion process (723 K). Within the first 20 seconds formation of metallic layers isolate 2D Oc layers with oIC CDWs that contribute sharp superlattice peaks in the SAED. These snapshots reveal sharpening of superlattice peaks—a clear indicator of enhanced CDW order. Cooling the sample midst transition stops the conversion and an interleaved polytype heterostructure is synthesized—confirmed by cross-sectional ADF-STEM.

Figure 2d, e shows atomic resolution micrographs of bulk 1T endotaxially converted to a polytype heterostructure. The atomic resolution images demonstrate endotaxial monolayer encapsulation of Oc-TaS2 (Fig. 2e, highlighted red) in Pr-layers. The Pr-TaS2 (bulk: 2H, 3R) are metallic above ~100 K. Previous work showed these metallic layers decouple CDWs out-of-plane and raise the critical temperature for commensurate quantum states (i.e., C-CDW) from ~200 K to ~350 K36.

Surprisingly, the endotaxial polytype heterostructure stabilizes long-range order in IC-CDWs at elevated (≳350 K) temperatures. The oIC-CDW phase has a correlation length comparable to the crystal lattice, quantified by comparing widths of both superlattice and Bragg peaks from in-situ selected area electron diffraction patterns (SA aperture: 850 nm diameter). The FWHM (full width at half maximum) of CDW peaks are 10% larger than the Bragg peaks (See Supplementary Fig. 4). This indicates the CDW is relatively ordered (i.e., spatially coherent) over the distances comparable to the parent atomic crystal (~102 nm).

This enhancement of long-range CDW order is accompanied by an increase of the resistivity of the TaS2 (Fig. 2f). Figure 2f shows temperature vs. in-plane resistivity measurement of 1T (brown) and endotaxial (red) specimen. The resistivity of endotaxial TaS2 is higher for IC-CDW phases (>358 K), despite having many metallic layers introduced to the system. We observe an increase in resistance anisotropy (out-of-plane vs. in-plane) when the TaS2 is thermally treated into endotaxial heterostructure (Supplementary Fig. 5). In Fig. 2f, the flake was electronically contacted from the bottom (Supplementary Fig. 6). In this geometry, a sufficiently strong insulating layer can reduce current in conducting layers above. This implies that oIC-CDWs have higher resistivity than bulk 1T-TaS2.

Hexatic melting of IC-CDW

Creating the oIC-CDW provides an ordered charge lattice that can be hexatically melted upon further heating. Hexatic melting is a uniquely 2D process wherein a crystal melts in two stages through the creation of dislocations and disclinations35,37,38,39,40. During this process, the reciprocal space structure continuously evolves. Initially, at lower temperatures (c.a. 350 K), the oIC phase is an ordered charge crystal with well-defined peaks in reciprocal space (Fig. 3c). As temperature rises, the CDW peaks continuously blur azimuthally as the density of dislocations and disclinations increases (Fig. 3d, e). Azimuthal blurring of the reciprocal lattice is characteristic of hexatic phases and reflects the loss of translational symmetry while maintaining some orientational order34. Eventually, at higher temperatures (c.a. 570 K), the hexatic crystal completely dissociates into an amorphous liquid state with a ring-like structure factor. Figure 3c–e are generated using a phenomenological Monte Carlo simulation wherein displacement of the CDW charge centers follow a temperature-dependent Maxwell-Boltzmann probability distribution (See Methods). Here, the incommensurate CDW hexatically melts while the underlying atomic lattice remains unchanged—in diffraction this corresponds to a blurring of CDW superlattice peaks and preservation of Bragg peaks.

Fig. 3: Hexatic Melting of IC-CDWs.
figure 3

a Averaged in-situ SAED patterns showing oIC-CDW superlattice peaks in endotaxial heterostructure. i—iii) As temperature increases (408 K, 523 K, 573 K), superlattice peaks continuously blur along azimuthal direction. b Quantification of superlattice peak profile. b-blue) Azimuthal width of the peak continuously increases with temperature—a key feature in hexatic melting process. b-red) Integrated superlattice peak intensity of oIC phase monotonically decays as temperature increases despite the increase in peak width; CDW is weakening. c–e Monte Carlo simulation of 2D Lennard-Jones crystal with increasing temperatures. This represents the charge density distribution. As temperature increases, the crystal progressively disorders with increasing numbers of disclinations and dislocations. Insets) Structure factor of the simulated crystals. Sixfold symmetry is apparent. As temperature increases, peaks diffuse prominently along azimuthal direction.

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During the hexatic melting of oIC-CDWs, superlattice peaks increasingly blur as temperature is raised—clearly visible in in-situ SAED at Fig. 3a-i) 408 K, Fig. 3a-ii) 523 K, and Fig. 3a-iii) 573 K. The blurring is anisotropic and more prominent along azimuthal directions as expected for hexatic phases (See Supplementary Fig. 7). The CDW peaks are quantified throughout the melting process in Fig. 3b. Azimuthal peak width (Fig. 3b, blue-triangles) increases continuously with temperature; roughly doubling when raised from 410 K to 570 K. Around 520 K the oIC has melted into a state that resembles the well-known IC-CDW for bulk TaS2. This CDW melting process is reversible and peaks sharpen when temperature is decreased. Notably, Bragg peaks do not show appreciable changes indicating only the electronic crystal is melting, not the TaS2 atomic crystal.

Although the CDW melting process appears hexatic, it is distinct from familiar liquid crystals, silica spheres, or atomic crystals, wherein the amplitude of the order parameter does not change. Here, quantitative analysis of the superlattice peak intensities (Fig. 3a-red) reveals the charge density wave amplitude decreases with temperature. This is expected as topological defects in CDWs (dislocations and disclinations) have locally divergent strain with elastic energy cost that forces a local amplitude collapse. These local CDW amplitude collapses have been observed at the center of topological defects in the 3D charge ordering of manganites1.

The CDW phase diagram for octahedral TaS2

Endotaxial synthesis of octahedrally coordinated TaS2 allows access to new phases of matter and construction of a phase diagram for CDWs using temperature (T) and disorder (σ). The CDW phase diagram for 1T-TaS2 is shown in Fig. 4. 1T-TaS2 exists with native disorder and the ordered, commensurate phase (C-CDW, Fig. 4g) is only observed at low temperatures. At room temperature, the CDW is a partially-ordered NC phase (Fig. 4f) that enters the hexatic IC phase upon heating (Fig. 4e). At high temperatures or high disorder, CDWs degrade or vanish. Unlike lower temperature (<350 K) CDW phases in TaS2 with chirality (broken mirror symmetry)36,41,42, in both hexatic and ordered IC-CDW phases, this symmetry is not broken. The high disorder regime was historically achieved by substituting tantalum ions with other metal species (e.g., Ti, Nb) or by forcing intercalates within the van der Waals gap24. At room temperature, mild substitution of titanium (1T-Ta0.7Ti0.3S2) drives the system into hexatic-IC CDW states (Fig. 4h), and as more titanium is substituted (1T-Ta0.3Ti0.7S2) CDW vanishes completely (Fig. 4i).

Fig. 4: Phase diagram of octahedrally coordinated TaS2.
figure 4

a Schematic temperature vs. disorder phase diagram of octahedrally coordinated TaS2. As extrinsic disorder (σ) decreases, more ordered CDW phases are stabilized. At room temperature, polytype heterostructures with low disorder stabilize C-CDW (d) instead of NC-CDW (f), and long-range ordered IC-CDW (c) phase instead of hexatically disordered IC-CDW (e). Furthermore, it stabilizes CDWs (b) at higher temperatures than bulk 1T-TaS2 can (TCDW ≅ 540 K52). Substitutional disorder, on the other hand, destroys long-range order and hexatic IC-CDW is stable at room temperature (h) and leads to complete destruction of CDW eventually (i). b–i Electron diffraction patterns showing superlattice peaks around a single Bragg peak reveal the charge ordering states. h, i are adapted from Wilson et al.24.

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The low disorder regime, now accessible by endotaxial engineering, provides room temperature ordered C-CDWs36 and a novel ordered IC-CDW at higher temperatures. Notably with low-disorder, the C to IC transition is direct and the NC phase does not appear. The IC phase is ordered, but the CDW can be continuously melted into a disordered hexatic-IC phase (as described in Fig. 3). The structure and boundaries of the CDW diagram are drawn with consistency with theoretical considerations for 2D symmetry breakings18. The curvature of the phase diagram boundaries is qualitative but has a physical functional form: energy is proportional to temperature and disorder squared (E ∝ T, σ2). Therefore, with the choice of (\(\sqrt{{{{{{{{\rm{T}}}}}}}}}\), σ) axis, the equi-energy surface is elliptical. Notably, this phase diagram shares similar features with nematic-CDWS19,43 and 2D colloidal particles44.

Notably, CDWs in endotaxial TaS2 are two dimensional and the oIC phase has enhanced order despite the 3D to 2D dimensionality reduction. In bulk 1T-TaS2 CDWs are quasi-2D with non-negligible out-of-plane interaction (Fig. 1h)45,46,47,48. Formation of endotaxial polytype heterostructures disrupts the out-of-plane interactions and CDWs reside in a protected 2D environment36. Stabilization of an ordered IC-CDW in 2D seemingly contradicts with Hohenberg-Mermin-Wagner theorem14,15 and Imry-Ma argument17 which state spontaneous symmetry breaking of continuous symmetry (e.g., IC-CDWs) is unstable at non-zero temperatures in 2D. While both principles do not prevent intermediate phases with short-range order, the 2D CDWs should be nonetheless more fragile to disorder18. An ordered IC phase can only emerge in ultra-clean environments. Here endotaxial synthesis protects CDW states by strain-free encapsulation in a chemically identical environment of metallic layers that shield disorder. The reduction of environmental disorder provided by endotaxy may prove essential to accessing ordered CDW states in low dimensions.

Discussion

In summary, we demonstrate that endotaxial synthesis of clean interleaved polytypic heterostructures can stabilize fragile quantum phases such as ordered CDWs even at high temperatures. Here, we stabilize and enhance 2D charge density waves (both long-range order and amplitude) in an endotaxially confined monolayer of 1T-TaS2. Surprisingly, the low-dimensional symmetry breaking of an ordered incommensurate CDW (oIC-CDW) appears, suggesting the quantum states reside within minimal extrinsic disorder. By enhancing CDW order the hexatic nature of IC-CDWs is revealed. Experimental observation matches advanced simulation of electron diffraction of charge lattices to provide the real-space evolution of 2D CDW melting. Heating the oIC-CDW in-situ TEM above 400 K we see a reversible hexatic melting process in which disclinations and dislocations destroy long-range translational symmetry of the CDW while maintaining its orientational order. The CDW melts well before the underlying atomic crystal changes. In 2D, CDWs are expected to manifest through vestigial electronic hexaticity—a weak CDW with substantial defects and short-range order. The nature of vestigial phases in CDWs remains poorly understood with little direct evidence. From these results, a CDW phase diagram for 1T-TaS2 is created and consistent with the predicted emergence of vestigial quantum order.

Methods

Simulated diffraction of charge lattices with heating

Charge density waves are electronic modulations describable in reciprocal space by three wave vectors (so-called, triple q) or in real-space as local charges arranged into a hexagonal lattice. For a fully ordered system, the charge lattice is a perfect lattice (Fig. 1b left), and the structure factor (Fig. 1b left inset) is also a perfect lattice. Here, the periodicity is equal to the incommensurate CDW wave vector qIC (or aIC in real-space). Traditional CDW theory elegantly describes ordered (or slightly disordered) systems using sparse representation in reciprocal space for ordered systems. However, a real-space basis readily describes topological disorder (dislocations and disclinations) in a charge density wave. This becomes particularly critical for IC phase (>350 K) of 1T-TaS2, where diffraction studies reveal azimuthally diffused superlattice peaks24 that we show to be consistent with topological disorder in CDWs. Describing disorder of CDW plays a critical role in simulating experimentally consistent diffraction patterns at high temperatures.

The hexatic melting of a real-space charge lattice is illustrated with phenomenological Monte Carlo simulations of the NPT ensemble (constant particle count, temperature, and pressure). The displacement of charge centers in a CDW follows a Maxwell-Boltzmann probability distribution at different temperatures. The interaction energy between charge centers is calculated using a shifted Lennard Jones potential truncated at 18.7 Å. From these first principles, the likelihood of forming dislocations and disclinations in a CDW lattice increases with temperature.

Diffraction of the simulated CDWs is calculated from the corresponding PLD of a 1T-TaS2 crystal. The displacements are small (≲10 pm), but clearly manifest as superlattice peaks with distinctive intensity in SAED. Notably, the superlattice peak intensities become stronger at higher ∣k∣; this is distinguishable from chemically ordered superlattice peaks that decay as ∣k∣ increases23. In TaS2, atoms displace toward the charge centers which is equivalent to a longitudinal displacement wave. Here, the displacement amplitude is proportional to the charge density gradient with a max displacement set at 7 pm. Electron diffraction is kinematically simulated under flat Ewald Sphere approximations using the Fourier transform of the displaced atomic lattice.

Electron microscopy

In-situ SAED was performed on Thermofisher Scientific (TFS) Talos (operated at 200 keV, SA aperture 850 nm) with Protochips Fusion Select holder and Gatan OneView Camera. Cross-sectional HAADF-STEM images were taken on JEOL 3100R05 (300 keV, 22 mrad) from ~150 nm thick TaS2 specimen flakes prepared on TFS Nova Nanolab DualBeam FIB/SEM.

TEM specimens were prepared by exfoliating bulk 1T-TaS2 and 1T-TaSxSe2-x crystals onto polydimethylsiloxane (PDMS) gel stamp. The sample was then transferred to TEM grids using home-built transfer stage. Silicon nitride membrane window TEM grid with 2 μm holes from Norcada and Porotochips Fusion Thermal E-chips. From optical contrast and CBED patterns, the samples (Fig. 1, 2) were estimated to be 20–50 nm thick49,50.

Synthesis and acquisition of bulk crystals

1T-TaS2 for in-situ SAED measurements and electronic measurements was acquired from HQ Graphene. 1T-TaSxSe2-x (x ≈ 1) for cross-sectional HAADF-STEM measurements was grown by the chemical vapor transport method with iodine as a transport agent. Stoichiometric amounts of the raw materials, high-purity elements Ta, S, and Se, were mixed and heated at 1170 K for 4 days in an evacuated quartz tube. Then the obtained TaSxSe2-x powders and iodine (density: 5 mg/cm3) were sealed in another longer quartz tube, and heated for 10 days in a two-zone furnace, where the temperature of source zone and growth zone was fixed at 1220 K and 1120 K, respectively. A shiny mirror-like sample surface was obtained, confirming their high quality. All CDW characterization was done on 1T-TaS2; Se-doped sample was used only for polytype characterization in cross-sectional HAADF-STEM (Fig. 2d, e).

Endotaxial synthesis of oIC-CDW in TaS2

Interleaved 2D TaS2 polytypes were synthesized by heating 1T-TaS2 to 720 K in high vacuum (<10−7 Torr) or in an argon-purged glovebox36. 1T-TaS2 was held at 720 K for ~10 min, then brought down to room temperature. Once the interleaved polytype is fully established, the oIC-CDW becomes stable electronic state above 350 K51.

Device fabrication and electronic measurement

For resistivity measurements, TaS2 flakes were transferred using PDMS gel stamp method to pre-fabricated bottom contacts. The fabrication of bottom contacts is detailed in ref. 36. The flake was sculpted into rectangular bar (~11 μm × 15 μm) using TFS Nova Nanolab DualBeam FIB/SEM (See Supplementary Fig. 6). The thickness of the flake was determined by AFM. For anisotropy measurements, SiNx membrane with pre-patterned gold electrodes was transferred over the flake (See Supplementary Fig. 5).

Resistivity vs. temperature measurements were performed in a Quantum Design Dynacool PPMS using a standard sample puck and an external Keithley 2400 series source meter. The sample was adhered to the puck backplane with silver paint, and contacts were wire bonded to the puck channel pads using 50 μm Au wire. To ensure sample thermalization, a baffle rod with an Au-coated sealing disk hovering < 1 cm above the sample was inserted into the PPMS bore, and the heating and cooling rate was restricted to <2 K/min. 10 μA current was sourced for four wire measurements. The current/voltage limits were chosen to keep electric fields below 10 kV/cm to avoid sample breakdown, as well as to keep current densities below 105 A/cm2 and prevent localized heating at low temperatures.