Atomic lattice disorder in charge-density-wave phasesof exfoliated dichalcogenides (1T-TaS2)Robert Hovdena, Adam W. Tsenb,c,d, Pengzi Liua, Benjamin H. Savitzkye, Ismail El Baggarie, Yu Liuf, Wenjian Luf,Yuping Sunf,g,h, Philip Kimi, Abhay N. Pasupathyb, and Lena F. Kourkoutisa,j,1

aSchool of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853; bDepartment of Physics, Columbia University, New York, NY 10027;cInstitute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada; dDepartment of Chemistry, University of Waterloo, Waterloo,ON N2L 3G1, Canada; eDepartment of Physics, Cornell University, Ithaca, NY 14853; fKey Laboratory of Materials Physics, Institute of Solid State Physics,Chinese Academy of Sciences, Hefei 230031, People’s Republic of China; gHigh Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031,People’s Republic of China; hCollaborative Innovation Centre of Advanced Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China;iDepartment of Physics, Harvard University, Cambridge, MA 02138; and jKavli Institute at Cornell for Nanoscale Science, Ithaca, NY 14853

Edited by Jian Min Zuo, University of Illinois, Urbana–Champaign, Champaign, IL, and accepted by Editorial Board Member John A. Rogers August 15, 2016(received for review April 25, 2016)

Charge-density waves (CDWs) and their concomitant periodic latticedistortions (PLDs) govern the electronic properties in several layeredtransition-metal dichalcogenides. In particular, 1T-TaS2 undergoes ametal-to-insulator phase transition as the PLD becomes commensu-rate with the crystal lattice. Here we directly image PLDs of thenearly commensurate (NC) and commensurate (C) phases in thin,exfoliated 1T-TaS2 using atomic resolution scanning transmissionelectron microscopy at room and cryogenic temperature. At lowtemperatures, we observe commensurate PLD superstructures,suggesting ordering of the CDWs both in- and out-of-plane. Inaddition, we discover stacking transitions in the atomic lattice thatoccur via one-bond-length shifts. Interestingly, the NC PLDs existinside both the stacking domains and their boundaries. Transitionsin stacking order are expected to create fractional shifts in theCDW between layers and may be another route to manipulateelectronic phases in layered dichalcogenides.

TaS2 | charge-density wave | 2D materials | electron microscopy | STEM

Layered transition-metal dichalcogenides (TMDs), such as TaS2or TaSe2, are prototypical charge-density-wave (CDW) systems

that spontaneously break lattice symmetry through periodic latticedistortions (PLDs). PLDs are associated with dramatic electronicchanges such as metal-to-insulator transitions (1). Upon coolingfrom the normal metal phase at >543 K, the 1T polymorph ofTaS2 undergoes several CDW transitions until it finally entersa strongly insulating phase at low temperature where the PLDis commensurate with the crystal lattice (2, 3). In addition tothermal and pressure-induced transitions (4), recent work onthin, exfoliated 1T-TaS2 flakes has demonstrated thickness-tuned conductivity and external electronic control (5). WhereasCDWs at the surface of bulk crystals have been carefully mappedusing scanning tunneling microscopy (STM), less is knownabout the CDW/PLD structure and stacking order in thin,exfoliated TMDs.Recent theoretical calculations (6–8) and surface measure-

ments (9–11) suggest that the electronic structure of 1T-TaS2 iscritically dependent on the CDW stacking order along the caxis. However, previous work has focused on phase changes ofthe CDWs alone and variations in atomic lattice stacking werenot discussed. Such changes in local topology can have a largeinfluence on the implementation of actual devices based on 2Dmaterials (12). This became apparent in bilayer graphene,where stacking boundaries dominate the bulk transport be-havior (13, 14). The layered TMDs have additional complex-ities—CDW/PLD structure, sensitivity to oxidation (5), andlattice stacking order—that solicit real-space characterizationwith atomic resolution.Here, we use aberration-corrected and cryogenic scanning

transmission electron microscopy (STEM) paired with modernexfoliation techniques to interrogate the PLD structure of thin

1T-TaS2 in both plan-view and cross-section, revealing local vari-ations in PLD coherence across layers and the presence ofstacking faults in the atomic lattice. We demonstrate that STEMprovides a direct measurement of PLD structures in both room-and low-temperature phases of CDW materials.

Results and DiscussionA PLD is a spatial modulation of nuclei positions that accom-panies the electric field of a CDW (15) and minimizes thecrystal’s free energy (16, 17). For 1T-TaS2, the atomic sites of theperfect lattice (r) are displaced (r′) by three modulation wavesand harmonics thereof:

r′= r+Am,n,l sin�qm,n,l · r+ϕm,n,l

�,n

qm,n,l =mq1 + nq2 + lq3;m, n, l∈Z

o.

[1]

The modulation q vectors are directly visible from reciprocal spacepeaks via electron diffraction (1, 5, 18). To allow direct correlationof the real and reciprocal space structure over smaller domains (∼5–100 nm wide) than possible by conventional electron diffraction,here we use atomic lattice images and their fast Fourier transforms(FFTs). In addition to the atomic Bragg peaks, the reciprocal spacestructure exhibits PLD peaks based on their wave vectors qm,n,l withintensities governed by the amplitude Am,n,l and phase ϕm,n,l of each

Significance

Low-dimensional materials, such as 1T-TaS2, permit uniquephases that arise through electronic and structural reshapingknown, respectively, as charge-density waves and periodiclattice distortions (PLDs). Determining the atomic structure ofPLDs is critical toward understanding the origin of thesecharge-ordered phases and their effect on electronic proper-ties. Here we reveal the microscopic nature of PLDs at cryo-genic and room temperature in thin flakes of 1T-TaS2 usingatomic resolution scanning transmission electron microscopy.Real-space characterization of the local PLD structure across thephase diagram will enable harnessing of emergent propertiesof thin transition-metal dichalcogenides.

Author contributions: R.H., A.W.T., I.E.B., P.K., A.N.P., and L.F.K. designed research; R.H., A.W.T.,P.L., I.E.B., Y.L., W.J.L., Y.P.S., and L.F.K. performed research; R.H., P.L., B.H.S., I.E.B., and L.F.K.analyzed data; Y.L. and W.J.L. grew specimens; Y.P.S. grew crystals; and R.H., P.L., B.H.S., I.E.B.,and L.F.K. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. J.M.Z. is a Guest Editor invited by the EditorialBoard.1To whom correspondence should be addressed. Email: lena.f.kourkoutis@cornell.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1606044113/-/DCSupplemental.

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PLD (19, 20). The reciprocal space structure of a single layer isderived in SI Appendix.For 1T-TaS2, the PLD phase transitions correspond to small

changes in q and A (3, 21, 22). In the low-temperature commen-surate (C) phase (<∼183 K) the PLD wave vectors are rationalfractions of the lattice constant—forming the familiar “Star ofDavid” with 13 Ta sites (Fig. 1A) in real space. At higher tem-peratures (280 < T < ∼354 K) the wave vectors are nearly com-mensurate (NC) with the Bragg lattice—each PLD wave vector (qi)undergoes a small rotation from ∼12° to 13.9° and increases itsmagnitude by ∼2%, although these values are temperature de-pendent and show hysteresis (3, 18).Here we observe, at atomic resolution, the PLDs in a TMD—

exfoliated 1T-TaS2—with STEM. High-angle annular dark-field(HAADF)-STEM uses elastically scattered high-energy elec-trons to obtain a projection image of the nuclei’s positions in athin specimen, where intensity scales to first order with theproton number (Z) of each nucleus (23–25). HAADF-STEMprovided atomic-resolution images of the NC and C phases uponin situ cooling from 293 to 95 K. Experimental details are pro-vided in SI Appendix.The transition to the C phase is clearly visible in real space with

cryo-STEM, and is marked by the appearance of a low-frequency (λ ∼1.2 nm) commensurate modulation consistent with a

ffiffiffiffiffi13

p×

ffiffiffiffiffi13

psupercell (Fig. 1D and SI Appendix, Figs. S3 and S5). Overlays inFig. 1D highlight a unit cell in the commensurate PLD. Whereasprevious STM results track 1T-TaS2 CDWs at the surface only (26–28), we measure modulations even in projection images of ∼65-layer-thick regions. Here, the thickness of the flake was determinedfrom convergent beam electron diffraction patterns recorded in thesame area (SI Appendix). The visibility of this ∼1.2-nm periodicityconfirms that the PLD stacking along the c-axis is at least partiallyordered for the commensurate phase. For disordered stacking, thesupercell would be lost when viewed in projection. Ordering of theCDWs/PLDs in the out-of-plane direction has previously beenstudied theoretically using free-energy calculations (16, 29, 30).Compared with the most ordered system, where CDWs are alignedin all layers (Fig. 1B), the energy is lowered by translating the

CDW from one Ta site to another Ta site (Fig. 1C), which reducesoverlap of interlayer charge (1, 16). Nakanishi and Shiba havepredicted several low-energy partially ordered CDW arrangements(30). For some, the CDW maxima occur only on a subset of the13 Ta sites (Fig. 1A). In projection such partial ordering wouldproduce periodic superstructures as we observe experimentally.The PLD is also visible in thinner specimens. Fig. 2 shows the

same 34-layer TaS2 flake at 293 K (Fig. 2A) and 95 K (Fig. 2B).Compared with the ∼65-layer flake in Fig. 1D, the real-spacecommensurate PLD modulation (λ ∼ 1.2 nm) in the thinnerregion appears more disordered (Fig. 2B). The observed increasein PLD disorder in this thinner sample may correlate with pre-vious conductivity measurements that showed that the CDWstructure becomes more metastable and the C phase suppressedas the number of TaS2 layers is reduced below ∼20 nm (5, 31).Note that our direct imaging results suggest C PLD disorder canexist even in 20-nm flakes. Quantifying the degree of disorder in-plane vs. out-of-plane is, however, hampered by the projectionnature of the imaging method.The transition from the NC to the C phase upon cooling is

confirmed in reciprocal space through HAADF-STEM FFTs. TwoFFTs of HAADF-STEM images from the same stacking do-main in a flake before and after cooling are shown as a compositeimage in Fig. 2C with the 93 K, C phase in blue and the 293 K, NCphase in red. The six bright peaks (circled white) mark the Braggspots of the atomic lattice. Additional sets of peaks surrounding thecentral beam correspond to the PLD wave vectors (SI Appendix).Most noticeably, second-order harmonic peaks mark the corners oflarge triangles—three of the large triangles for each phase are drawnover the FFT. The room-temperature triangles (red) are rotated andsmaller than the low-temperature triangles (blue), confirming theNC–C phase transition. Note that image compression and dis-tortion artifacts due to sample drift at low temperature ham-pered perfect alignment of the FFTs in Fig. 2 C and D.The NC–C phase change is more noticeable at low frequen-

cies. In the commensurate phase, a peak occurs at the six first-order q positions (Fig. 2D, blue). The NC phase shows a set of

95° K

TaS

A B C

D

Fig. 1. PLD ordering and atomic resolution HAADF-STEM imaging of thin C phase 1T-TaS2. (A) Within a layer, the commensurate PLD/CDW contains 13 Tasites in a hexagonal supercell (sulfur not shown). (B) Simple stacking of layers results in aligned PLDs with centers (marked red) atop each other. (C) Atranslation of the PLD between layers can be characterized by stacking vector T’ that connects central Ta sites (red arrows). (D) At 95 K the C-PLD structure isvisible in HAADF images of thicker exfoliated flakes, suggesting at least partial ordering of the PDLs in the out-of-plane direction. The PLD repeat structure ishighlighted by a blue parallelogram with 1.2-nm sides.

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PLD peaks surrounding each first-order q position (Fig. 2D,red), each with reduced intensity compared with the C peaks.Low-frequency spots in NC 1T-TaS2 have been reported with

electron diffraction (1), although often obscured by the zero-beam intensity, and have not been discussed. Because the NCPLD wave vectors are not commensurate with the Bragg peaks avast array of additional spots is geometrically permitted (detailsin SI Appendix) (1, 32, 33). We suggest that the array of low-frequency NC peaks observed here (Fig. 2D) constitutes high-order PLD harmonics from a first-order Bragg reflection. In theC phase, these high-order harmonics cannot be distinguished asthey lie at the same position. However, the existence of high-order harmonics in the NC PLD suggests that the first-orderpeaks of the C phase contain a coherent superposition of high-order harmonics. We observe changes in the appearance of theselow-frequency NC satellites between and across thin TaS2flakes—with asymmetric “moon” shapes and the appearance of afirst-order harmonic at the center of three satellites (SI Appen-dix, Fig. S2 D–F)—indicating local structure variation. However,tracking structural changes on short length scales such as defectsor stacking faults is difficult in Fourier space. These changes arerevealed by real-space imaging.The NC PLD real-space structure of 1T-TaS2 was characterized

in plan-view and cross-section using aberration-corrected HAADF-

STEM. Variations in the planar Ta–Ta interatomic distance wereextracted directly from the HAADF image using image analysisbased on a peak fitting algorithm (SI Appendix). The plan-view NCPLD structure displays visible variations in the Ta–Ta spacing de-spite being a projection of many layers (Fig. 3A and SI Appendix,Fig. S6). This can only occur if the interatomic spacings throughoutmany layers are correlated. Fig. 3A shows local domains in the NCphase (highlighted in green) with boundaries (dark regions) de-fined by an increased Ta–Ta interatomic spacing—reminiscent offractured Stars of David. In cross-section (<100> direction) we findthe PLD displays local stacking-order variations (Fig. 3B). Locallyordered regions containing three layer periodicities (Fig. 3D),consistent with the out-of-plane component measured in the FFT(Fig. 3C), were found directly adjacent to disordered regions (Fig.3E). Thus, the NC PLD is not fully coherent throughout thethickness of the flake and exhibits stacking faults, suggesting dis-order both in-plane and out-of-plane.To distinguish the PLDs from an amplitude modulation, all Ta

centers were determined using six-parameter Gaussian fits toreal-space HAADF-STEM data and a Fourier transform wastaken of the peak positions only. The presence of superlatticepeaks in the resultant FFT can only originate from atomic dis-placements (Eq. 1) and confirms our assertion of directly mea-suring PLDs. Using this approach, we observe PLDs in both

13

34 layers

A

B

DC

Fig. 2. Atomic resolution HAADF-STEM imaging of NC-to-C phase transition of thin 1T-TaS2. Upon cooling to 95 K, the room-temperature phase transitions fromthe NC (A) to the C phase (B) with C-PLD ordering visible in the HAADF image of 34-layer TaS2. (C) FFT of NC (red) and C (blue) images show hallmark PLD peakswithin the hexagonal Bragg peaks (marked white). (D) The NC phase has sets of three satellites occurring at low frequency, which converge into single spots in theC phase. (C) The second-order PLD peaks in the NC phase appear as singular spots that form large triangles (red triangles) that rotate and expand upon com-mensuration (blue triangles) at lower temperature. (Scale bar, 10 Å for A and B; 0.05 Å-1 for C and D.) Image processing described in SI Appendix.

A B

C

D

E

Fig. 3. Disorder in the PLD structure in exfoliated NC 1T-TaS2. (A) In plan-view (<001>), distortions in the atomic positions visualized by superposition of anHAADF-STEM image (gray) with a map reflecting the Ta–Ta interatomic spacing (green). (B) PLD domains in cross-section (<100>) provide visible modulationsin real space. (C) Additional peaks in the FFT (0.86 Å-1 field of view) show an out-of-plane component to the PLD vector. The strength and coherence of thePLD in cross-section is not uniform, with well-ordered (D) and less-ordered (E) regions. Cross-section images (B, D, and E) have been bandpass-filtered withcolormap applied to enhance PLD visibility. Image processing described in SI Appendix.

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cross-section and plan-view (SI Appendix, Figs. S6 and S7). In theC phase, the atomic displacements due to PLDs were between 11and 15 pm (SI Appendix, Fig. S3). These displacements are aboveour measurement precision around 3 pm (SI Appendix, Fig. S4)and consistent with previous bulk X-ray measurement (32);however, higher accuracy may be achievable with recent imageacquisition and nonrigid registration schemes (34–36). The ap-pearance of PLDs remained relatively stable and was not local toregions exposed to the beam, in contrast to other beam-inducedrestructuring recently observed in related materials (discussionin SI Appendix) (37, 38).In addition to disorder in the PLDs, crystallographic stacking

domains and their boundaries were revealed in exfoliated 1T-TaS2without destruction of the CDW. In Fig. 4A, 1T-TaS2 appears asbright Ta atoms in a trigonal array. This is the expected stacking forthe perfect 1T polymorph, which we denote as A..A.. (Fig. 4 C andG). However, A..B.. stacking domains with a hexagonal array of Taatoms were also present in the same flake (Fig. 4B). Both stackingarrangements in regions near the stacking boundary contain NCPLD peaks in the FFTs (Fig. 4 A and B, Insets).The boundary between stacking orders is an in-plane translation

of one bond length (1.94 Å) that occurs over several nanometers(illustrated in Fig. 4 D and H). It is a translation of top and bottomlayers separated by a single interlayer fault (hence A..B.. notation)as shown in cross-section (Fig. 4 E–H). A stacking boundaryspanning ∼3 nm is shown experimentally in Fig. 4D. Here, thetransition is qualitatively consistent with both compressive andshear strain components (illustrated in Fig. 4C) as previouslyreported for graphene (13). Geometric phase analysis (SI Appen-dix, Fig. S11) of this region confirms the transition contains com-pressive strain (>1.5%) confined to an ∼3-nm region. HexagonalTa (A..B..) domains in 1T-TaS2 were minority regions but not

rare—boundaries were identified in many of the characterizedflakes. No fewer than three stacking faults were found across the∼7-μm-long and less than 50-nm-thick cross-section sample. In oneinstance, a hexagonal A..B.. domain transitions to a thin A..A..domain roughly 15 nm wide, then returns back to hexagonal A..B..or B..A.. stacking (SI Appendix, Figs. S12 and S13).We expect a lattice translation will also translate its CDW

structure, creating unique topological properties at the stackingboundary and between the adjacent layers of the stacking fault.The observed A..B.. domains (Fig. 4B) create a fractionaltranslation in the CDW where a layer’s CDW peaks (on Ta sites)lie at an adjacent layer’s sulfur sites. Previous theoretical (6) andexperimental (9, 10) results already demonstrated the impor-tance of CDW stacking order on the electronic properties of 1T-TaS2; however, fractional translations were not considered. Weexpect that the electronic structure will be distinct between thelayers at the stacking fault and could dominate the properties inthin films.

ConclusionsIn summary, direct imaging of periodic lattice displacements inlayered TMDs (1T-TaS2) revealed the presence of disorder in-trinsic to PLDs or crystal stacking. At room temperature wedemonstrate that these two forms of disorder can coexist inthe system. Compared with surface-sensitive techniques such asSTM, HAADF-STEM probes the nuclei positions of the entirethin specimen in projection, with particular sensitivity to high-Zelements like Ta. With cryo-STEM we observed phase transi-tions in the CDW material—e.g., the NC-to-C phase transitionof exfoliated 1T-TaS2. In the C phase, the PLD superstructure isresolved in projection images of specimens as thick as ∼65 layers,suggesting at least partial ordering of the CDW in the out-of-plane

10 Å

5 Å

Ta S A..B.. A..A..

plan-view cross-section

5 Å

10 ÅA..B.. A..A..

A

B

A

A

A B E F

GC

D H

Fig. 4. Atomic imaging of stacking-order domain boundaries in thin 1T-TaS2. Bright atoms represent Ta in these HAADF-STEM images. (A and E) Oftenobserved, a trigonal stacking (denoted A..A..) arrangement in which all Ta atoms lie atop each other when viewed along the c axis (planar vector). (B and F)Hexagonal stacking (denoted A..B..) was also observed with roughly half of the layers having Ta sites shifted one bond length relative to the other layers.(A and B, Insets) A cropped FFT from each specimen region with NC PLD peaks present in both stacking domains. (C and G) Illustrations show the stackingarrangements as they transition from A..A.. to A..B.. (D) The domain boundary between the two stacking orders transitions continuously over ∼30 Å fromtrigonal (Left) to hexagonal (Right) stacking. A transition is shown in (D) plan-view (<001>) and (H) cross-section (<100>).

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direction. Aberration-corrected electron microscopy at roomtemperature revealed disordered regions in the NC PLD andlattice in both plan-view and cross-section. Furthermore, changesin atomic lattice stacking orders and the corresponding stackingboundaries were resolved at room temperature. These stackingfaults should create fractional translations in the CDW and areexpected to affect the electronic properties especially in thinfilms. A systematic study across temperatures, combined withaberration correction, could unveil the kinematics of phasechange but will require further instrument optimization thatprovides stability for atomic resolution imaging at a wider rangeof temperatures. Looking forward, our work opens up the pos-sibility to explore microscopic origins of metastable phases andphase transitions in TMDs using temperature-controlled STEM.

ACKNOWLEDGMENTS. The work at Cornell was supported by the David andLucile Packard Foundation and made use of the Cornell Center for MaterialsResearch Shared Facilities supported through the National Science FoundationMaterials Research Science and Engineering Center (NSF MRSEC) program(Grant DMR-1120296). The FEI Company Titan Themis 300 was acquiredthrough the NSF Major Research Instrumentation Program (Grant NSF-MRI-1429155), with additional support from Cornell University, the Weill Institute,and the Kavli Institute at Cornell. Sample fabrication at Columbia Universitywas supported by the NSF MRSEC program through Columbia in the Centerfor Precision Assembly of Superstratic and Superatomic Solids (Grant DMR-1420634). Salary support was provided by Air Force Office of ScientificResearch (Grant AFOSR FA9550-11-1-0010 to A.N.P.). P.K. acknowledgessupport from Army Research Office (Grant W911NF-14-1-0638). Y.L., W.J.L.,and Y.P.S. acknowledge support from the National Key Research andDevelopment Program (Grant 2016YFA0300404), the National NatureScience Foundation of China (Grants 11674326 and 11404342), the JointFunds of the National Natural Science Foundation of China, and the ChineseAcademy of Sciences’ Large-scale Scientific Facility (Grant U1232139).

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