Correlation between the static dielectric constant and threshold electric field for sliding charge density wave conduction

-SolidState Coummnications, Vo1.49,No.l1, pp.1013-1017,1984 Printedin Great Britain.

0038-1098/84 $3.00 + .OO PergamonPress Ltd.

CORRELATION BETWEEN THE STATIC DIELECTRIC CONSTANT AND THRESHOLD ELECTRIC FIELD FOR SLIDING CHARGE DENSITY WAVE CONDUCTION Wei-yu Wu, A. Janossy," and G. Griiner Department of Physics, University of California, Los Angeles, CA 90024 (Received 31 October, 1983 by A. Zawadowski)

Experimental data on the low frequency dielectric constant E and the threshold field ET for the onset of sliding charge density wave conduction are presented for pure and niobium doped orthorhombic TaS3. It was found that the cET is independent of impurity concentration and of temperature in the temperature range between 100 K to 190 K. We point out that the classical single particle model of Griiner, Zawadowski, and Chaikin; the deformable medium model of Fukuyama and Lee and the semiconductor model of Bardeen all predict EE to be independent of impurity concentration. The numerical estimates are wit T;.in an order of magnitude in agreement with the present experiments.

Charge density wave (CDW) systems exhibiting CDW conduction at low electric fields are recently in the focus of experimental and theoretical investigations.' At present no microscopic theory is able to account for the broad variety of experimental observations. The theoretical approaches are widely different: the mod 1 of Griiner, Zawadowski, and Chaikin 5 describe the CDW system as 3 classical particae, Fukuyama and Lee and Lee and Rice assume that the condensate is a deformable medium, while BardeenS suggests that quantum effects are essential in the dynamics of charge density waves. The classical model2 views the CDW system as a rigid macroscopic entity exposed to an average pinning potential of the impurities. The potential is periodic with period given by the wavelength h of the CDW. An electric field of sufficient strength lifts the CDW over the potential maxima leading to a current c yi!g1 state. In the deformable medium model the CDW phase is locally adjusted so that the sum of the elastic energy of the CDW deformation and the impurity pinning energ is minimized. In the tunneling model f the charge transport is due to macroscopic quantum tunneling through the pinning potential. In all models the pinning potential has a central role in determining the low field and low frequency properties. In the most investigated systems, NbSe3 and TaS3, it is extremely small so that the static dielectric constant, at zero biys field, E. can be as high I7 as 10 -10 and on the other hand the thres*

hold electric field ET for the gnget of sliding CDW conductivity as low ’ as 10-1-10-2 V/cm. The classical model treats the CDW condensate as a single particle, having an effective charge e and mass m, with a coordinate x acted on by an external electric field EeiWt in a weak periodic pinning potential of strength mwo2. The intertia term is usually neglected as experimentally the systems investigated so far appear to be overdamped. Consequently, the equation of motion is

1%+w2 T dt

iwt 0

AF(x/h) = =+

where T is the damping parameter and F(x/X) is a periodic function determining the form of the pinning potential. From (1) we find a threshold field E where the current carrying state deve T ops ET

= Kmoo2 We

,

(2)

where K = F(1/2) is a constant characteristic of the pinning potential at its maximum. For a quadratic potential repeated every wavelength, K = l/2, while for a sinusoidal potential, K = 1/2n = = 0.16. On the other hand, the static dielectric constant ne 2 E = 4rr. 0 2 mw 0

so that a simple relation holds: 4nKneX quadraticpotential sE (4) oT = i 4 KneA sinusoidal potential

On leave from the Central Research Institute for Physics, Budapest, Hungary 1013

1014

THE STATICDIELECTRICCONSTANTAND THRESHOLDELECTRICFIELD Vol. 49, ijo.11 5 In the tunneling model, the nonlinear a relation similar to that given by conductivity is due to collective tunEqs.(4) and (7). neling across the pinning gap Eg. It is The main difference is the appearance the analogue to Zener tunneling in a of p ff which may be important at temband semiconductor with gap A where the pera ?ures near to transition temperature field dependent conductivity has the fi * However, near T the yeak pinning form a&roximation also H ails. In our discY&ion of experimental results we u -exp(-Eo/E) (5a) emphasize the effect of impurities at with temperatures well below Tp. = A*,/4hvFe (5b) The product neX may also be deterEO mined from the ratio of the excess curand the dielectric constant is given by rent, arising from the depinned CDW, ~~~~u~~~yt~~,88rcalled narrow band noise 4nne2h2 E= (6) L .Y

.

ICDW=neX .

Combining Eli. (5) and (6) we obtain

”

EE

0

= nneX

(7)

.

The threshold field E is of the order of EO in this model. 5TWriting ET = 4KTE0 we have EET

= 4nKTneX .

(8)

Therefore the prediction of the classical and semiconductor models are essen' tially the same. We also note that both are valid at T = 0, temperature dependent effects, such as n(T) are not considered in the models. The estimates 8f Fukuyama and Lee3 and of Lee and Rice lead to a similar expression for EOET. This theory is more realistic than the classical model, as it takes into account the impurity induced deformation of the CDW'SJ however, the change of these deformations as a static electric field is applied is not given. An upper limit of E--is given by estimating the minimum fieTd necessary to slide the CDW rigidly and in this respect there is no difference from the classical model. In the weak pinning case and for simplicity in a one dimensional system the mode13r4 yields: hv ET = 81~~

(9)

aF 0

'eff

is a numerical constant of order where of unity, L is an average domain size y the relative values of determined f! impurity and elastic energies. Peff is an effective CDW electron density (normalized to the total electron density) which depends on the dynamics of the system, at temperatures far below 1. The the Peierls transition Peff static dielectric constant within the same model3 is 4nne2 a4i3 Lo2 (10) 2 m VF where c is a numerical constant of order unity. Combining Eqs. (9) and (10) - .I/3 c; u = neh = 4xn'neh , (11) EOET 2npeff E0 =c-

(12)

We note that Eq. (12) represents the characteristics of the current carrying condensate. In this paper we report measurements on pure and doped orthorhombic TaS3 to determine the relation between ~~ and ET. We find that for samples with strongly different impurity levels E has the same value as predicted by tT; e above models. The value of neh is in rough agreement with that found from the narrow ~~G~e=Pfs~n~r~~u~~~~~se~a~~~~l and Samples of two nominally pure TaS3 batches and two niobium doped TaSQ batches were measured. The-nominally pure batches were of different quality, the one grown at UCLA will be referred to as "high purity TaS3". The nominal compositions of the doped batches were Ta .sJ99NP.opS3 and Ta 29p oosS3. Dc con uctivi y and thres o d fie d data as a function of dopant concentration of terials were presented else:;:::.rs A rf bridge at frequency range between 0.5 MHZ to 100 MHz was used to measure the sample rf capacitance as a function of temperature. The absolute values of dielectric constant were determined by sample capacitance and geometrical factors, the latter calculated from the room temperature resistance, with room temperfture conductivity value DRT = 2.6.10 (Q-cm)-l. Threshold fields were measured together with the dielectric constant during the same run. For the impure samples a pulse technique was used to avoid sample heating effects. All data are taken by two contact method; relatively long samples were used (2.5 nun for the highest purity) to minimize contact resistance problems. Measurements on other samples demonstrated that in TaS3 contact resistance is small. We found that the amplitude of the rf exciting field has to be kept well below threshold field to avoid hysteresis effects in the ac current-voltage characteristics. An exciting field with amplitudes below 10 % of the threshold field was generally applied; however, some hysteresis was still observed at

Vol. 49, No. II

1615

THE STATICDIELECTRICCONSTANTAND THRESHOLDELECTRICFIELD

low temperatures and frequencies. The frequency dependence of the dielectric constant, measured on the nominally pure sample, is shown in Fig.1. Also shown in the figure is the functional behavior expected for a simple harmonic oscillator response. While there are serious deviations from the behaviour expected for a harmonic oscillator, this will be discussed in a separate publication. It is also evident from Fig. 1 that the dielectric constant, measured at 1 MHz or below, represents well the E(w=O) limit. The overall behaviour of E(W) was always found to be similar to that displayed in Fig. 2, and in all cases experimental data below 1 MHz were used for co. E (T) for different impurity concentra ?a ions is shown on Fig. 2. As a function of temperature, eO(T) has the same form for all samples; however, even small quantities of impurities reduce the absolute value significantly. Our mainlresult is displayed on Fig. 3. It shows that even for grossly different pinning strengths, the static dielectric constant is inversely proportional to the threshold field. ET for the high purity TaSS and the 0.02% Nb doped TaS3 samples differ by a factor 50. It should be noted that according to our previous studiesI on the same material, ET is not proportional to the impurity concentration c but rather ET - c2 as expected for weakly pinning

100

140 Temperature

180

220

(K)

Fig. 2. Dielectric constant vs. temperature (left side scale) +: pure TaS3, A: Ta~gggM3~001S3, : TaO_998Nb_O02S3; threshold field vs. temperature (right side scale) for pure TaS3.

l

012345 F(MHz)

0 Threshold Field E+V/cml

t 0

I

20

I

I

40 60 Frequency (MHz)

I

60

Fig. 1. Dielectric constant vs. frequency for pure TaS3 sample at T = 195 K. Full line is a fit to classical oscillator model. The insert shows low frequency data.

Fig.

3.

Dielectric constant vs. threshold field for pure and niobium doped TaS3, a: pure TaS3 samples (from different places), l : Nb doped TaS3 samples with different Nb concentrations). The dashed line corresponds to 'OET = const.

1016

Vol. 49, luo.II

TIiESTATIC DIELECTRIC CONSTANT AND THRESHOLD ELECTRIC FIELD

impurities. * Thus our result implies that E - I/c2. The same impurity dependence has been found in organic quasi one dimensional systems with a Peierls distorted ground state.I* Previous experiments on irradiated NbSe3 samples I5 showed a linear decrease of E and linear increase of ET with impurity concentration, in agreement with the prediction of strong impurity pinning. In our case ET is proportional to n.2, direclty confirming that impurit& weakly pin the CDW condensate. EO and E are correlated not only for samples oT different purity but show an inverse variation as a function of temperature as shown on Fig. 2. While at 160 K a well defined maximum in ET is observed, E has a minimum at the same temperature. Our results on the temperature dependence of E agree well with those of Wang et al. T2 and of Mihaly et al.16 Figure 4 displays the product EEL for the high purity sample, where E is measured at f = 1 MHz.

quadratic and to the sinusoidal potential. We note that E is unchanged for applied bias electric fields less than ET, suggesting that a quadratic potential may be more appropriate. We verified the field independence of E on high purity samples between w/2r = 0.5 and 20 MHz and similar conclusions were arrived at by Tucker et a1.17 In this picture at fields just above ET a sudden breakdown occurs, the potential cannot have a smooth maximum since this would lead to a divergence in E(E) at ET, which is not observed. In the framework of the tunneling model KT may be obtained from an analysis of th CDW conductivity data. It was found 5 that E. = 5ET fits best the observed nonlinear conductivities for TaS3, and therefore KT = 0.05. Finally, for the deformable CDW model w take the estimates of Fukuyama and Lee 3 of 2aI/3 = I.89 and c = 1.59. These values lead to K' = 0.02. The above theoretical estimates of K may be compared to the experimental value Kexpt extracted from the present measurements and from the published data on ICDW/v by writing the measured product as EET

. 0.

.. ..

.

.

‘3:: ..

le.e

le

l

= 4rrK

expt neh

*

(‘2)

We find that at all temperatures below 190 K for the pure TaS3 sample (and similar values for the impure samples), the product has almost the same value

l

.e

.. .

EET 2 I7 A/MHz cm2 while from Refs.

II

and I2 at T = 120 K

ICDW/v = neX = 40 A/MHz cm2 ; thus K I

TP

1 J

'50 Temperature

(Kl

Fig. 4. ~~~~ as a function of temperature measured on pure TaS3. To compare our data with those derived from narrow band noise, we have to make assumptions on the numerical constants appearing in expressions (41, (7), and (IO). Our best estimates are2 K = 0.5-0.15 for the classical K = 0.05 in the tunneling mode, ~"::;-for K' = 0.02 in the Fukuyama-Lee model the following reasons. For the classical model the two values correspond to a

expt

= 0.03 .

Thus the experimental value is in an order of magnitude agreement with theories. In conclusion we have pointed out that widely different theoretical models describing CDW systems predict that cOET is independent of impurity concentration and lead to the same order of magnitude estimate for this product. Our experiments are consistent with this statement, and we find that not only is "oET independent of impurity concentration but its value has the same order of maqnitude as predicted by theories. For TaS3-we find that EOET is constant with temperature up to close to the Peierls transition temperature. We know of no theoretical model, as yet, which would predict this behaviour. We wish to thank F. Czito for preparing the samples used in this study. This work was supported by the National Science Foundation under Grant No. 81-21394.

Vol. 49, No. 11

ThE STATIC DIELECTRIC CONSTANT AND THRESHOLD ELECTRIC FIELD

We acknowledge discussiong8with the authors of the preceding paper . While in general similar conclusions are drawn, a difference of an order of magnitude in the value of K is found. We trace this

to the inadequacy of the classical oscillator model for extractin: ;a ;; Ih:ely different frequencies (IO measurements and 9.10' Hz in those of Ref. 18).

References 1.

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

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See, e.g., the review by N.P. Ong, Can. J. Phys. 7575 (1982); G. Griiner, Comments on Solid State Physics 10 (1983) G. Griiner, A. Zawadowski, and P.M. Chaikin,Phys. Rev. Lett. 46, 511 (1981). H. Fukuyama and P.A. Lee, Phys. Rev. B 11, 545 (1978). P.A. Lee and T.M. Rice, Phys. Rev. B 19, 3970 (1979). John Bardeen, Phys. Rev. Lett. 45, 1978 (1980); Molecule Crystals and Liquid Crystals 81, 1 (1982) G. Griiner, L.C. Eppie, J. Sanny, W.G. Clark, and N.P. Ong, Phys. Rev. Lett. 45, 935 (1980). A. Zettl, C.M. Jackson and G. Griiner, Phys. Rev. B 2, 5773 (1982). R.M. Fleming and C.C. Grimes, Phys. Rev. Lett. 42, 1423 (1979). A. Zettl, G. Griiner, and A.H. Thompson, Phys. Rev. B 26, 5760 (1982). P. Monceau, J. Richard, and M. Renard, Phys. Rev. Lett. 45, 43 (1980) A. Zettl and G. Griiner, Phys. Rev. B 3, 2091 (1983). Z.Z. Wang, H. Salva, P. Monceau, M. Renard, C. Rouceau, R. Ayroles, F. Levy, L. Guemas, and A. Mehrschaut, J. Physique 44, L311 (1983) P.L. Hsieh, F. de Czito, A. Janossy,and G. Griiner, J. de Physique 44, c3-1753 (1983) A. J&nossy, K. Holczer, P.L. Hsieh, C.M. Jackson, and A. Zettl, Solid State Conunun. 43, 507 (1982). W.W. Fuller, G. Griiner, P.M. Chaikin and N.P. Ong, Phys. Rev. B 23, 6259 (1981) G. Mih$ly, Gy. Hutiray, and L. Mihbly, Phys. Rev. B 28, 4896 (1983) J. Tucker, private communication G. Mih&ly, L. Mihaly and H. Mutka, Solid State Comm. preceeding paper