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ARTICLEOPEN

Direct observation of mono-layer, bi-layer, and tri-layer charge
density waves in 1T-TaS2 by transmission electron microscopy
without a substrate
Daiki Sakabe1,2, Zheng Liu3,4, Kazutomo Suenaga2,4, Keiji Nakatsugawa1,2 and Satoshi Tanda1,2
Charge-density-waves, which occur mainly in low-dimensional systems, have a macroscopic wave function similar to superﬂuids
and superconductors. Kosterlitz–Thouless transition is observed in superﬂuids and superconductors, but the presence ofKosterlitz–Thouless transition in ultra-thin charge-density-waves systems has been an open problem. We report the direct realspace observation of charge-density-waves with new order states in mono-layer, bi-layer, and tri-layer 1T-TaS2 crystals using a low
voltage scanning-transmission-electron-microscopy without a substrate. This method is ideal to observe local atomic structures andpossible defects. We clearly observed that the mono-layer crystal has a new triclinic stripe charge-density-waves order withoutsatisfying the triple q condition q1 + q2 + q3 = 0. A strong electron-phonon interaction gives rise to new crevasse (line) type defects
instead of disclination (point) type defects due to the Kosterlitz–Thouless transition. These results reafﬁrm the importance of theelectron-phonon interaction in mono-layer nanophysics.
npj Quantum Materials (2017)2:22 ; doi:10.1038/s41535-017-0025-8

INTRODUCTION
Dimensionality and topology are the most important parameterscharacterizing physical systems. For example, the integral
and fractional quantum Hall effects (QHE)1, 2 are observed onlyin two-dimensional systems such as metal-oxide-semiconductorﬁeld-effect transistors, GaAs/AlGaAs interfaces, and graphene.3
Moreover, the conductivity of the QHE is characterized by
topological numbers. Dimensionality and topology are also ofimportance in the Kosterlitz-Thouless (KT) transitions.4, 5 The KT
transition is a phase transition that occurs only in a twodimensional XY model, and vortices or vortex-pairs (topologicaldefects) are known to play an important role. KT transitions areobserved in systems that have macroscopic wave functions (MWF)such as two-dimensional superconductors6 and ultrathin ﬁlm
superﬂuids.
Charge density wave (CDW)7, 8 is a phenomenon in which
dimensionality and topology are of particular importance. A CDW
is a modulation of electric charge in low-dimensional conductors
caused by electron-phonon coupling and has a MWF 9 such as
superconductors, superﬂuids and quantum Hall liquids. Additionally, the properties of a CDW are changed depending on its
topology.10–12
Tantalum disulﬁde with hexagonally packed TaS6 (1T-TaS2(Fig. 1(a)) is a typical CDW material. 1T-TaS2 is a layered compound
called a transition metal dichalcogenides (MX2), which induces
two-dimensional CDW with wave-number vectors qi (i = 1, 2, 3)
termed triple q (Fig. 1(b)). MX2 belongs to the group of van der
Waals materials characterized by their layered crystalline structures. A CDW in this material takes four different states depending
on temperature (Fig. 1(c)).

How do the CDW properties change when we use thin samples?
There is a possibility that the properties differ from those in higher
layers (bulks).13–15 There has been a recent debate on whether thecommensurate CDW phase exists in ultrathin ﬁlms of 1T-TaS2.16–20
However, the samples considered in these studies either contain asubstrate or interacts with the surrounding environment, which
inevitably alter the properties of the material. However, it ispossible that different CDW phases emerge in standing-freeultrathin 1T-TaS2 as the thickness decreases down to a single layer.
For example, the KT transition may occur in CDW systems.
In this paper, we report the properties of 1T-TaS2 ultra-thin ﬁlms
including a mono-layer. We obtained images of 1T-TaS2 using
scanning transmission electron microscopy (STEM). Figure 2 clearlyshows an image of the crystal structure. STEM is a measurement
method that does not require a substrate and causes little or no
damage to the samples. Therefore, STEM is well suited for themeasurement of ultrathin samples. We were able to make mono-,bi-, and tri-layer 1T-TaS2 samples using the exfoliation method (c.f.
Method section) for the ﬁrst time. Therefore we used this technique
to observe formation of different CDW phases in tri-layer, bi-layer,
and mono-layer samples.

RESULTS
Tri-layer CDW
Figure 3(a) shows an STEM image of 1T-TaS2 at room temperature.
Figure 3(b) is a three-dimensional intensity plot of the area shownby the yellow frame in Fig. 3(a). As seen from the ﬁgure, the brown
circles form hexagonal lattices. It is a feature of Commensurate (C-)

1
Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan; 2Center of Education & Research for Topological Science & Technology, Hokkaido University,
Sapporo 060-8628, Japan; 3Inorganic Functional Materials Research Institute, AIST, Nagoya 463-8560, Japan and 4Nanomaterials Research Institute, AIST, Tsukuba 305-8565, Japan
Correspondence: Satoshi Tanda (tanda@eng.hokudai.ac.jp)

Received: 2 November 2016 Revised: 1 March 2017 Accepted: 30 March 2017

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Direct observation of mono-layer, bi-layer, and tri-layer
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CDW that super-lattices of C-CDW form such large hexagonallattices (Figs. 3(d) and 3(e)).
Figure 3(c) shows a Fourier transformed image (FTI) of Fig. 3(a),where certain satellite peaks are present. The appearance ofpowerful satellites is a feature of C-CDW state. The q vectors arecalculated from Fig. 3(c) with the values of |q| = (0.280(8) ± 0.003)|a∗|that is rotated by ψ = 13.3(7) ± 1.2° with respect to the Bragg spots.
The C-CDW satellites were conﬁrmed in at least 10 other STEM
images of 1T-TaS2 samples (Supplementary material 1). These
results are in good agreement with the reported values for the

Fig. 1 Properties of 1T-TaS2 a 1T-polytype structure. The red spheres
are tantalum atoms. The yellow spheres are sulfur atoms. b The Fermi
surfaces of 1T-TaS2.12 The nesting vector (green vectors) are mutuallyequivalent. The sum of the q vectors is 0 (Triple q). c CDW states
depend on temperature in bulk 1T-TaS2. The blue arrow represents
the cooling cycle. The red arrow represents the heating cycle. C:
Commensurate state,12 T: Triclinic state14, 15, 21 which has stretchedhoneycomb lattices. Between 220 and 280 K the T-satellites areobservable but not the NC-satellite or the C-super-lattice reﬂection,even after thermal cycling. NC: Nearly commensurate state,12 IC:
Incommensurate state,12 N: Normal metal state

C-CDW state: |q| = (0.277 ± 0.003)|a∗|, ψ = 13.90°.15 From the above
evidence, we surprisingly discovered that C-CDW occurs in trilayer 1T-TaS2 at room temperature. Figure 3(f) shows the satellite
patterns of the tri-layer sample. The triple q condition is clearlypreserved.
Bi-layer CDW
Figure 4(a) shows a STEM image of the bi-layer 1T-TaS2 at room
temperature. The CDW super-lattices in the bi-layer are different
from those in the tri-layer. Figure 4(b) shows a FTI of Fig. 4(a). The
CDW satellites are largely diffused. Thus, a super-lattice is alsopresent in the bi-layer (Figs. 4(c) and 4(d)) but it is not as clearlydeﬁned as in the case of the tri-layer. However, it is obvious that
there are triple q vectors (Table 1(b)). This CDW has anisotropic
triple q vectors such as T-phase14, 15, 21 and stripe phase.22 For
these types, the CDWs form domains with domain walls
corresponding to discommensuration.23 Consequently, the systemminimizes its energy by making super-lattices in these domains
similar to those in the C-phase. For this reason, it is valid toconsider that domains are formed in this sample. Figure 4(c)shows an enlarged view of the yellow frame in Fig. 4(a) withinverted contrast. The size of Fig. 4(c) is 100 Å squared. The size issimilar to the C-CDW domain size in the NC or T-phase.14, 15, 24
However, the C-type super-lattices such as those in the tri-layer
crystal are not observed in Fig. 4(c). Figure 4(d) shows the FTI of
Fig. 4(c) and the result is similar to Fig. 4(b). We performed Fouriertransforms (FT) at different locations in Fig. 4(a) and conﬁrmed
similar satellite patterns. The sizes of domains that exist in the bilayer crystal appear to be smaller than those in the bulk material.
Unlike the tri-layer samples, clear super-lattices and honeycomb
lattices are not seen. In view of the q vector’s length, the CDW
state in bi-layer is similar to the stripe phase in 2H-TaSe2.22
Figure 4(f) shows the satellite patterns of the bi-layer samples. It isshown that the triple q conditions start to be broken.
Mono-layer CDW
Figure 5(a) shows an image of mono-layer 1T-TaS2 at room
temperature. The mono-layer sample is different from the tri-layer
and bi-layer samples. There are shade lines (crevasses) visible inthe ﬁgure, and super-lattices are present in the yellow square
marked D. These crevasses were not found in the bi-layer and trilayer crystals. Figure 5(b) shows the intensity proﬁle along the redline in D. The ordered structures do not have long-range

Fig. 2 STEM image of a thin layer sample of 1T-TaS2 including several layers. STEM captures images based on information obtained fromscattered electrons, and thus a domain with a lot of scatterers is brighter. Thus, the magnitude of the brightness corresponds to the number oflayers. a The darkest domain (right side of ﬁgure) is a bi-layer. The brightest domain (upper left side of ﬁgure) has four layers. In addition, theintermediate domain is a tri-layer. b The brightest domain has two layers, the darkest domain has one layer
npj Quantum Materials (2017) 22

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Fig. 3 Tri-layer 1T-TaS2 a STEM image of tri-layer 1T-TaS2 at room temperature. Surprisingly, super-lattices of C-CDW are seen throughout theentire sample and are particularly obvious in the yellow frame in the lower left of this image. The super-lattices form hexagonal structures as
seen in Fig. 3(e). b Top- view of the three-dimensional intensity plot of the area in the yellow frame in Fig. 3(a). Higher scattering magnitudes
are shown in red. Brown circles show super-lattices. Purple vectors are super-lattice vectors (A, B). c Fourier transformed image (FTI) of Fig. 3(a).
q1, q2, q3 are C-CDW satellites. Satellite peaks are clearly present. This is due to an overlap of different diffraction orders. d A sketch of thetantalum layer of 1T-TaS2.25 a, b are basic lattice vectors. The red points are Ta atoms and the green points are Ta atoms forming the center ofthe star-like super-lattice. A, B are super-lattice vectors in C-CDW (A = 4a + b, B = -a + 3b, | A | = | B | = √13|a|). e A sketch of super-lattices in CCDW state.25 The super-lattices form a new hexagonal lattice with basic vectors A and B. This is called a √13 × √13 structure. f Satellite
patterns of the tri-layer sample. The orange points are Bragg peaks of the lattice. The blue arrows are nesting vectors. The green arrow is -q1-q2,
which overlaps with q3, so the sum of q vectors is 0

correlation and exist as domains. Figure 5(c) shows an enlarged
view of the yellow frame in Fig. 5(a). The contrast of this image isreversed from Fig. 5(a) and thus the black points correspond to Ta
atoms. The super-lattices shown by blue circles do not form ahexagonal structure (Fig. 5(c)). Figure 5(d) is the FTI of the yellow
frame in Fig. 5(a). We conﬁrm similar satellite patterns byperforming FT at different location in Fig. 5(a). The properties ofthese satellites are shown in Table 1(c). The triple q vectors in the
mono-layer break the threefold symmetry similar to the T-phase(Fig. 5(e)).14, 15
DISCUSSION AND CONCLUSION
Here, we summarize the results presented in the previous
sections. In the tri-layer samples, C-CDW clearly occurs even atroom temperature. This result is surprising because the C-CDW
phase does not appear in the bulk samples above 220 K (Fig. 1(c)).
In the bi-layer samples, satellites similar to the stripe phase in 2HTaSe2 are observed. Moreover, satellites similar to the T-phase in
1T-TaS2 are present in the mono-layer samples. However, thesephases were not observed at room temperature in the bulk
samples. In particular, the latter two have never been observed in
the bulk samples without the cooling-heating cycle (Fig. 1(c)). To
explain these results, we consider the following mechanisms.
First, the CDW in the tri-layer sample is C-type. This can be
explained by the negative pressure effect. The CDW transition
temperature (TCDW) of MX2 shows an increasing tendency with
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increasing interlayer distance.26 In fact, the TCDW is increased bymechanical exfoliation in TiSe2.27 The C-phase was not observed in
refs16–18 probably because their samples were not standing-free
and the negative pressure was lost. However, evidences of the Cphase were reported in mono-layer at low temperature (notstanding-free)19 and in the surface of a thick 1T-TaS2 sample20
where the negative pressure effect takes a dominant role.
Second, we consider the bi-layer and mono-layer results. It isdifﬁcult to apply the above discussion to bi-layers and monolayers because these phases should not exist under the conditionsof this measurement (Fig. 1(c)). Previous studies have consideredthat the stabilization of structures with anisotropic charge
conﬁgurations such as the stripe phase (bi-layer) and the Tphase (mono-layer) can be explained by the inter-layer Coulombinteraction. The conventional Ginzburg–Landau approaches23, 24
support this idea. However, the stabilization of a structure such as
the T-phase in mono-layer cannot be explained by the inter-layer
Coulomb interaction. Therefore, we require a new mechanism.
Rotational-symmetry-breaking point defects such as vortices ordisclinations were not discovered during a detailed survey of Fig. 5(a). There is a fundamental difference between defects in CDW
and defects in superconductivity. In superconducting systems, apoint defect such as an Abrikosov vortex attempts to be formed.
On the other hand, in CDW systems, an in-plane line defect suchas a domain wall attempts to be formed. In fact, domains areinevitably generated in the T-phase and the stripe phase. There isa difference between two domains in the CDW phase θ of the
npj Quantum Materials (2017) 22

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Fig. 4 Bi-layer 1T-TaS2 a STEM image of bi-layer 1T-TaS2 at room temperature. Super-lattices of CDW are seen through- out the entire sample
and are particularly obvious in the yellow frame in the middle of this ﬁgure. b FTI of Fig. 4(a). The CDW satellites shown by the yellow arrows arelargely diffused. c Enlarged view of the yellow frame in Fig. 4(a) with inverted contrast. The brightest circle in Fig. 4(c) corresponds to thedarkest circle in Fig. 4(a). Black hexagons correspond to super-lattices. Unlike in the tri-layer sample, super-lattices do not have clear hexagonal
structures in the bi-layer. Local order structures, which are shown by red circles, are present in the bi-layer. d FTI of Fig.4(c). The CDW satellites
shown by the yellow arrows are largely diffused. These are similar to those shown in Fig. 4(b). e Satellite patterns of the bi-layer sample. Theorange points are Bragg peaks of the lattice. The blue arrows are nesting vectors. The breen arrow is -q1-q2 slightly deviates from q3, so the sumof q vectors is approximately 0

CDW MWF Ψ = |Ψ| exp(iθ). Therefore, the entropy increases
because the degree of freedom of the phase θ becomes large.
In other words, a CDW does not need to generate vortices
because it has topological defects equivalent to vortices in the KT
phase from the start. Accordingly, we can conclude that there are
no vortices or vortex-pairs in 1T-TaS2.
To explain the structures in the bi-layer and mono-layer
samples, it is necessary to reconsider triple q. This condition
exists for the three-dimensional order of CDW.28 If triple q is
broken, the discrepancy between conventional studies and the biand mono-layer results is resolved, because traditional theories are
based on triple q and three-dimensional crystals (bulk). An
examination of Fig. 3(f), Fig. 4(e) and Fig. 5(e) reveals that triple
q is broken with decreasing dimensionality. Moreover, the stripe
structure in the mono-layer emerges because triple q is broken(Fig. 5(f)).
In conclusion, CDWs occur in tri-layer, bi-layer and mono-layer
crystals. In a mono-layer sample, the CDW does not exhibit the KT
phase that accompanies disclination type defects. Instead, we
found CDW with domain wall type defect structures. This structure
is a new triclinic stripe state without satisfying condition q1 + q2 +q3 = 0. It is not necessary to maintain triple q in pure twodimensional CDW systems (Table 1(c), Table 1(d)). Consequently,
new states are created in the mono-layer and bi-layer samples.
The stripe structure formed by breaking the triple q condition in
npj Quantum Materials (2017) 22

the mono-layer may be useful for understanding other stripe
structures such as copper oxides29 and iron-based superconductors30 in terms of anisotropic charge order. Moreover, a strong
electron-phonon interaction forms shadow crevasses (Figs. 5(a)and 5(f)). This shows that the electron-phonon interaction is ofcentral importance in thinned samples. This idea is applied tosystems in which an electron-electron interaction plays the mostimportant role such as charge order in organic conductors.31, 32
New equations and models are needed if we are to realize pure
two-dimensional systems. In addition, it is suggested that breaking of three-dimensional order causes new structures to beformed.
METHODS
Sample preparation
The single crystals of 1T-TaS2 were grown in excess sulphur by the usual
iodine vapor transport method. The prereacted powder of 1T-TaS2 and acertain amount of excess sulphur were put in one end of a quartz tube andthe tube was sealed in vacuum. The ampule was heat-treated in such a
way that the mixture at one end of the quartz tube was at 950–830 °C andthe temperature of the other end was 70–80 °C lower. It was found thatsingle crystals were grown not only in the lower temperature end but also
in the hotter one. The quartz tube was rapidly quenched into water toinsure the retention of the 1T-phase.
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Direct observation of mono-layer, bi-layer, and tri-layer
D Sakabe et al.

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Table 1. (a) Parameters of q vectors for the Bi-layer sample: Two of the q vector lengths are the same. This is a feature of the stripe phase. The
magnitude of the q vectors is shown due to the three-fold symmetry. (b) Parameters of q vectors for the mono-layer sample. Only the q2 value of the
Nearly commensurate phase is shown due to the three-fold symmetry. (c) It is conﬁrmed that the lattice symmetry is maintained. The symmetry of
triple q is clearly broken. Correlation lengths were estimated by auto-correlation analysis
Experimental results
(a)
q
(b)
q1
q2
q3
(c)
q1
q2
q3
(d)
Higher layer
Tri-layer
Bi-layer
Mono-layer

Tri-layer| qi | / | a∗ |0.280(8)Bi-layer| qi | / | a∗ |0.287(2)0.277(2)0.287(1)Mono-layer| qi | / | a∗ |0.323(0)0.276(3)0.293(8)Bulk data (Previous works)
ψ
13.3°
ψi
9.0°
10.0°
11.5°
ψi
7.5°
15.5°
19.0°
q1 + q2 + q3
=0
=0
≈0
≠0

Commensurate phase| qi | / | a∗ |0.277
Nearly-commensurate phase| qi | / | a∗ |

ψ
13.90
ψi

0.283

12.7°

T-phase (T = 270 K)14, 15| qi | / | a∗ |
0.288
0.303
0.286
Correlation length

ψi
15.6°
13.4°
11.84°

70 ± 25 Å
30 ± 10 Å
7.5 ± 2.5 Å

Fig. 5 Mono-layer 1T-TaS2 a STEM image of mono-layer 1T-TaS2 at room temperature. There are shadow crevasses (Shown by green lines, see
supplementary material 2 for an enlarged view with eyeguides). These correspond to areas with few scatterers. D shows domains withordered structures. b An intensity plot along the red line in D. The orange arrows show super-lattices enhanced in Fig. 5(c). c An enlarged imageof D in Fig. 5(a) with inverted contrast. The black hexagons shown by the blue ellipses are super-lattices. Super-lattices do not form honeycomb
lattices. d FTI of D in Fig. 5(a). The transformed region is tiny, so the peaks are broad. However, we conﬁrm the presence of triple q vectors. e
Satellite patterns of the mono-layer sample. The orange points are Bragg peaks of the lattice. The blue arrows are nesting vectors. The green
arrow is -q1-q2 which clearly differs from q3, so triple q condition q1 + q2 + q3 = 0 is broken. f The charge conﬁguration is reproduced from thesatellites in Fig. 5 (e). The structures correspond to shadow crevasses (red frame) and stripe structure (blue arrow)
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npj Quantum Materials (2017) 22

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Exfoliation
The thin samples are made using the exfoliation method. That is, thepresence of the van der Waals gap with bonding makes it possible toexfoliate ﬁlms of MX2 with various thicknesses from its bulk in a similarmanner to graphite. Some of the ﬂakes were randomely chosen and cleaved
using Scotch tapes and then transferred to transmission electron microscope
microgrids following the method developed by Meyer and co-workers.33

Scanning transmission electron microscope
We used low voltage scanning transmission electron microscope (STEM).
This method does not require a substrate and causes little or no damage tothe samples.34 Therefore, STEM is well suited for the measurement of
ultrathin samples. We used this technique to observe formation ofdifferent CDWs in tri-layer, bi-layer, and mono-layer samples.

ACKNOWLEDGEMENTS
We thank Toshiro Tani, late Shoji Tanaka and late Takashi Sambongi for the
instruction of sample preparation techniques and donation of some of the samples
used in this experiment. We also thank the aforementioned professors, Koichi
Ichimura, Toru Matruura and Junya Ishioka for stimulating discussions. Zheng Liu andKazutomo Suenaga acknowledge support from Grant-in-Aid for Scientiﬁc Researchon Innovative Areas (MEXT KAKENHI Grant No. 25107003) and the JST Research
Acceleration Program. This work was supported by JSPS KAKENHI (No. 26287069).

AUTHOR CONTRIBUTIONS
K.S. and S.T. contributed to the original idea and supervised the project. S.T. and D.S.
contributed sample preparation. Z.L., K.S., S.T. performed the experiment. D.S., Z.L.
and S.T. analyzed the data. All authors contributed to the interpretation of the results.
D.S., K.N. and S.T. wrote the manuscript and supplementary materials. All authors readand approved the ﬁnal manuscript.

COMPETING INTERESTS
The authors declare no competing interests.

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© The Author(s) 2017

Supplementary Information accompanies the paper on the npj Quantum Materials website (doi:10.1038/s41535-017-0025-8).

npj Quantum Materials (2017) 22

Published in partnership with Nanjing University