Transport properties of NbSe3

1890

Physica 109 & I IOB (1982) 1891~1~1t)0 North-Holland Publishing Compan},

TRANSPORT PROPERTIES OF NbSe3 Pierre M O N C E A U Centre de Recherehes sur les Tr~s Basses Tempdratures, C.N.R.S., B P lOO X, 3b;042 (irenoble-(/edex, France

The consequences of the formation of two indepcnden! charge density waves on the physical properties of NbSca arc reviewed. Particularly, it is shown that under pressure NbSe~ becomes a bulk superconductor. The non-linear properties of NbSe3 are described. Above a critical electric field, extra-conductivity and noise are measured. The extra-conductivity is associated with the depinning and the motion of the charge density waves. The noise is the superposition of broad band noise and periodic structures. These frequencies are described as due to the modulation of the current carried by the charge density wave in the anharmonic pinning potential. The number of condensed electrons under the gaps reduced by the lattice distorsion is measured for each charge density wave.

!. Introduction T h e unusual transport properties of NbSe~ [l] have a r o u s e d considerable interest in recent years. Like m a n y c o m p o u n d s with a restricted dimensionality, NbSe3 undergoes structural phase transitions associated with charge density wave formation (CDWs). T h e o p e n i n g of a gap at the Fermi surface which results from the lattice distortion induces anomalies in all the physical properties, such as resistivity [21, specific heat [3], the Hall effect [4], and t h e r m o p o w e r [5]. These phase transitions are the c o n s e q u e n c e of a delicate competition between the electronic and elastic energies which can be easily modified, by pressure for instance [6]. H o w e v e r . the more fascinating properties of NbSe3 are related to the extra-conductivity which is associated with the motion of the C D W s [7]. In fact, one year before the BCS theory Fr6hlich [8] had p r o p o s e d a model for the superconductivity where a C D W could m o v e without d a m p i n g in the lattice if its phase was invariant by translation. Lee, Rice and A n d e r s o n [9] showed that in real systems the phase of the C D W was pinned by c o m m e n surability with the underlying lattice, or by impurity pinning. But if an electric field is applied with sufficient strength, the C D W can b e c o m e 0378-4363/82/0000-0000/$02.75 @ 1982 N o r t h - H o l l a n d

d e p i n n e d and then moves in the lattice carrying a current [10l. In section 2 we review the static properties of NbSe~ and in section 3 we discuss the competition between C D W and superconductivity, with pressure as parameter. T h e nonlinear transport properties of NbSe) are described in sections 4 and 5.

2. Static properties of NbSe3 NbSe3 was synthetized for the first time in 1975 by Meerschaut and Rouxel [1]. T h e structure consists of infinite chains of selenium trigonal prisms stacked on top of each other by sharing the triangular faces. The niobium atoms arc located at the centre of the prisms. The m o n o clinic unit cell is f o r m e d with six chains which call be separated into three groups of two according to the distance between the S e - S e bondings in the basic triangle of each trigonal prism. The short S e - S e distances on two types of chains suggest a covalent bonding (Se,) -~ . T h e t e m p e r a t u r e variation of the resistivity is shown in fig. 1. T w o anomalies are visible at TI = 145 K and T2 = 59 K which were ascribed to the formation of the C D W s . New superlattice spots a p p e a r in the diffraction patterns. The

P. Monceau I Transport properties of NbSe3 0.6~-

i

i

i

i

i

i

c;..;

1891

140

145

......

'

150

155

.........

T' K:

oP"

dP"

0.5 o, o/

oO/

mb 0.~ m

oo

• /

°°

c~

oo / /"

o ," ,

~ o° , / o ,o / ~o,,

0.2

y o -'° o -°"

,e"

0.~

oo' ,o,o"

16 0.1

0 0

°°°o 50

100

150

200

250 T ( K )

300

Fig. 1. Variation of the resistivity of NbSe3 along the chains axis as a function of temperature (from ref. 2).

-7

.

/~" .~'~ p. ~-"

, heating

,o D" j,

o cooUn~,,~

o"

. . . . .

wavevectors of the distortions are incommensurate with the lattice and so q~ (0,0.243_+ 0.003, 0) at T1 and q2 (½, 0.259-+ 0.003, I) at 7"2, respectively. The increase of the resistivity below T1 and T2 is a consequence of the gap formation at the Fermi level which withdraws some of the conduction electrons. However, below Tz, the gaps do not affect the whole Fermi surface and NbSe3 remains metallic. From band calculation it was shown that only four chains participate in the conduction [11], and from estimation of the ionicity of the bondings we conclude that there are two electrons per unit cell to be shared between four niobium atoms. With the spin degeneracy the Fermi level in the one-dimensional picture would be exactly at 0.25 b* if the two types of conducting chains were equivalent. In fact, they are not exactly identical and the distortions take place at 0.243 b* and 0.259 b*. Using dark field electron microscope studies, Fung and Steeds [12] have examined the coherence of the C D W lattice. They observed domains whose typical dimensions are 2 # m x 200 ,~ x 200 ,~. The C D W formation can be observed on many physical properties, e.g.S. Tomic et al. [3] found two specific heat anomalies at 7"1 and 7"2, as shown in fig. 2. Pretransitional effects were

.o~" y J ~o,o~ +o,e

T (K) s's ....

6'o ....

ds ....

7'o

Fig. 2. Specific heat as a function of temperature: upper part for the Ti transition; lower part for the T2 transition (from ref. 3).

detected up to about 7 K above T~. From the total charge in entropy associated with the transitions and comparison with the total conduction electron entropy at T~ or T2 (~/TI,2), it was concluded that 25% of the conduction electrons were condensed at T~ and 30% at T2.

3. CDW and superconductivity Both the C D W transition temperatures and the amplitudes of the resistivity anomalies are suppressed by pressure [6]. T2 decreases sharply with pressure with an initial slope d T 2 / d P = -6.25 K/kbar. NbSe3 becomes superconducting when the lower C D W transition is totally suppressed around 5.5 kbar. For this pressure the resistive superconducting transition Tc is 3.5 K. When the pressure is increased further, Tc shows a slight decrease. In the pressure range where T2 varies strongly with pressure, T~ decreases rapidly and a superconducting transition cannot be detected below 5,5 kbar. The variation of 7"2 and Tc as functions of pressure is drawn in fig. 3.

7Yansp~rt prop~'rtics el

t S02

60

\

5(

\

\

4

\, X~kX,'

z

x z 0I

©

%,\ \

~30 z

x, " "k

cB

z 0c~) 12:

i ,,

u 20

10

i7

,

i

i

•

\'h£'c

diamagnetic susceptibility has been measured below 2.~ K by Burhlllan cl al. [151 which i,', at very hw, t e m p e r a t u r e (a few tens of millikelxms) less than 1% tff X,4:r. Fhc t c m p c r a t u r u dependence of the SUl+cruonducting critical current and the absence of a total Meissner clRx:t exclude bulk superconducti',ity, and ',t filamentary model for the superconducting transition has been prt>posed 114]. I'aking into account the o b s c r \ a t i o n of ( ' I ) W domain,, it can be assumed that the ( ' l ) W t>tdcr p a r a m e t e r in zero mskte the borders between two domains m which the phase of the ( ' I ) W in c~mslant. At low t c m p e r a t u r c these borders t~ccotnc superconducting which lead to an h l h o m o g e n e o u s suf~erconductivity. This asst,mption can a c c t ~ u n t f o r [ h e sanlple d e p c n d e l l l behaviour because of the distribution of d o m a i l > in diflerent samples.

i J

0

1

F i g . 3. V a r i a t i o n conducting

2

3

& P(kbar)

of the ('I)W

transition

5

~

tlansition

T< as a f u n c t i o n

r7

7": a n d t h e s u p e r -

of pressure

4. Non-linear properties

('flora rot.

( +) I

The superconductivity of NbSe.~ under pressure is also established by a total Meissner effect. The anisotropy of the electronic properties of NbSe~ can be obtained from the anisotropy of the superconducting critical fields. Near 7. thc anisotropy can be described by an effective mass model such as H~2jHd+-+(m,/mll) I'e. Experimentally it is found that the ratio between the effective masses when the electrons are travelling parallel or perpendicular to the chain direction (along the c axis) is a r o u n d 30, which is in g o o d agreement with the anisotropy of conductivity measured by Ong and Brill [13]. At ambient pressure a drop in resistivity below 2.2 K has been m e a s u r e d on many samples. The amplitude of this drop is sample d e p e n d e n t . The resistivity is strongly dependent on the current density, and the critical current decreases exponentially .with t e m p e r a t u r e [14]. A small

The amplitudes of the resistive anomalies arc strongly reduced by weak electric fields (typically 1 V/cm for f j and a few tenths of V/cm for T:) [16] and are frequency d e p e n d e n t [17. IS]. Thb, extra-conductivity was interpreted as the conductivity associated with the motion of the C D W when the energy gained by the electric field o v e r c o m e s the pinning energy. This depinning electric field E, was calculated by l,ee and Ricc [lll] and was observed for the first time bv Fleming and Grimes [14]. 4.1. ('ritical electric Oeld

An easy m e t h o d to put rote evidence thc critical field is the study of the differential resistance. Fig. 4 shows the variation of d V / d l measured with an a.c. bridge (33 Hz) when a d.c. current is swept in the sample. E,, is defined when d V/dl starts to decrease. A b o v e JE'~ noise at 33 Hz is easily detected. The shape of thc variation of d V/dI near E~ is strongly tern-

P. Monceau / Transport properties of NbSe3

1893

I

(:IV

dl

6])

Sample B15

i

v

i

Sample B15

d-~{l(Q)

55.5

T= 130.9 K

10Q

,

I (I.LA)

48.2Q

•I•T= L 0

I L l 100 200

~~

s~sn

5.5 K

"ll't~

~ Ir llrll'

f'l k''

54.4 ½

I (IJ.A) 300

400

500

I 100

I 200

I 300

I 400

I(I~A)

I 5oo

Fig. 4. Variation of the differential resistance dV/dl as a function of the applied current at different temperatures (from ref. 7).

perature dependent principally at low temperature where dV/dI shows a sharp drop with a deep minimum. However, negative resistance was never found. The role of impurities on the depinning of the C D W can be studied by doping the samples. Two types of impurities were distinguished by Lee and Rice [10]. The strong pinning impurities fix the phase of the C D W at each impurity site and E~ is proportional to the impurity concentration, c. A weak pinning impurity cannot pin the phase of the CDW, but the fluctuations of the pinning potential inside a domain with a size L can. In this case Ec varies as c 2. In fig. 5 we have drawn the variation of Ec as a function of the inverse of the resistance ratio p a r a m e t e r for samples doped with titanium, zirconium (which are non-isoelectronic with niobium and therefore considered as strong pinning centers) and with tantalum. We find that the behaviour of all these impurities is similar and seems to reveal a strong pinning character, contrary to the Brill et al. results [20].

lv4~

, Ec } mV/cm)

I

i

I

m=i

103

mm

102

oeOo a ) oo o

1

C

10"2

)

~

j

• Zr doped sampie.¢ • Ta • Ti ', ~~ o pure NbSe3 10"1

1/RRR

1

Fig. 5. Variation of the critical electric field for the lower CDW transition measured at the temperature where the resistivity is maximum for samples doped with titanium, zirconium, tantalum, and for pure samples as a function of the inverse of the resistance ratio between 300 and 4.2 K.

P. Monceau / Transl)ort properties o]" NbSe3

1894

III I

4.2. Expressions f o r the extra-conductivity ~

The earlier non-linear measurements showed that the c o n d u c t i v i t y f o l l o w e d an e x p - ( E , / E ) e x p r e s s i o n i n t e r p r e t e d as the t u n n e l l i n g of elect r o n s t h r o u g h the C D W g a p [16, 17]. But the

3

3

I

N I 1[1[

l

's

+-~

///

*

w h e r e eg is the pinning gap, e* = e ( m / M v ) is the effective c h a r g e with m the b a n d mass and MF the F r 6 h l i c h mass, ~ 1 0 ~ m . T o a c c o u n t for the critical field B a r d e e n i n t r o d u c e s a c o r r e l a t i o n length L n e c e s s a r y to a c c e l e r a t e the wave [221 . T h e c o n d u c t i v i t y can be written as ~r = o-~,+ crbP ( x ) , with 1\ P ( x ) = {1 \ -7)e

~,,

'

and with

Ill]

I

[

[ I 111~1

]

1

I I I I1

I0e

10 7

I09

Frequency ¢012+ (Hz) c o n d u c / i ' d t y in NbSc~ at T

in Re cr(oJ) as f o u n d for o t h e r o n e - d i m e n s i o n a l m a t e r i a l s . In fig. 7 we show t h e B a r d e e n tit of P ( x ) o b t a i n e d as a function of E/E~. for d.c. m e a s u r e m e n t s at several t e m p e r a t u r e s [23] a n d as a function of co/w, for a.c. c o n d u c t i v i t y m e a s u r e m e n t at 42 K [18]. A n o t h e r p r o o f of the C D W m o t i o n is the Hall v o l t a g e m e a s u r e m e n t s in the n o n - l i n e a r regime. m a d e i n d e p e n d e n t l y by K a w a b a t a et al. [24] a n d T e s s e m a a n d O n g [25]. In fig. 8 it can be seen that the Hall wHtage is n o n - l i n e a r a b o v e the s a m e c u r r e n t w h e r c the resistivity d r o p s , but is linear as a function of the electric field well a b o v e the critical field. T h e s e results can bc ?

_o 30r ' i

~~ \

-~ 20

x = E/E~.. B a r d e e n also r e l a t e d the n o n - o h m i c b e h a v i o u r with the f r e q u e n c y d e p e n d e n t a.c. c o n d u c t i v i t y . H e f o u n d that the a.c. c o n d u c t i v i t y follows the s a m e r e l a t i o n as a function of the f r e q u e n c y w/(oc, or as a function of the electric field E/E~.. a)~ is the pinning f r e q u e n c y d e f i n e d by oo~ ~%/h. T h e r e is a scaling r e l a t i o n b e t w e e n oo~ and E~, such as h(,oc = e*LE~. T h e a.c. c o n d u c t i v i t y (r(w) was m e a s u r e d by G r f i n e r et al, [18] and the f r e q u e n c y d e p e n d e n c e is r e p r o d u c e d in fig. h. T h e c o n d u c t i v i t y rises s m o o t h l y from the d.c. to the high f r e q u e n c y limit w i t h o u t any m a x i m u m

"

\

Fig. f~+ F r e q u e n c y d e p e n d e n t 42 K ( f r o m ref. IS).

~-e~ E , = 4he * vF "

Re o+ " Tmcr

.,

a c t i v a t i o n e n e r g y E , was m u c h s m a l l e r than k T . B a r d e e n has d e v e l o p e d a t h e o r y w h e r e E , is r e l a t e d to the f r e q u e n c y of t h e o s c i l l a t i o n s of the C D W a r o u n d p i n n i n g c e n t r e s [21]. C o h e r e n t C D W is a s s u m e d to t u n n e l t h r o u g h the p i n n i n g gaps. In this case

t I t lIT

\

,. /,i/]/

g

I

l

NbSe3 T:42K

R ~

0.8

~)

] i

~ [o-(E)-o-0)/% • 24.1K:

9 4 ,~

,

• s0.zK

(o.-(co)-o-o)/o.- b 0

2o 40 60

42.5K

..._.._------o~

T(K)

0.6 f

0.4 0.2

× : E / E T or w/co T Fig. 7. Plot of the p r o b a b i l i t y P ( x ) f o r the t u n n e l l i n g of the ( ' D W d e r i v a t c d by B a r d c c n as a f u n c t i o n of v E,'E, o r w/rod E, is the critical electric field. ~o~ is the p i n n i n g f r e q u e n c y ( f r o m rcf. 22).

P. Monceau / Transport properties of NbSe3 1

T

1

i

O

T

O

(ET)

1.0

0

O

O

Z i/

)

.A~ . . . . . .

/ "J

o

er"

L

0,

. . . . . . . .

Eb (V/cm)

1

L . . . . . . . . .

T=48K

2

3

|

4

lb(mA) Fig. 8. T h e Hall voltage VH and the normalized resistivity

R(1)/R(O) at 48 K as a function of the applied current lh and as a function of the electric field Eb. The curves are displaced by 0.1 mV along the ordinate (from ref. 24).

interpreted as the motion of the C D W parallel to the chains for both transitions.

4.3. Phenomenological model The C D W can be thought of as a particle with mass, charge and friction. In motion the current carried by the C D W is - n e v , where v is the drift velocity of the wave and n the number of electrons condensed below each C D W gap. The forces acting on the C D W are electric forces, damping forces and pinning forces. We have estimated that the main interaction between the phase of the C D W and the impurities was via Friedel oscillations which have the same oscillatory behaviour with q = 2kF. At Tc, domains where the C D W has a constant phase are nucleated. When T decreases, the size of the domains grow and the C D W lattice can be described as a multidomain network with domain walls inside which the order parameter is sup-

1895

posed to be zero. This hypothesis is supported by the observation of Fung and Steeds [12] and the multifilamentary superconducting properties of NbSe3 at low temperature [14]. In each domain the summation of the pinning forces over impurities gives a net pinning force with a periodic dependence with the phase 4) of the C D W [7, 26]. For a single domain we have shown that the current carried by the C D W is the superposition of a continuous current and a modulation with periodic components multiple of a fundamental frequency v. The variation of v with E is proportional to ~v/(E/Ec)2 - 1. A similar phenomenological model was developed by Gr/iner et al. [27]. If the current is regulated, d W d I shows an infinite negative differential resistance at Ec which was not observed experimentally. But by taking a Gaussian distribution of critical electric fields for the assembly of domains in the sample, this discontinuity at Ec can be suppressed. However, as pointed out by Sokoloff [28], the overdamped non-linear equation derived in this model will always give an infinite dr~dE at Ec. As we show in section 5, the experimental v(E) variation shows an upward curvature. Therefore this model explains qualitatively the behaviour of NbSe3 but shows severe limitations.

5. Dynamics of the CDW Above the critical electric field Ec, Fleming and Grimes [19] have shown that noise was generated through the voltage leads. This noise is the superposition of a broad noise and periodic structures. As explained in subsection 4.3, we have interpreted these frequencies as the modulation of the current carried by the C D W in the pinning potential [26, 7].

5.1, Fourier analysis of the noise These eigenfrequencies are measured by a

P. Monceau / "l)'ansport properties of NhSe~

1896

noise voltage

and also a third one. /~,, are detected. The whole frequency spectrum can be described by these three f u n d a m e n t a l frequencies and their harmonics. For this sample with well-defined frequencies the fundamental frequencies were detected up to 1(t0 M H z for E - 10 E~ and their harmonics at a r o u n d 400 M H z [7].

S a m p l e B17

T: 35.9 K

i

spectrum

analyser

Edc IJ

(mV/cm

2~o I

2F1

105

!

l

% 2Fo ,

3F°

3F^

_~ ,~-,~

.L

,~ "~''

2F0

~r~"

:Lg--~-'~r,. 800

!

5.2. Synchronization of the motion Of the ( ' D W hv an external r.L field

...... liT' /

400 600

~-

Fn

9~.__~s/

~'-"~ 200

~

~

.....

0

~

o.2~v

0

200

400

95..~5

3~o

600

If the C D W moves it1 the crystal with a modulated velocity, it must be possible to synchronize this motion by an external field [26]. We have applied a d.c. current to the sample to bring it to the non-linear state and we superpose a r.f. field with a constant amplitude. W e sweep the frequency and we measure the low frequency (33 Hz) differential resistance. When the frequency (or harmonics) of the m o d u l a t e d current equals the r.f. frequency there is interference which is detected by a peak in dV/dl, as shown in fig. 1(). The f u n d a m e n t a l frequency is defined as the firsl frequency which appears

BOO 1000

Fig. 9. Fourier spectrum obtained by direct noise analysis al T = 35.9 K. The critical electric field is 80.4 mV/cm.

Fourier analysis of the noise voltage with a spectrum analyser. Fig. 9 shows the Fourier spectrum for different electric fields at T = 35.9 K. For this sample d V / d I shows a sharp drop at E , 8 0 . 4 m V / c m . Just a b o v e E'~ a f u n d a m e n t a l frequency, F0, appears with its harmonics. W h e n E is increased further, a second fundamental, F~,

dV(~)

Sample B15 T=44.7 K

IF, 0

T=112.4 K Irf=165~A 12F0

,"

~ ~

]

400 ~.A

350

I

ro 2.5 C21

%

lh,;

F,.

"~-k/I

V MHz) / I

0

4

I

B

I

12

I

16

I

20

1

j

~o

'

850

2~ 3Fo

F2 .

,sr-o

'

,

,

i

i

1

3

-

FO 5F0 ~ ~

800

i

I"

I q(MHz)

5

7

9

Fig. IlL Differential resistance dV/dl as a function of the external r.f. frequency in the range 0.1 21)MHz at T T = 112.4 K.

44.7K and

P. Monceau / Transport properties of NbSe3

5.3. Electronic condensation by the CDWs

when the r.f. amplitude is increased. We have verified that the fundamental frequencies obtained by direct noise analysis or by the synchronization experiment are exactly the same, except near Ec where the coupling between the a.c. and d.c. fields changes the Ec value. Again the frequency spectrum can be analysed with three fundamental frequencies. For several samples, at different temperatures, it was found that the ratio between two of these fundamental frequencies was 3/2. In fig. 11 we have plotted the variation of the fundamental frequency as a function of E for the two CDWs.

2sl

I

I

In subsection 4.3 it was assumed that the current carried by the C D W is JcDw = nev. The drift velocity v = 2Tru/O, where Q=27r/A, is the C D W wavelength. So there is a linear relation between Jcow and u: JCDW = n e a p .

/CDW c a n be measured directly from the non-

linear characteristics V(I) assuming that JCDW ~-" J ( 1 - R / R N ) when J is the total current, R the

I

~(NHz) Nb

1897

L

Se 3 SampLe

I

I

B15

20

•', T= 35./, K

& T=99 K

O T= 39.2 K

•

T= 112.4 K

v

•

T= 130 K

T= 44.5 K

o T= 52.5 K 15

10

E (mV/cm)

100

200xx

400

600

80(]

1000

1200

Fig. I 1. Variation as a function of the electric field of the fundamental frequency measured in the synchronization experiment for temperatures concerning both CDWs.

P. Monceau / Transport properties of NbSe3

1898

resistance for this current and RN the ohmic resistance for J ~ (). In fig. 12 we have plotted the same frequencies as in fig. I 1, but this time as a function of J('Dw m e a s u r e d at each temperature. All the v(E) curves gather in a compact pattern, v is linear with Jcgw up to a r o u n d 1 0 0 A / c m 2 and shows a slight curvature for higher JCDW. T h e inverse of the slope of u(JcDw) is proportional to ne, the n u m b e r of c o n d e n s e d electron below the C D W gap. We find that this n u m b e r is the same for the two C D W s , and is a r o u n d 1.0 x 1021cm ~. This n u m b e r is o b t a i n e d assuming a resistivity at r o o m t e m p e r a t u r e of 0 6

I~)(MHz)

20

40

I

F

a r o u n d 250/x[~cm used for the m e a s u r e m e n t of the cross-section of the samples. Following the discussion in section 2, if only four chains participate in the conduction with 0.5 electron per niobium, the total n u m b e r of electrons at r o o m t e m p e r a t u r e will be 3.9× 102~cm 3. For each C D W the n u m b e r of electrons affected by the gap is a r o u n d 1× 102~cm ~. From the linear specific heat m e a s u r e d between 0.15 and 1 K ( y - 24.5 erg/gK 2) [29] it was d e d u c e d that the n u m b e r of electrons below the two C D W s was a r o u n d 102~cm ~. So we obtain a c o h e r e n t picture of the electronic concentration in NbSe~. 60

80

-I

100

T

120 T~

! Nb Se 3 Sampte B 15

[

i

,~ o v D •

0 < 20--

T= 35.4 T = 39.2 T= 44.5 T= 52.5 T=99

K K K K K

| /\ "I

.

10 ~

Jcdw (A/cm2) 0

I 100

I 200

l 30o

I 4o0

500

Fig. 12. Variation of the fundamental frequency (the same asin fig. l l ) a s a function ofJcDw thccurrent carried bythc ('DW for the two CDWs: upper part for JcDw < |00 A/crn2: lower part for JcDw up to 400 A / c m ~.

P. Monceau / Transport properties of NbSe3

6. Conclusions Since 1975 NbSe3 has provided a neverending source of new electronic properties. Although this c o m p o u n d cannot be described as onedimensional, the two independent charge density waves seem to take place on two different types of chains. The electronic charges available on each chain are due to the strength of the Se-Se bonding in the trigonal prism. The pressure has been seen to be a useful tool to study the coexistence between C D W and superconductivity. It must be noted that above 5.5 kbar, when NbSe3 is a bulk superconductor, the upper C D W is still present and NbSe3 in this case is more like a layered dichalcogenide as NbSe2. The nonlinear properties of NbSe3 have made this compound the first for exhibiting the Fr6hlich conductivity associated with the motion of the C D W . The tunnelling theory of Bardeen seems to describe very well the extra-conductivity as a function of the electric field, or frequency. The frequencies in the noise can be associated with the motion of the C D W in the anharmonic pinning potential. By a relation independent of any model we have deduced the number of condensed electrons below the gap in good agreement with heat capacity measurements and with electronic concentrations at room temperature and at helium temperature. However, the exact depinning mechanism is not very well understood. It is assumed that the C D W moves as a whole but the non-linear properties can be due to C D W dislocations motion. The existence of domains where the phase of the C D W is constant is not proven, and the conditions at the domain walls might be more complicated than previously considered.

Acknowledgements ! would like to thank L. Guemas, A. Meerschaut and J. Rouxel from the Laboratoire de Chimie Min6rale de Nantes for providing the

1899

samples. Most of the experiments reported were performed with J. Richard. They form part of the thesis of d o c t o r a t e s sciences d'6tat he submitted in June 1981 to the University of Grenoble. I would like to thank J. Bardeen, J. Friedel, A. Libchaber, M. Papoular and M. Renard for helpful discussions.

References [l] A. Meerschaut and J. Rouxel, J. Less Common Metals 39 (1975) 197. [2] P. Haen, P. Monceau, B. Tissier, G. Waysand, A. Meerschaut, P. Molini6 and J. Rouxel, in Proceedings of the Fourteenth International Conference on Low Temperature Physics, Otaniemi, Finland, vol. 5, M. Krusius and M. Vuorio, eds. (North-Holland, Amsterdam, 1975) p. 445. [3] S. Tomic, K. Biljakovic, D. Djurek, J.R. Cooper. P. Monceau and A. Meerschaut, Solid State Commun. 38

0981) io9. [4[ N.P. Ong and J.W. Brill, Phys. Rev. 1318 (1978) 5265. [5] R.D. Dee, P.M. Chaikin and N.P. Ong, Phys. Rev. Len. 42 (1979) 1234. [6] A. Briggs, P. Monceau, M. Nunez-Regueiro, J. Peyrard, M. Ribault and J. Richard, J. Phys. C13 (1980) 2117. [7] P. Monceau, J. Richard and M. Renard, Phys. Rev. B, to be published; J. Richard, P. Monceau and M. Renard, Phys. Rev. B, to be published. [8] H. Fr6hlich, Proc. Roy. Soc. A223 (1954) 296. [9] P.A. Lee, T.M. Rice and P.W. Anderson, Solid State Commun. 14 (1974) 7/13. [111] P.A. Lee and T.M. Rice, Phys. Rev. BI9 (1979) 3970. [11] D.W. Bullen, Solid State Commun. 26 (1978) 563. [12] K.K. Fung and J.W, Steeds, Phys. Rev. Len, 45 (1980) 1696. [13[ N.P. Ong and J.W. Brill, Phys. Rev. B18 (1978) 5265. [14] P. Haen, J.M. Mignot, P. Monceau and M. NunezRegueiro, J. Phys. C6 (1978) 7113. [15] R.A. Buhrman, C.M. Bastuscheck, J.C. Scott and J.D. Kulick, in Inhomogeneous Superconductors, D.W. Gubser, T.L. Francavilla, S.A. Wolf and J.R. Leibowitz, eds. (American Institute of Physics, New York, 1980). [16] P. Monceau, N.P. Ong, A.M. Portis, A. Meerschaut and J. Rouxel, Phys. Rev. Len. 37 (1976) 61t2. [17] N.P. Ong and P. Monceau, Phys. Rev. BI6 (1977) 3443. [18] G. Gr(iner. L.C. Tippie, J. Sanny, W.G. Clark and N.P. Ong, Phys. Rev, Lett. 45 (1980) 935. [19] R. Fleming and C.C. Grimes, Phys. Rev. Lett. 42 (1979) 1423: and R. Fleming, Phys. Rev. B22 (1980) 5606. [20] J.W. Brill, N.P. Ong, J.C. Eckert, J.W. Savage, S.K. Khanna and R.B. Somoano, Phys. Rev. B23 (1981) 1517. [21] J. Bardeen, Phys. Rev. Lett. 42 (1979) 1498. [22] J. Bardeen, Phys. Rev. Lett. 45 (19811) 1978.

l OI )( )

P. Mom'eau i Transport properties o[ NhSe.,

[23] J. Richard and P. Monceau, Solid State Commui1. 33 (lYgll) 635. [24] K. Kawabata. M, ldo and T. Sambongi, J. Phys. Soc. Jap., in press. [25] G.X. T e s s e m a and N.P. Orig, Phys. Rev. B23 (1981) 5~( 17. [2(q P. Monceau, J. Richard and M. Renard, Phys. Rc~. l,ell. 45 (1~80) 43.

[27] (i. Griincr, A. Zawadowski and P.M. ('haikin, l'h>~ Rev. Letl. 4(~ (1981) 51 I. [2N] J.B. Sokololf, Phys. Rev. B23 (It,~Nl) 1992, [2q] J.C. l,asjaunias and P. Monceau. Solid Statc ('omunm., n~ be published.