Table Of ContentCritical current in charge-density wave transport
A. A. Sinchenko
Moscow state Engineering-Physics Institute, 115409 Moscow, Russia
V. Ya. Pokrovski,S. G. Zybtsev, I. G. Gorlova, Yu. I. Latyshev
Institute of Radioengineering and Electronics, Russian Academy of Sciences, 103907 Moscow, Russia
1
0 P. Monceau
0 Centre de Recherches sur Les Tr`es Basses Temp´eratures, C.N.R.S., B.P. 166, 38042, Grenoble C´edex 9, France
2 (February 1, 2008)
n We report transport measurements under very high current densities j, up to ∼ 108 A/cm2, of
a
quasi-one-dimensional charge-density wave (CDW) conductors NbSe3 and TaS3. Joule heating has
J
been minimized by using a point-contact configuration or by measuring samples with extremely
0 small cross-sections. Abovejc ≈107 A/cm2 wefindevidencefor suppressionof thePeierlsgap and
1
development of the metallic state. The critical CDW velocity corresponding with j0 is comparable
] with the sound velocity, and with ∆/~kF (kF is the Fermi wave vector), which corresponds to the
l depairing current. Possible scenarios of the Peierls state destruction are discussed.
e
-
r PACS Numbers: 71.45.Lr, 73.40.Ns, 74.80 Fp
t
s
.
t
a The discovery of non-Ohmic conductivity in quasi- figurations will not allow to achieve high enough values
m one-dimensional charge-density wave (CDW) materials of j.
- has opened great expectations concerning the so-called Hereafter we propose two approaches for overcoming
d
Fr¨ohlich superconductivity [1]. However, the experi- this problem. The first one is the point contact con-
n
o ments up to now have showed that the CDW conduc- figuration formed between two thin whiskers of NbSe3.
c tivity under the highestelectricfields asymptoticallyap- It is well known that the electric field is localized near
[ proachesavalueclosetothe”normal-stateconductivity” a point contact in a small region with a characteristic
andneverexceedsit. Thisconductivityisestimatedfrom size of the order of the point contact diameter, d. In
1
v the extrapolationof the temperature dependent conduc- the case d << l (l is the mean free path) the length for
4 tivity above the Peierls transition [2]. The hypothesis energy relaxation is much longer than that correspond-
2 whichcanbenaturallyrisen,namelythattheCDWstate ing to the formation of the point contact resistance and
1
issuppressedathighcurrentswasrejectedbyx-raysmea- the heating effect is strongly suppressed [7]. Thus, a
1
surements of the CDW satellite profiles in the sliding point contact is a very convenient configuration for high
0
1 state [3], [4] and by narrow-bandnoise measurements at current measurements. We have used the configuration
0 high current densities j (up to 3·104 A/cm2 for TaS3 proposed in Ref. [8]. The electric contact between two
t/ [5]): in the latter case, it was shown that the main part NbSe3 stripe–like single crystals with perpendicular bc
a
of the current is carried by the coherently sliding CDW – planes is formed at low temperatures by means of a
m
with no reduction of its charge density. On the other precise mechanical motion transfer system, so that the
- hand, the CDW velocity cannot grow up to infinity. So, current through the contacts flows along the b-axis. The
d
n the question concerning the existence of an upper limit samples selected for the experiment had typical dimen-
o for the velocity of the sliding CDW is still undecided up sions: along the b-axes L ≈ 1 mm, along the c-axes
b
c to now. L ≈10÷50 µm and along the a∗- axes L ≈1 µm.
c a
:
v To our knowledge, it has been reported only one in- Disadvantages of the point contact configuration are
i dication in favour of the local suppression of the Peierls a probability for having a non-predicted barrier at the
X
energy gap 2∆, and that in K0.3MoO3 [6]. This effect, boundary between the samples and a non-uniform cur-
r
a attributed to a high current density near the metal – rent distribution. So we have performed high–current
CDW surface was observed at a high degree of injection measurements of extremely thin samples of TaS3 with
of normal carriers through a Au–K0.3MoO3 boundary. a cross-section area . 10−3 µm2 and a typical length
Estimation of the critical currentdensity gavea value of 5÷10 µm. The cross-section area is estimated from the
j = 4.8·107 A/cm2. However, it is not clear if the gap value of the room-temperature resistance of the samples
c
suppression reported in Ref. [6] is associated with the [9]. Due to the very good thermal contact with the sap-
high CDW velocity, or is induced by the injected quasi- phiresubstratessuchsamplescansustainextremelyhigh
particules. Foraclarificationofthesituationitwouldbe current densities with a relatively small Joule heating.
highlydesirabletoobservethisphenomenondirectly. Ev- The main results presented below are insensitive to the
idently, Joule heating in the previous experimental con- exact value of heating.
1
800
1/R , which is proportional to the point–contact area,
ds
for more than 20 different point contacts. The depen-
700
dence is close to be linear. The proportionality between
I0 andtheconductivitymeansthatthecurrentdensityis
600
constant for all contacts and is evidently determined by
300 fundamental properties of the material. For ρ=3·10−4
Ωcm (Ref [11]) and for l=100nm, we estimate the mean
) 250 value for the CDW currentdensity j0 =5.9·107 A/cm2.
W(
d
R
200 0.8
180
0.6
160 )
A
m 0.4
(
-0.8 -0.4 0.0 0.4 0.8 I0
I (mA)
FIG. 1. Current dependence of the differential resistance 0.2
Rd(I)ofNbSe3–NbSe3 pointcontacts. T =77K.Thearrows
indicate I0
0.0
Let first analyse our results with the point con- 0 2 4 6
103/R (W -1)
tact configuration. Figure 1 shows typical dependen- ds
cies of the differential resistance R (I) for three differ- FIG.2. Critical current I0 as a function of inverse satura-
d
ent NbSe3-NbSe3 point contacts obtained at T=77 K. tion differential resistance of NbSe3–NbSe3 point contacts.
R (I) monotonously decreases with the increase of the
d
For making clear if the abrupt change in conductiv-
injected current revealing the CDW sliding. The thresh-
ityofNbSe3 atj ∼107 A/cm2 reallyrevealsatransition
old electric field for initiation of the CDW sliding, E ,
T
intoametallicstate,i.e. acritical(depairing)currentfor
is achievedat a very small current, so the plateau in the
the CDW, or is associated with contact phenomena un-
curves corresponding to the pinned state of the CDW is
der inhomogeneous conditions, we performed transport
indistinguishable in this scale. At very high current R
d
measurements of extremely fine samples of TaS3. We
is close to the resistancevalues which wouldbe observed
selectedthismaterial,asitdemonstratesapurelydielec-
in the absence of the Peierls transition [2]. In this re-
tric behavior below T ≈ 220 K. So, a transition into
gion, practically for all investigated contacts we clearly P
a metallic state should be more obvious for it. Besides,
observedasharpdecreaseoftheresistanceatthecurrent
TaS3 crystals can be easily splitted and make possible
I0 (indicatedbyarrowsinFig.1). AboveI0 theresistance
the preparation of samples with a cross section area be-
is slightly growing with current, evidently reflecting the
low 10−3 µm2.
Joule heating. The growth of R with heating should be
Typical results of transport measurements are shown
the case for a metallic state. We could not measure the
in Figure 3, which illustrates “raw” dependencies of the
Rd(I) dependence far above I0 because the contacts are
conductivity of a representative sample at different tem-
very unstable in this region and often burn.
peraturesasafunctionofthecurrentdensity(opensym-
The exact determination of the CDW current density
bols). These data have to be corrected of Joule heating.
corresponding to I0 is complicated in the case of NbSe3.
We have estimated its value by two ways. First, we no-
The unit cell of NbSe3 contains three different types of
ticed,thatattemperatureswellaboveT (typicallyT >
chains. Inthetemperaturerangefrom59Kto145Ktwo P
250 K) the non-linear conductivity due to CDW fluctu-
types of chains are in the normal state and one is in the
ations becomes negligible; therefore, the slight change of
CDW state [2], but at high electric field we can assume
resistancewith voltage,δR≡R(V)−R(0)∝V2, is only
that the injected current is homogeneously distributed
providedby heating. The comparisonofδR withdR/dT
over the chains, because in this case the CDW conduc-
tivity is close to the normal-state value. So I ≈ jπd2/4, atseveraltemperaturesyieldstheestimateofheatingasa
functionofJoulepower,W. Thesecondestimateisbased
where j is the current density, and the point contact di-
on the dependencies R(j) obtained at low temperatures.
ameter may be estimated from the well known Sharvin
formula [10]: R = lρ/d2, where ρ is the normal state We noticed that at the highest currents the temperature
ds
of the samples exceeds T , and that at a certain cur-
resistivity and R is the saturation value of R at high P
ds d
rent density each curve R(j) (and R (j)) demonstrates
current. Fig. 2 shows the variationof I0 as a function of d
2
8
a minimum corresponding with the minimum of R(T),
which is observed around T = 250÷300 K. Thus, the
M
powerW attheminimumofR(j)providestheestimate
M
of heating δT = T −T, where T is the ambient tem-
M
perature. The dependence W vs. T is approximately 6
M
linear, its slope giving the required value dT/dW. Both
1
ways give dT/dW ≈ 105 K/W for samples with dimen- -
sions5µm×10−3 µm2. KnowingthevalueofW ateach -5W - 0.15 kV/cm
0 4 - 0.42 kV/cm
V and dT/dW we thus know the temperature for each , 1 - 1.11 kV/cm
point of each curve. Interpolating the set of I-V curves R - 2.38 kV/cm
we got isothermal dependencies and thus the correction 1/ - 3.30 kV/cm
- 3.90 kV/cm
for heating. The curves obtained after this temperature
2 - 4.70 kV/cm
correction are shown in Fig.3 (solid lines). One can see
that the curves for T < T intersect at j = 107 A/cm2.
P
For j > 107 A/cm2 the growth of conductivity tends to
saturate value. However, we cannot determine exactly 0
the asymptotic behavior of the curves, because our re- 100 200 300
T, K
sults for high currents are very sensitive to the value of
FIG.4. A set of temperature dependencies of the conduc-
dT/dW used for the temperature correction.
tivityoftherepresentativeTaS3 sampleatfixedelectricfields
indicatedintheplot. Thebrokenlineshowstheconductivity
8
at E ≪ET (E =0.1 V/cm).
6 Thevalueofthenon-linearcontributiontoj0asafunc-
-77 K
-1 -96 K tion of temperature is presentedin Fig.5 for TaS3 (black
-5W -134 K circles) and for a stable point-contact NbSe3-NbSe3 for
10 4 -203 K whichwesucceededinobtainingthetemperaturedepen-
, dence of the currentI0 (open circles). Both temperature
R
1/ andcurrentscalesarenormalizedbythevalueofTp (145
2
K for NbSe3 and 208 K for TaS3) and the value of j0
at T = 0.62T respectively. As seen in the figure, the
p
0 value of j0 for both materials has a little tendency to
0.0 0.5 1.0 1.5 2.0 2.5 decrease with increasing temperature. The growth of j0
j, 107A/cm2 for TaS3 at T → TP is probably due to the growth of
FIG.3. Conductivity as a function of j at several temper- non-collective contributions to the current. In fact, at
atures indicated in the plot. The solid lines show data after the highest temperatures (Fig.5) the linear contribution
the temperature correction with dT/dW = 1.3·105 K/W. toj0,i.e. j0∗R/R(0)),iscomparablewiththenon-linear
The dimensions of theTaS3 sample are 4.7 µm×10−3 µm2. part of the current.
To ascertain if TaS3 really exhibits a transition into a 1.2
metallicstate,wehaveplottedtheconductivitymeasured
at a given current as a function of temperature. Fig.4
showssuchasetofdependencies. Forcomparisonwealso )
p
show the temperature dependence of the conductivity at 2T 0.8
a low field E ≪ET (ET ≈25 V/cm). For E .3 kV/cm 0.6
the temperature dependence of the conductivity demon- =
T
strates a dielectric behaviour (dR/dT < 0). While for (0
I
E . 500 V/cm, the high-field conductivity approxi- )/ 0.4
T
mately follows the behaviour of the conductivity mea- (0
I
sured at low-field [12], at higher E the activation energy
decreases, and for E0 = 3.3 kV/cm (j0 = 107 A/cm2)
the conductivity is nearly independent of temperature. 0.0
0.4 0.6 0.8 1.0
Increasing the current further results in the metallic be-
T/T
haviour of conductivity, i.e. dR/dT > 0. We emphasize p
FIG. 5. Normalized temperature dependencies of critical
that this result and the value of the current j0 are quite
current densities for TaS3 (black circles) and NbSe3 (open
insensitive to the value of dT/dW taken for the Joule
circles). Thelinear contribution to j is subtracted
heat correction [13].
3
Analyzingourexperimentalresultswiththepointcon- est possible time for the gap suppression or recovering
tact technique we are led to the assumptionthat the ob- is ∼ h/∆, which could be treated as the lowest possible
served anomalies at j = j0 are related to the suppres- time of a PS act. If the PS frequency exceeds the criti-
sion of the CDW state at high current density. Indeed, cal value, the gap has no time to restore before another
the conductivity of the CDW is less than the normal wavelength comes, and the area of the gap suppression
state conductivity at any current. So, the sharp drop of expands throughout the sample. So, the PS time limita-
theresistanceoftheNbSe3–NbSe3 pointcontactsreveals tion from below gives the same value of critical current.
the transition from the CDW conductivity to the nor- Nucleationofthemetallicstateresultingfromacontinu-
mal state conductivity. Similarly, a metallic behaviour ous increase of PS processeswas consideredearlier as an
isdemonstratedinverysmallcross-sectionTaS3 samples approachtothePeierlstransitionfromlowtemperatures
above j0. The fact that the transition into the metallic [16].
state in the latter case is more gradual can be ascribed Inconclusion,wehaveforthefirsttimeconsideredthe
tothe non-uniformdistributionofthe CDWvelocitiesin questionaboutthe criticalvelocityoftheCDWandpro-
thevolumeofthesample,whilethe pointcontactprobes posedanexperimentalanswertoit. ForTaS3 andNbSe3
only several wavelengths. Evidently, the transition of we clearly observed a Peierls state – normal metal tran-
TaS3 into a metallic state is not complete, and in the sitionatj0 ∼107 A/cm2. Thecriticalvelocity,v0,ofthe
vicinityofT =Tp thedielectricbehaviourisobservedup slidingCDWcorrespondingtothevalueofj0 approaches
to the highest fields (Fig.5). By analogy with supercon- the speed of sound, and is comparable with ∆/q.
ductors this may be associated with the development of We are thankful to S.V. Zaitsev-Zotov for permanent
a kind of mixed state in the CDW at high currents. helpintheexperimentanddiscussions,andtoS.N.Arte-
The magnitude of the critical current densities for menko for helpful discussions. This work has been sup-
different CDW materials are approximately the same: ported by the Russian State Foundation for Basic Re-
j0 = 5.9 · 107 A/cm2 for NbSe3, 107 A/cm2 for TaS3 search(grantsNo99–02–17364,No99–02-17387,andNo
and4.8·107 A/cm2 forK0.3MoO3 [6]. Ithastobe noted 98–02–16667), by the twinning research programme 19
that,forthelattercompound,thesuppressionofthegap from CNRS, and by the State programme ”Physics of
has been observed directly. Solid-State nanostructures” (No 97-1052).
What could be the physical mechanism of this transi-
tion? The theoretical description or even the considera-
tionofthisphenomenondoesnotexistuptonow. There-
fore, we canonly propose qualitative explanationsof the
effectswehaveobserved. Firstofall,letestimatetheve-
locity of the CDW motion corresponding to the critical
[1] H. Fr¨ohlich, Proc. RoyalSoc. A223, 296 (1954).
current density, j0. The usual formula v =j0/ne, where
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G. Gru¨ner (Elsevier Science, Amsterdam, 1989);
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s
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4
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1047 (1988).
[13] The Joule power at j = j0 provides temperature gain
about 15 K.
[14] ForNbSe3 vs =5.5·105 cm/s (P. Monceau, L. Bernard,
R. Currat, F. Levy, and J. Rouxel, Synthetic Met-
als 19, 819 (1987)), for K0.3MoO3 — 4.5 · 105 cm/s
(M.Saint-PaulandG.X.Tessema,Phys.Rev.B39,8736
(1989)), and for TaS3 — 4·105 cm/s (M.H. Jericho and
A.M. Simpson, Phys.Rev. B 34, 1116 (1986))
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5
