Journal of the Physical Society of Japan
Vol. 77, No. 9, September, 2008, 093708#2008 The Physical Society of JapanLETTERS

Field-Induced Discommensuration in Charge Density Waves in o-TaS3
Katsuhiko I NAGAKI, Masakatsu TSUBOTA, Kazuki H IGASHIYAMA, Koichi I CHIMURA,
Satoshi TANDA, Kenichiro YAMAMOTO1 , Noriaki H ANASAKI1 , Naoshi I KEDA1 ,Yoshio NOGAMI1 , Takayoshi I TO2 , and Hidenori T OYOKAWA2
Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Kita 13 Nishi 8, Kita-ku, Sapporo 060-8628
1
Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Okayama 700-8530
2
Japan Synchrotron Radiation Research Institute, 1-1-1 Koto, Sayo, Hyogo 679-5198(Received March 28, 2008; accepted July 22, 2008; published September 10, 2008)

We report a synchrotron X-ray study of charge density waves (CDWs) in an o-TaS3 crystal. We
found that two independent CDWs coexist in the temperature range of 130 – 50 K. These waves areincommensurate and commensurate CDWs with longitudinal wave vectors qc ¼ 0:252c and 0:250c ,respectively. The temperature and electric current dependences of the intensity of the two CDW satellites
were measured. We found that the commensurate CDW was converted to the incommensurate CDW at
80 K by inducing current ﬂow. Our observation was interpreted in terms of the dynamics of topologicaldefects. We determined the edge dislocation conﬁguration from the electric current dependence of theintensity of the two CDWs. The result implies for the ﬁrst time that discommensurations are induced in
the commensurate CDW by applying an electric ﬁeld.
KEYWORDS: charge density wave, o-TaS3 , discommensuration
DOI: 10.1143/JPSJ.77.093708

Dislocations on the macroscopic order are an attractive
subject, particularly when they become ordered and exhibit
a new spatial periodicity. A well-known example is themixed state of a superconductor under a modest magnetic
ﬁeld, where vortices form the Abrikosov lattice.1) A dual
phenomenon is predicted in charge density waves (CDWs):
that is, when an electric ﬁeld is applied perpendicularly to
the CDW chain direction, dislocations can enter the CDW toform a mixed state as a type-II superconductor.2)
Since the degree of freedom of the CDW order parameteris larger than that of a conventional superconductor,3) one
can expect to observe more variety of dislocations, by
analogy of 3 He superﬂuids and liquid crystals. Moreover, incontrast to superconducting vortices, which have no eﬀect
on X-rays and therefore cannot be studied using them, theorder parameter of a CDW couples with the lattice distortionand modiﬁes diﬀraction; hence, high-resolution synchrotron
studies can now be conducted.4–6)
In this article, we report the discovery of a mixed state asa result of our synchrotron X-ray study of CDWs in o-TaS3
performed at SPring-8. We measured the temperaturedependence of Bragg and satellite peak proﬁles precisely
down to 7.3 K with and without current ﬂowing through thesample. We found that at 50 –130 K, the mixed state exists
stably with the coexistence of two kinds of CDWs, attributed
to the commensurate and incommensurate wave vectors.
From the electric current dependence of the intensity ofthe two CDWs, we demonstrated the evolution of edge
dislocations of CDW, i.e., discommensurations.7) The result
implies that the dislocations are induced in the commensurate CDW by applying an electric ﬁeld along the chain
direction. This is the ﬁrst such report for a CDW.
We investigated a quasi-one-dimensional conductor oTaS3 on its CDW properties. It undergoes a Peierls transition
at TP  218 K to an incommensurate CDW. In contrast to
similar materials, e.g., NbSe3 , the whole Fermi surface ofE-mail: kina@eng.hokudai.ac.jp

o-TaS3 contributes to the transition. In a previous X-ray
study,8) it was shown that the CDW wave vector q attemperatures around TP is incommensurate, qc  ð0:255 
0:003Þc , and by reducing temperature it becomes nearlycommensurate below 100 K, where qc  ð0:250  0:004Þc .
The single crystal of o-TaS3 used in this study wassynthesized by the standard chemical vapor transport
method. The reaction and crystal growth were undertaken
in an evacuated quartz tube using tantalum and sulfur
powder. A piece of ribbonlike crystal was then placed on acopper sample holder with an insulating glass layer. The
sample dimensions were 5 mm  12 mm  27 mm. A gold
ﬁlm was then deposited on the crystal and electrodes wereformed using silver paste. Electric current was fed froma low-level current generator (Keithley 6221), while thevoltage drop at the sample was monitored with a highimpedance voltmeter (Keithley 617) to prevent the voltmeterfrom shunting the sample current.
The X-ray study was performed at BL02B1 of SPring-8.
The incident beam passed through a double-crystal monochromator. The wavelength was 0.61984(89) Å, which wascalibrated with standard CeO2 powder prior to the measurement. A synchrotron beam of 0.5 mm diameter was
irradiated through a hole of the sample holder. The irradiatedarea of the sample was 1.3 mm away from the electrodes.9)
Diﬀraction was monitored with a position-sensitive twodimensional detector, Pilatus-100K,10) located 1303.7 mm
away from the rotation center of a four-circle diﬀractometer.
Each pixel contains a 320-mm-thick silicon sensor, followed
by a charge-sensitive ampliﬁer, a single-level discriminatorand a 20-bit counter. An individual pixel is operated in the
single-photon counting mode, and the resulting data is freeof crosstalk between pixels. Hence, the apparatus provides
an angular resolution of 0.007559 , corresponding to one
pixel (172  172 mm2 ) of the two-dimensional detector. The
sample was ﬁxed during exposure, typically for a durationof 100 s. The sample was cooled to 7 K by a refrigerator
mounted on the diﬀractometer. Temperature stability was

093708-1

LETTERS

J. Phys. Soc. Jpn., Vol. 77, No. 9

7.3 K

50 K

30 K

80 K

K. INAGAKI et al.

130 K

180 K
Fig. 1. Bragg (top) and satellite (middle) proﬁles
obtained at 180, 130, 80, 50, 30, and 7.3 K for ao-TaS3 crystal. Vertical axes in the intensity maps
denote the c -direction. The cross section of eachsatellite proﬁle along the c -direction (white dottedline) is shown in the bottom panels. Here, 20 is thecenter of the detector. The shape of the Bragg peakshows no signiﬁcant change; that of the satellite
peak evolves with decreasing temperature. The two
peaks at 80 K are attributed to the commensurate
and incommensurate CDWs, denoted c and ic,
respectively.

1000

0

0

0.05

0.1

2θ−2θ 0 (deg)Intensity: min

−0.05

0

0.05

2θ−2θ 0 (deg)

0.1

600

80 K
400

200

0
−0.05

0

0.05

2θ−2θ 0 (deg)

0.1

600

130 K

Intensity (arb. units)cIntensity (arb. units)

200

0
−0.05

50 K

400

200

200

0
−0.05

0

0.05

0.1

2θ−2θ 0 (deg)

180 K

400

0
−0.05

0

0.05

0.1

2θ−2θ 0 (deg)

−0.05

0

0.05

0.1

2θ−2θ 0 (deg)maxmaintained within 0:01 K in the temperature range of themeasurement. The sample was thermally connected with aheat anchor, and the temperature increase by Joule heating
was less than 1 K even at the largest current (30 mA at 80 K).
Before each measurement, several reciprocal points were
scanned to assign the peaks in order to prevent from
confusing it with any spurious signals.
Figure 1 shows the temperature evolution of the Bragg(002) and satellite ð1; 1; 2Þ þ q peaks obtained at 180, 130,80, 50, 30, and 7.3 K. The position of the satellite peak wasdetermined to be q ¼ ð0:5; 0:125; 0:25Þ, which agrees withthe results of previous studies8,11) within experimental errors.
We also conﬁrmed that the intensity of the satellite peak
rapidly decreases at temperatures higher than the Peierls
transition temperature.
The predominant feature in the satellite proﬁles is thechange in the number of peaks (Fig. 1). When the system
undergoes Peierls transition at 218 K, a satellite peak begins
to develop in intensity and correlation. The initial positionof the peak lies around qc ¼ ð0:255  0:002Þc . When we
reduced temperature, a second peak emerged close to theﬁrst. This second peak appeared at 130 to 50 K, while attemperatures below 50 K the number of peaks returned
to unity. The diﬀerence between the two q’s is only
1:3  103 c , or two pixels at the detector; however, this is
still larger than the spatial resolution of the experiment (i.e.,
1 pixel). In addition, since no anomalies were found in the
Bragg peaks in the whole temperature range, we can rule out
the possibility of the presence of any artifacts.
The positions of the two q’s at 80 K were assigned to beqc ¼ ð0:252  0:002Þc and q0c ¼ ð0:250  0:002Þc , where
q and q0 denote the satellites for higher and lower temperatures, respectively. Hence, the CDWs at higher and lower
temperatures are assigned as incommensurate and commensurate, respectively. The result should be compared withknown behavior of o-TaS3 . In a previous X-ray study.8) it
was shown that the wave vector at around TP is incommensurate, qc  ð0:255  0:003Þc , and by reducing temperature it becomes nearly commensurate below 100 K, whereqc  ð0:250  0:004Þc . The error bars were mainly the
result of the resolution of the experimental setup used at thattime. For example, the full width at half maximum of thediﬀraction peak was as large as 0:01c in the experimentdescribed in ref. 11; however, our synchrotron study has anadvantage in terms of the sharpness of the beam, which leads

1

Incommensurate

Ic /(Iic+Ic)

0400

Intensity (arb. units)

200

ic

600

30 K

Intensity (arb. units)

Intensity (arb. units)

Intensity (arb. units)

600

7.3 K

400

Commensurate
0

0

100

TP = 218K
200

300

T (K)

Fig. 2. Phase diagram of o-TaS3 deduced from this study. Solid circles
represent the intensity of a commensurate CDW, Ic , normalized by the
total intensity of both the commensurate and incommensurate satellites,
Iic þ Ic . The commensurate CDW begins to develop at around 130 K. The
two q’s of the CDW coexist until 30 K, at which the entire condensate
undergoes an incommensurate–commensurate transition.

to a resolution better than 1  103 c . In this context, ourdata can be understood as a natural extension of the previous
results.
Details of the incommensurate–commensurate transition
were investigated through the intensity evolution of the two
CDWs. The use of the Pilutus detector10) facilitates thedetermination of the intensity of the peaks. Since thedetector contains a two-dimensional array of photon counters, the signal of each pixel is directly proportional to theintensity of incident X-rays. Hence, the intensity of eachpeak can be obtained simply by numerical integration fromthe two-dimensionalpﬃﬃﬃﬃ proﬁle. Statistic error of the intensity
is estimated as N , where N is the number of detected
photons. In typicalN  104 , resulting in apﬃﬃﬃﬃ experiments,
2
relative error of N =N  10 .
Figure 2 shows the relative intensity of the commensurate
CDW (q0c ¼ 0:250c ) normalized by the total satellite
intensity, Ic =ðIic þ Ic Þ. The broken line in the ﬁgure is a
guide for the eyes. It is shown that at 50 –130 K, where
two CDWs coexist, the intensity of the commensurate
CDW increases at lower temperatures. The main diﬀerence
revealed in this study is that the incommensurate CDW is
not locked to be commensurate, although its wave vector
approaches that of the commensurate CDW. The commen-

093708-2

LETTERS

surate CDW begins to appear separately at around 130 K anddevelops at lower temperatures.
Let us compare this observation with those of previoustransport studies of o-TaS3 . Takoshima et al. reported ananomalous increase in longitudinal conductivity below
100 K and attributed it to soliton transport.12) Although theobservation was made before the temperature dependence of
the wave vector was measured,8) the onset temperature of
the anomaly roughly coincides with the appearance of thecommensurate CDW. Our data also support the results of theprevious study,8) and in addition, the observed extension of
discommensuration is consistent with the soliton transport
concept. Moreover, Zaitsev–Zotov found that there are twokinds of nonlinear conduction in thin samples of o-TaS3 .
One is a sliding motion, which is observed at high temperatures, and the other results from the quantum creep of
the wavefront observed at low temperatures.13) This is alsoeasily understood if we accept that two kinds of CDWs cancoexist in o-TaS3 , as shown in Fig. 2.
Since the longitudinal wave vector qc is very close tobeing commensurate, it is important to discuss the possibilityof discommensuration. If the wavenumber 2kF is very close
to the commensurate length Ma, where M is an integer, anda is the lattice constant, discommensuration will occur per
length ls .7) This length is naively related to the diﬀerence
between the CDW wave vector and the commensurate
length, as expressed byq ¼ 2=Mls :

0 μA

It

incommensurate
5000

0.2

V (V)

0.4

0

10

20

I (μA)

30

Intensity (arb. units)

0.04

commensurate

0

200

0.05

0.1

−0.05

0

0.05

0.1

2θ−2θ 0 (deg)max

for the incommensurate (commensurate) CDW, and at alarger current, the discrepancy decreases slightly.
In addition to the intensity evolution, the observed peakwidth also exhibits interesting behavior. Figure 4(c) shows
the transverse (across the current ﬂow) peak width for bothpeaks. The width of the incommensurate satellite decreased
from 0.07 to 0.05 at 0 and 6 mA, respectively. Since thetransverse peak width is inversely proportional to the lengthof the correlation, the observed data imply that the transverse correlation is broadened by a factor of 1.4. In contrast,
the transverse peak width of the commensurate CDW does
not change signiﬁcantly.
We illustrate the change in transverse correlation length
schematically in Fig. 5. As discussed above, there are
discommensurations, namely defects in the incommensurate
CDW. Since the two CDWs have diﬀerent wave vectors,
there must be a misalignment of wavefronts at the border
between these CDWs. In our case, since q in the incommensurate CDW is larger than that in the commensurate
CDW, it is possible for dislocations to be located between
them. In Fig. 5, the solid lines represent the wavefront, andthe hatched circles represent edge dislocations in the phase.
There are additional wavefronts between two discommensurations.
The observed change in the peak proﬁle can be understood if the length of the discommensurations is increased,

c

0

80 K

Fig. 3. Current dependence of the Bragg and satellite proﬁles obtained at
80 K. The legends are the same as those in Fig. 1.

0.02

0

30 μA
400

0
0

Intensity: minincommensurate

0.06

200

2θ−2θ 0 (deg)commensurate

00

FWHM (degrees)

ICDW (μA)

R0=21.56 kΩ
20Intensity (arb. units)

a
T=80K

80 K

400

−0.05

0.08

b

600

0 μA

0

ð1Þ

10000

30 μ A

600

In our case, M ¼ 4 and q ¼ qc  q0c ¼ 0:002c . This gives
the mean separation between discommensurations ls ¼ 418
Å. We will discuss this issue in detail later.
We investigated the current dependence of the satellite
proﬁle to reveal the nature of each peak. Figure 3 shows the
Bragg and satellite proﬁles at currents of 0 and 30 mA
obtained at 80 K. Again, no signiﬁcant change was observedin the Bragg peak, whereas the satellite peak proﬁle depends
on current. At this temperature, the threshold current of the
CDW was 6 mA (or a threshold electric ﬁeld of 0.1 V/cm).
Hence, the observed change in the satellite proﬁle should
reﬂect the collective motion of the CDW.
A comparison of the 0 and 30 mA proﬁles of the satellite
peak reveals several remarkable phenomena. The intensities
of both peaks of the 0 mA proﬁle appear similar, while thoseof the 30 mA peak exhibit signiﬁcant diﬀerences, in that theintensity of the top peak (commensurate) decreased whilethat of the bottom peak (incommensurate) increased. The
evolution of the two peaks is shown in detail in Fig. 4. An
increase in ﬂowing current increases the intensity of theincommensurate peak, while that of the commensurate peakdecreases [Fig. 4(b)]. At 6 mA, a hump (a dip) was observed

40

K. INAGAKI et al.

Intensity (arb. units)

J. Phys. Soc. Jpn., Vol. 77, No. 91020

I (μA)

093708-3

30

Fig. 4. (a) Charge density wave current as a functionof applied voltage at 80 K. The arrows indicate thepoints at which diﬀraction was obtained. (b) The
intensities of satellite peaks of incommensurate(solid circles) and commensurate (open circles)
CDWs. (c) Transverse peak widths of incommensurate (solid circles) and commensurate (open circles)
CDWs. The solid lines in (b) and (c) are guides forthe eyes.

LETTERS

J. Phys. Soc. Jpn., Vol. 77, No. 9

I=0

I > IcLs

Fig. 5. Schematic illustrations of the evolution of
two coinciding CDWs. The solid lines represent the
CDW wavefront. The hatched circles indicate edge
defects in the CDW phase. There are additional
wavefronts between the two defects, or discommensurations at a distance ls . The widths of the commensurate and incommensurate CDWs are denotedc and ic , respectively. By inducing a current ﬂow,
the lengths of the discommensurations are stretched,resulting in the expansion of the incommensurate
CDW.

Ls

ξic

ξic

ξc

ξc

resulting in the expansion of the incommensurate CDW. At
present, there is no microscopic mechanism that agrees
quantitatively with the observed phenomena. However, it isworth noting that the edge dislocations in a CDW moveeasily in the transverse direction.14) For complete understanding, we must determine the force exerted on thedislocations when the CDW is in motion, thus increasing the
portion of the incommensurate CDW. The key to what mightlie in the concept of the ‘‘type-II CDW’’ introduced by
Hayashi and Yoshioka.2) They suggested that dislocations
can penetrate a CDW and screen the applied transverse
ﬁeld. This is analogous to the role of vortices in a superconductor. Although previous analyses of the type-II CDW
have mainly focused on incommensurate CDW systems, theapproach will provide a suitable explanation of the theobserved temperature and current dependence of CDW
evolution.
We undertook a synchrotron X-ray study of o-TaS3 crystal
down to 7 K. Our observation settles an old but open
question about the CDW phase in o-TaS3 . We found that two
kinds of CDWs coexist in the 50 –130 K temperature range,
and attributed them to commensurate and incommensurate
wave vectors. From the electric current dependence of theintensities of both CDWs, we determined the conﬁgurationof edge dislocations of the CDW. This picture is moresophisticated than the ﬁrst prediction of discommensuration.7) We have demonstrated that the ratio of commensurate
intensity to incommensurate intensity is a function of
applied ﬁeld. As a result, this method will provide a
powerful tool for the investigation of commensurate–incommensurate competitions. This work will also have an
impact on related topics. For instance, the ‘‘1/8 problem’’ ofhigh-Tc superconductors is now understood as the commensurate lock-in of dynamical stripe order.15) Future studies ofo-TaS3 , particularly at low temperatures and with reduced
dimensions, will reveal a detailed picture of the nature of
dislocation dynamics.

K. INAGAKI et al.

Acknowledgments
This work is partly supported by a Grant-in-Aid forthe 21st Century COE program, ‘‘Topological Science andTechnology’’. The authors are grateful for the intensive useof the SPring-8 beamline BL02B1 through project number
2007A0010.
1) A. A. Abrikosov: Zh. Eksp. Teor. Fiz. 32 (1957) 1442 [Translation:
Sov. Phys. JETP 5 (1957) 1174].
2) M. Hayashi and H. Yoshioka: Phys. Rev. Lett. 77 (1996) 3403.
3) P. W. Anderson: Basic Notions of Condensed Matter Physics(Addison-Wesley, Reading, MA, 1984).
4) E. Sweetland, A. C. Finnefrock, W. J. Podulka, M. Sutton, J. D. Brock,D. DiCarlo, and R. E. Thorne: Phys. Rev. B 50 (1994) 8157.
5) K. L. Ringland, A. C. Finnefrock, Y. Li, J. D. Brock, S. G. Lemay, andR. E. Thorne: Phys. Rev. B 61 (2000) 4405.
6) R. Danneau, A. Ayari, D. Rideau, H. Requardt, J. E. Lorenzo, L.
Ortega, P. Monceau, R. Currat, and G. Grübel: Phys. Rev. Lett. 89(2002) 106404.
7) W. L. McMillan: Phys. Rev. B 14 (1976) 1496.
8) C. Roucau: J. Phys. (Paris) 44 (1983) C3-1725.
9) The experimental conﬁguration in this study provided a bulk behaviorof the CDW. Hence our observation diﬀers qualitatively from those of
spatially resolved X-ray studies of CDWs: D. DiCarlo, E. Sweetland,
M. Sutton, J. D. Brock, and R. E. Thorne: Phys. Rev. Lett. 70 (1993)
845; D. Rideau, P. Monceau, R. Currat, H. Requardt, F. Nad, J. E.
Lorenzo, S. Brazovskii, C. Detlefs, and G. Grübel: Europhys. Lett. 56(2001) 289; D. Le Bolloc’h, S. Ravy, J. Dumas, J. Marcus, F. Livet,
C. Detlefs, F. Yakhou, and L. Paolasini: Phys. Rev. Lett. 95 (2005)
116401.
10) H. Toyokawa, M. Suzuki, Ch. Brönnimann, E. F. Eikenberry, B.
Henrich, G. Hülsen, and P. Kraft: AIP Conf. Proc. 879 (2007) 1141.
11) K. Tsutsumi, T. Sambongi, S. Kagoshima, and T. Ishiguro: J. Phys.
Soc. Jpn. 44 (1978) 1735.
12) T. Takoshima, M. Ido, K. Tsutsumi, T. Sambongi, S. Honma, K.
Yamaya, and Y. Abe: Solid State Commun. 35 (1980) 911.
13) S. V. Zaitsev-Zotov: Phys. Rev. Lett. 71 (1993) 605.
14) N. P. Ong and K. Maki: Phys. Rev. B 32 (1985) 6582.
15) S. A. Kivelson, I. P. Bindloss, E. Fradkin, V. Oganesyan, J. M.
Tranquada, A. Kapitulnik, and C. Howald: Rev. Mod. Phys. 75 (2003)
1201.

093708-4