PHYSICAL REVIEW B 81, 113101 共2010兲

Nonlocal transport in the charge density waves of o-TaS3
Katsuhiko Inagaki,1,2 Masakatsu Tsubota,1 and Satoshi Tanda1,2
1Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Kita 13 Nishi 8 Kita-ku, Sapporo 060-8628, Japan
2Center of Education and Research for Topological Science and Technology, Hokkaido University,

Kita 13 Nishi 8 Kita-ku, Sapporo 060-8628, Japan
共Received 2 December 2009; revised manuscript received 29 January 2010; published 5 March 2010兲
We studied the nonlocal transport of a quasi-one-dimensional conductor o-TaS3. Electric transport phenomena in charge density waves include the thermally excited quasiparticles and collective motion of charge
density waves 共CDWs兲. In spite of its long-range correlation, the collective motion of a CDW does not extend
far beyond the electrodes, where phase slippage breaks the correlation. We found that nonlocal voltages
appeared in the CDW of o-TaS3, both below and above the threshold field for CDW sliding. The temperaturedependence of the nonlocal voltage suggests that the observed nonlocal voltage originates from the CDW evenbelow the threshold field. Moreover, our observation of nonlocal voltages in both the pinned and sliding states
reveals the existence of a carrier with long-range correlation, in addition to sliding CDWs and thermally
excited quasiparticles.
DOI: 10.1103/PhysRevB.81.113101

PACS number共s兲: 71.45.Lr, 72.15.Nj

Nonlocal properties in charge density waves 共CDWs兲
have been attracting interest for decades.1–3 Since electrictransport phenomena include collective motion,4 it is natural
to expect a sliding CDW to be a possible source of nonlocal
transport.1 The correlation of the CDW phase has been estimated in the 1 – 100 ␮m range,1,5–13 which is long enough toallow experimental studies. The correlation inside the sliding
region has been confirmed. However, it has been shown thatthe correlation of a sliding CDW does not extend far beyond
the electrodes, where phase slippage may destroy thecorrelation.2,3
In this Brief Report, we report a nonlocal transport phenomenon with a quasi-one-dimensional conductor o-TaS3.
Following the pioneering work by Gill,1 we comparedcurrent-voltage characteristics obtained with normal andtransposed electrode configurations, as well as with nonlocal
detection 共Fig. 1兲. We found that nonlocal voltages appearedin the CDW of o-TaS3, both below and above the thresholdfield for CDW sliding. The sign of the observed nonlocal
voltage was opposite to that of the spreading resistance.14,15
In addition to this, the temperature dependence of the nonlocal voltage suggests that the observed nonlocal voltage originates from the CDW. Moreover, our observation of nonlocal
voltages in both the pinned and sliding states reveals theexistence of a carrier with long-range correlation, in addition
to sliding CDWs and thermally excited quasiparticles. Finally, we compared our observation to the coexistence of two
CDWs in o-TaS3 共Refs. 16 and 17兲 and found it is closely
related to topological dislocations in CDWs.
We performed a four-probe measurement, which requires
a voltmeter with a high input impedance so that the leakage
current to the voltmeter becomes negligible. For fully gapped
CDW materials, such as o-TaS3, the use of four-probe measurement is usually difficult especially at low temperatures
where the sample resistance often exceeds the typical input
impedance of a voltmeter, for example, Zin ⬃ 1 G⍀. We exploited an electrometer 共Keithley 6512, Zin ⬎ 200 T⍀兲 tomeasure the voltage drop of the o-TaS3 samples.
o-TaS3 crystals were synthesized with a standard chemical vapor transport method. A pure tantalum sheet and sulfur

powder were put in a quartz tube. The quartz tube wasevacuated to 1 ⫻ 10−6 Torr and heated in a furnace at
530 ° C for two weeks. The electrodes were made using
50-␮m diameter silver wires glued with silver paint. Goldthin film was deposited on the crystal before the silver wires
were attached to reduce the contact resistance to 1 ⍀ atroom temperature. The spacing between the electrodes wastypically 200 ␮m and the sample cross section was 50⫻ 5 ␮m2 共width⫻ thickness兲.
Figure 2 shows the temperature dependence of the resistance of a o-TaS3 crystal. The result shows the well-known
features of o-TaS3, a Peierls transition temperature of 220 K,an Arrhenius-type temperature dependence with an activation energy of 790 K, and a deviation from the Arrhenius plot
below 100 K. We checked the contact resistance by comparing the four- and two-terminal resistances and found it wasnegligible in the room temperature to 40 K range. We also
confirmed that the result was unaffected by the difference
between substrates by comparing data obtained with thesilica and sapphire substrates. Based on these considerations,
we confirmed that the four-terminal measurement was prop-1098-0121/2010/81共11兲/113101共4兲a) normalI+V-Ib) transposed+ V -c) nonlocal

I-V+FIG. 1. 共Color online兲 Configurations for the measurements: 共a兲normal configuration, 共b兲 transposed configuration, and 共c兲 nonlocal
configuration. The polarity of the voltmeter in the nonlocal configuration provides a positive value when the spreading resistance isdominant.

113101-1©2010 The American Physical Society

PHYSICAL REVIEW B 81, 113101 共2010兲

BRIEF REPORTS

R (Ω)

104

102

1000.01−11/T (K )0.02

FIG. 2. Temperature dependence of sample resistance. Brokenline is an Arrhenius fit R ⬀ exp共T / T0兲, with T0 = 790 K.

erly performed over the entire temperature range of the measurement.
Figure 3 shows the current-voltage 共I-V兲 characteristics at
130 K in the normal and transport configurations, as well as
the nonlocal voltage. The I-V characteristics with the normal
configuration 共black line兲 and with the transposed configuration 共red line兲 coincide in a low current regime where Ohmic
behavior is observed. Above the threshold of nonlinear conduction, we detected a discrepancy between the two configurations. This discrepancy can be understood as the phase-slip
voltage accompanied by CDW sliding.1,2 When the CDW
slides under a condition where the regions outside the current
electrodes are strongly pinned, elastic deformation is inducedin the CDW. In the vicinity of each electrode, the elastic
deformation relaxes by breaking CDW phase continuity. In
the transposed configuration 关Fig. 1共b兲兴, the measured voltage is affected by the phase slip, in contrast to the normal
configuration 关Fig. 1共a兲兴, hence the difference between thesetwo configurations as shown in Fig. 3 reveals that the phaseslip really occurred in the sample.
We also observed nonlocal voltage as shown in Fig. 3共green line兲 by using the nonlocal configuration 关Fig. 1共c兲兴.
The result shows that at 130 K, a negative voltage was detected at a pair of electrodes 200 ␮m away. The magnitude−100

T=130 K

0Vn

Vnonlocal (µV)

Vn, Vt (mV)

0200

Vnonlocal

100−200
Vt−10
I (mA)

1FIG. 3. 共Color online兲 Current-voltage characteristics at 130 K
for the normal, transposed, and nonlocal configurations, denoted byblack, red 共gray兲, and green 共light gray兲 curves, respectively.

of the nonlocal voltage was around 200 ␮V at 1 mA. This
voltage was large enough to be measured with our ultrahigh
impedance voltmeter, whose minimum detectable voltage
was 10 ␮V. The voltage was proportional to the injectedcurrent, with kinks at ⫾0.3 mA, above which the slope of
the I-V curve became moderate. The emergence of a voltage
at the nonlocal probes is fascinating since Gill reported that
there was no detectable signal in the CDW state of NbSe3.1
Such an attempt has also been made for other CDW systems,
however, the nonlocal effects were unlikely to extend overthe electrode, except via strain distribution.3
We first compared our observation to a trivial source,
known as spreading resistance, which could affect the nonlocal voltage probes.14,15 When the current is injected from atiny electrode into a bulk sample, it cannot flow homogeneously until it spreads over a cross section. In the vicinity ofthe electrodes, the flow lines are curved and some of themtravel in the opposite direction to the counterelectrode. At thesample surface, the electric potential U共x兲 of position x isexpressed by冏冏

cosh共␲l/t⬘兲 − exp共␲x/t⬘兲t⬘,U共x兲 = − E arccosh␲
sinh共␲l/2t⬘兲

共1兲

where E denotes an applied field, l is the electrode length,
and t⬘ = t冑A is a reduced thickness with A being the anisotropic ratio of conductivity.14,15 In addition, the effective
cross section for the current is limited to the specific distance⬃t⬘ and an additional contribution to resistance emerges,
known as spreading resistance. An important feature ofspreading resistance is that it obeys Ohm’s law since its nature is the restriction of the current path. In our configuration
for nonlocal detection 关Fig. 1共c兲兴, the contribution of the
spreading resistance must generate a positive voltage between the voltage probes.
In fact, the observed nonlocal voltages were negative asshown in Fig. 3. Moreover, the temperature dependence ofthe nonlocal voltage suggests that CDW is closely related toits origin. Figure 4共a兲 shows the temperature evolution of thenonlocal voltages at 130, 180, and 250 K. At 180 K, although
the kink and nonlinearity became less pronounced, the nonlocal voltage was negative. In contrast, at 250 K, above thePeierls transition 共T P = 220 K兲, the polarity was reversed andbecame positive. The slope of the I-V curve was 2.1⫻ 10−2 ⍀. This is in good agreement with the estimation of
spreading resistance 2.8⫻ 10−2 ⍀ estimated using Eq. 共1兲
with an anisotropy ratio of A = 500.15 To confirm that this is
not an artifact from the measurement circuit, we performed
several sets of experiments, including a comparison of thedata while inverting the polarity of the electrodes of both thecurrent generator and the voltmeter. We also checked thereproducibility by using different specimens and cryostats.
All the data were consistent and we concluded that the observed negative nonlocal voltage was really a property of thesamples. Hence it is unlikely that the nonlocal voltage can be
attributed to the trivial spreading resistance, whereas its attribution to CDW is plausible.
In addition, the voltages were nonlinear functions of thecurrent with apparent kinks 共Fig. 3兲. The positions of the113101-2

PHYSICAL REVIEW B 81, 113101 共2010兲

BRIEF REPORTSa)b)

200VI+--+--+--+

V>00Vnonlocal (µV)−200
−10T=250 K
010c)

200

V<0VI+

0−200

T=180 K
−505d)

200

VI+

0−200 T=130 K−10I (mA)

1FIG. 4. 共Color online兲 共a兲 Temperature evolution of the nonlocal
voltages at 130, 180, and 250 K. Polarity inversion was seen below
and above the Peierls transition, 220 K. 共b兲 Schematic diagram offlow lines to provide spreading resistance. 共c兲 Possible correlation
between current and voltage probes via dislocation lattice. 共d兲 Correlation of sliding CDW is Fig. 1 exceeded over current probes.

kinks in the nonlocal voltage were found to be close to thethreshold of nonlinear conduction of the CDW. When thesample was in a CDW state, the Peierls gap opens at Fermi
surfaces, so that thermally activated quasiparticles and collective motion of the CDW contribute to electric conduction.
The former provides Ohmic currents and, as discussed
above, might contribute to positive nonlocal voltages. Hence,a quasiparticle is also ruled out as a major contributor to thenonlocal voltage and the collective motion becomes a candidate for the nonlocal voltage. Nevertheless, the observed
kinks are clearly related to the onset of CDW sliding.
For the sliding CDW to provide the nonlocal voltage,probed 200 ␮m away from the emitting electrodes, thephase correlation length of the CDW should be at least comparable to or longer than the traveling length. There are several estimations for the phase correlation length ranging from
1 to 100 ␮m.1–13 X-ray diffraction typically provides thelengths of the order of 1 ␮m,9,11,12 whereas other kinds ofestimations based on CDW dynamics provide longer valuesof up to 100 ␮m.1,6,7,13 Moreover, the phase coherence
length is a strong function of defect concentration and will
differ for different materials and even for samples of thesame material. Consequently, a consideration of the correlation length does not deny the possibility of a sliding CDW
being the origin of the nonlocal voltage.
However, even if the CDW correlation could extend sucha distance, the standard interpretation of the phase-slip voltage suggests that the phase correlation might be lost in thevicinity of the electrode.1,2 As shown in Fig. 3, the difference
between the voltages of the normal and transposed configurations implies that the CDW is in the sliding state with aconsiderable rate of phase slip.2 Moreover, it should be notedthat the nonlocal voltage was observed even below the kinks.
Hence, the source of the nonlocal voltage must be present
whether or not the CDW slides.
Now we may propose a possible model based on theabove discussions. Since the CDW phase correlation is de-stroyed in the vicinity of the electrodes and the nonlocal
voltage is also seen below the kinks, we must seek for adifferent transport mechanism originated from the CDWstate, rather than sliding. Its properties should include Ohmicbehavior and it should possess a spatial correlation over at
least 200 ␮m. A recent synchrotron diffraction study reportsthat two kinds of CDWs, incommensurate and commensurate CDWs, coexist in o-TaS3 共Ref. 16兲 and a subsequentultrafast optical pump-probe study of o-TaS3 also provides
evidence for two types of CDW phases.17 Discommensuration or a lattice of topological dislocations18 exists from thePeierls temperature to around 50 K.16 Each topological dislocation is accompanied by a charge, which can move along
the chain direction of a CDW. The distance between dislocations is determined by the difference between the CDW
wavelength and the lattice constant of the pristine lattice. The
advantage of this model as regards explaining the nonlocal
voltage relies on the correlation length of the dislocation
lattice. Hence, the question now moves to how far can thecorrelation be extended.
Coulomb repulsion plays a major role in the interaction
between the dislocations since each dislocation is accompanied by an electric charge. In some CDW materials, such as
NbSe3, uncondensed electrons remain at the Fermi surface,leading to the screening of the Coulomb potential. In the caseof o-TaS3, the entire Fermi surface contributes to the CDW
and at low temperatures, the density of thermally activatedquasiparticles is very low, so that the screening of the Coulomb potential becomes negligible. This helps to increase thecorrelation length of the dislocation lattice. We believe this is
the most plausible model for explaining the observed nonlocal voltage.
Consequently, the observed nonlocal voltage may havethree difference origins, as expressed byVnonlocal = Vspread + Vdislocation + Vsliding ,共2兲

where Vspread, Vdislocation, and Vsliding denote spreading resistance, the correlated motion of the dislocation lattice, andCDW sliding, respectively. Under our experimental conditions, each term contributes as follows: Vspread ⬎ 0 for alltemperatures, Vdislocation ⬍ 0 and 兩Vspread兩 ⬍ 兩Vdislocation兩 below
the Peierls temperature, and Vsliding ⬎ 0 above the CDW sliding threshold. Each term is schematically illustrated in Figs.
4共b兲–4共d兲. By using these terms, Eq. 共2兲 provides qualitative
explanations for the observed peculiar behavior as shown inFigs. 3 and 4. It should be noted that the polarity of Vsliding ispositive, thus coinciding with Vspread. This might be causedby the backflow of quasiparticle current accompanied by
CDW sliding.19
Finally, we discuss the possible relationship between ourobservation and the soliton transport in a commensurate
CDW.4 Previous studies have suggested that the lowtemperature transport of o-TaS3 should be understood as aCDW soliton.20,21 Experimentally, the anisotropy of conductivity was found to be increased at low temperatures along
the chain direction.20 Although the excitation energy was estimated to be 250 K, the previous results failed to detect anytraces of the soliton at temperatures at which they should beexcited. Assume that our observation of nonlocal voltage is113101-3

PHYSICAL REVIEW B 81, 113101 共2010兲

BRIEF REPORTS

an emergence of soliton transport. The phase diagram ofo-TaS3 共Ref. 16兲 shows that there is commensurate CDW at
130 K. Hence, if the lifetime of the excited soliton is longenough to travel over the 200 ␮m, it can be a candidate tothe origin of the nonlocal voltage. Since we lack unambiguous evidence for the relationship to the CDW soliton withinour study, we will pursue the nature of this nonlocal voltage
in further studies, including the use of optical,17 acoustic,22and diffraction12,16 methods.
To summarize, we studied the nonlocal transport of aquasi-one-dimensional conductor o-TaS3. We found that
nonlocal voltages appeared in the CDW of o-TaS3, both below and above the threshold field of CDW sliding. The tem-1

We are grateful to K. Ichimura, K. Yamaya, Y. Toda, M.
Hayashi, and Y. Nogami for fruitful discussions. One of theauthors 共K.I.兲 thanks the Japan Society for the Promotion ofScience for financial support via a Grant-in-aid for Scientific
Research 共Kakenhi兲.

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perature evolution of the nonlocal voltage suggests that theobserved nonlocal voltage originates from the CDW. Moreover, our observation of nonlocal voltage in both the pinned
and sliding states reveals the existence of a carrier with longrange correlation, in addition to a sliding CDW and thermally excited quasiparticles.

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