Effect of Er-substitution on superconducting and metal-insulator transitions in 2212 bismuth cuprate

PHYSICA Physica C 266 (1996) 335-344

ELSEVIER

Effect of Er-substitution on superconducting and metal-insulator transitions in 2212 bismuth cuprate A. Sattar a, j.p. Srivastava a, *, S.V. Sharma b, T.K. Nath b a Department of Physics, Aligarh Muslim University, Aligarh-202002, India t, Department of Physics, Indian Institute of Technology, Kanpur-208016, India

Received 11 January 1996

Abstract

Results of a systematic study of lattice parameters and resistivity on Bi2Sr2Ca I_ xErxCu208 + 8, with value of x in the range 0.0 < x < 1.0 are reported. The quality of samples has been examined by XRD and resistivity measurements. The suppression of superconductivity is attributed to the effect of disorder. The resistivity behaviour in the insulating regime is analyzed in the hopping conduction approach. The nature of the density of states as determined using the Ortuno and Pollak model is found to be concave near E F. At the MIT, the localization length diverges and the metallicity vanishes following a scaling law with the critical exponent, /x = 1. The high value of differential activation energy suggests multiphonon assisted hopping at low temperatures.

1. Introduction

Since the discovery of the Bi-Sr-Ca-Cu-O high T~ superconductor [1], an exhaustive study of this class of materials has been carried out. The studies have revealed several important aspects which are yet to be satisfactorily understood. The change in charge carrier concentration is one of the most important effects for the study of these superconducting cuprates because it predominantly determines various physical properties of the system, such as transition temperature (T~), electrical and magnetic properties [2-8]. It could be brought about by several methods e.g. doping [9]. But the relation between doping and superconductivity is still not clear for this system.

* Corresponding author.

It is believed that the different cationic substitutions at different sites in a cuprate system lead to change in cartier concentration and increase the disorder in system. In the presence of sufficient disorder the dynamics of e - e interaction becomes important, affects the final pairing [10] and ultimately results in metal-insulator-superconductor transition (MIST). Metal-insulator-superconductor transition and its associated physical properties have been investigated by several workers [4,5,8] in Bi-Sr-Ca-Cu-O (Bi-2212) system through substitution of trivalent rare earth ions for divalent Ca ion. Despite all this work, no conclusive results on the electronic transport properties could be obtained. Most of the investigations on high Tc superconductors are focused on the composition range where the samples are superconducting. Comparatively less amount of work has been done at nonsuperconducting concentrations. But in order to understand the mechanism of supercon-

0921-4534/96/$15.00 Copyright © 1996. Published by Elsevier Science B.V. All rights reserved PII S0921-4534(96)00360-7

A. Sattar et a l . / Physica C 266 (1996) 335-344

336

ductivity it is important to know the origin of insulating state as well as the basic character of the metallic state induced by the cation substitution. Hence, we focus our attention on the whole composition range of the samples. If the substituting cation is aliovalent to a cation at certain site, oxygen stoichiometry may give some ambiguity in the transport properties of the polycrystalline samples. In this respect BiESrECaCUE08+ a (Bi-2212) cuprate has some advantage. Firstly, the oxygen stoichiometry is relatively invariant when the samples are prepared with cationic substitution in an identical thermal environment [3]. Secondly, it has only one kind of Cu-ion [11]. Thirdly, the fundamental crystal structure of this

system does not change during the transition due to RE ion doping [3]. However, subtle changes in structure occur due to modulation effects which has no significant impact on superconductivity and normal state properties [3,12]. And lastly, samples of good quality and capable of giving reproducible experimental data can be prepared easily. In view of the above mentioned interesting characteristics of the (Bi-2212) cuprate we thought it proper to extend studies on this system by doping it with a rare earth ion like Er 3+. Eremina et al [13] report that Er 3+, most probably, occupies Ca 2+ site. But no systematic work on Er doping has been done so far and most of the related electronic transport

oI

_o,

0

=

~

~

~

X = 0.0

"'t

et

o ~lg

-~l °° /I °1 tl A I1 , I

t

~;,,o~

^

z

It /lltAtl

~

e

=

/W~'~

o'

r',

/I A II

)~/ll k

lI/I/l/Ut

~+J t] " v

o ~ ,-

, =

.

¢: J~

z

=

•

l-z_

mO

°,

z=

"~'

,,'l

o

~ o

/I

Jt

,

X --.1.0

t,e=

.

o

~o

to

,.g

o

I

65

55

45 DIFFRACTION

35 ANGLE

25

15

2 e (deg)

Fig. 1. X - r a y diffraction patterns in the samples with 0.0 < x < 1.0 o f B i 2 S r 2 C a I _ x E r x C u z O s + a.

A. Sattar et a l . / Physica C 266 (1996) 335-344

phenomena remain unexplained. In the present paper we report a systematic study of variation of lattice parameters and the transport properties of Er-doped BiESrECa l_xErxCu208+ ~ compositions (0.0 < x < 1.0). In addition to above, we have studied the scaling dependence of conductivity and the nature of density of states near Fermi level.

2. Experimental The samples of Bi2Sr2Ca l_xErxCu208+8 (0.0 < x < 1.0) composition were prepared by standard solid state reaction technique using appropriate quantity of well mixed oxides and carbonate of 99.99% purity. Stoichiometric amounts of Bi203, SrCO 3, Er203, CaCO 3 and CuO were ground in an aget mortar and pestle for 2 hrs using acetone as the grinding medium. The above product has been calcined in air at 820°C for 24 hrs followed by furnace cooling. Calcined material was reground for 2 hrs and pressed into pellets (1.0 cm dia and 0.2 cm thickness) at the pressure, 6 t o n / c m 2 and finally sintered at 865°C for

337

90 hrs. Sintering temperature was increased from 865 ° to 880°C with increasing value of x as higher sintering temperatures are required for samples with higher concentration of Er in order to achieve single phase samples [8]. The final product was checked for its quality through XRD and resistivity measurements. Powder X-ray diffraction measurements were made with a Rich and Seifert Isodebyeflex 2002 Diffractometer using CuKot radiation. The electrical resistivity measurements were performed by standard four probe dc method using closed-cycle helium refrigerator (CTI and Cryosystems, USA) in the temperature range 10-300 K. For this measurement the samples were cut into bar shaped (1.0 × 0.3 × 0.2 cm) and contacts were made by applying highly conductive silver paste. The resistance was directly measured with a Datron 1071 autocal multimeter with a constant current of l0 mA. The temperature was measured using a Lakeshore DRC-82C temperature controller. The temperature stability was around +_0.05 K. The resolution in (Ap)/p was better than 1 part in 10 4.

Table 1 (a) Calculated and observed XRD data for Bi2Sr2CaCu208 + and c = 30.67 + 0.02 ,&

having orthorhombic structure with lattice parameters a = b = 5.42 _+ 0.02 ,~

(hM)

dobs(,&)

d¢,l (/~)

I robs -dcal I (,&)

(007) (008) (I 13) (115) (0 0 10)

4.32 3.82 3.59 3.25 3.07

4.37 3.82 3.58 3.25 3.06

0.05 0.00 0.01 0.00 0.01

I/lmax %

(117) (200) (119)/(0 0 12) (210) (2 0 10)

2.88 2.71 2.55 2.43 2.02

2.88 2.71 2.55/2.54 2.42 2.03

0.00 0.00 0.00/0.01 0.01 0.01

100 71 70 7 68

(1 1 13) (220)/(0 0 16) (2 0 12) (1 l 15) (0 0 18)

2.01 1.91 1.85 1.80 1.71

2.01 1.92/I.91 1.86 1.80 1.70

0.00 0.00/0.01 0.01 0.00 0.01

67 52 24 62 8

(315) (2 2 10) (317) (2 0 16)/(2 1 15) (319)/(2 2 12)/(0 0 20)

1.65 1.62 1.59 1.56 1.53

1.65 1.62 1.60 1.56 1.53

0.00 0.00 0.01 0.00 0.00

24 42 45 29 51

8 62 29 89 59

338

A. Sattar et al./Physica C 266 (1996) 335-344

3. Results and discussion

3.1. Structural analysis The powder X-ray diffraction pattems (XRD) of some selected samples of Bi 2Sr2Ca I _ xErxCu 208 + 8 (0.0 < X < 1.0) are displayed in Fig. 1. The presence of the 2212 phase as the major phase in all these samples is clearly evident. However, a pure single 2212 phase has been achieved only for samples 0.0 < x < 0.6. The effect of doping is observed for x > 0.6 when one extra peak appears around 20 = 28.6 ° . In this system some structural modulation is expected along b-axis [14]. So, actual crystal structure determination is impossible. However, we could index the pattern as orthorhombic unit cell. The crystallographic data for the sample x = 0.0 and x = 1.0 are given in table la and lb respectively. We interpret the observed components 1113/2010,

220/0016 and 3 1 9 / 2 2 1 2 / 0 0 2 0 of different reflection lines as their split components in the orthorhombic phase (Fig. 1). The doping with other RE ions is known to split only 200 lines as reported by earlier workers [4,6,8]. We have calculated the a, b and c cell parameters by using significant intense peaks which are drawn in Fig. 2. The difference between the a and b cell parameters is small and almost the same for x < 0.475. The value of b increases with x for x > 0.475 whereas a remains constant. The c parameter continuously decreases with x. In the well studied system of Y substituted Bi2212 the a parameter does not remain constant and is found to increase with increase in dopant concentration [8]. But, the dependence of lattice parameters on dopant concentration in the present system is generally the same as for other RE substitutions in this system [4,14]. Further, the substitution of divalent Ca by trivalent RE elements is expected either to

Table 1 (b) Calculated and observed XRD data for Bi2Sr2ErCu2Os+ a having orthorhombic structure with lattice parameters a = 5.41 + 0.02 ,~, b = 5.46 + 0.02 ,~ and c = 30.27 + 0.03 ,~,

(hkl)

dobs (.~)

dcaj(,~,)

Idobs-- dcalI(~,)

(006) (013) (015) (008) (113)

4.98 4.78 4.07 3.78 3.60

5.04 4.80 4.06 3,78 3.59

0.06 0.02 0.01 0.00 0.01

17 10 11 38 31

(115) (0 0 10) (117) (200) (119)/(0 0 12)

3.24 3.03 2.87 2.71 2.52

3.24 3.03 2.87 2.70 2.53

0.00 0.00 0.00 0.01 0.01

48 79 100 53 81

(210) (1 1 11) (2010) (I 1 13) (220)

2.43 2.24 2.02 1.99 1.92

2.42 2.24 2.02 1.99 1.92

0.01 0.00 0.00 0.00 0.00

14 vw 63 52 30

(0 0 16) (2 0 12) (1 1 15) (0 0 18) (315)

1.89 1.83 1.78 1.69 1.65

1.89 1.84 1.79 1.68 1.65

0.00 0.01 0.01 0.01 0.00

25 28 38 17 20

(2 2 10) (317) (2 0 16) (319)/(2 2 12) (0 0 20)

1.61 1.60 1.55 1.53 1.51

1.62 1.59 1.55 1.53 1.51

0.01 0.01 0.00 0.00 0.00

44 45 27 28 35

I/Imax %

A. Sanar et a l . / Physica C 266 (1996) 335-344

339

30.70 30.60 3050 30.40 30.30

g 30.2~ c~

s4oH~ b

5.35~

S.40H~ a

5'351' ~ I

I

I

!

t

I

t

0. 2

I

0.4

I

I

t

I

0.6

I

I

I

I

0.8

I

I

I

I

1.0

X " dopant conc. Fig. 2, Lattice parameters a, b and c for the samples with 0.0 < x < 1.0 inBi 2 Sr 2Ca l_ x ErxCu 2O8 + ~-

modify the copper valency or to pull some oxygen into the structure or both in order to maintain the charge neutrality [3]. In this system there is a large vacant space in BiO plane [15]. The decrease of the c parameter may be understood on the following basis. As the Er 3+ content increases, the interlayer distances A z(Cu-Ca-Cu) and A z(Ca-Sr) expand but AZ(Sr-Bi), AZ(Bi-Bi) and AZ(Sr-Bi-Bi-Sr) shrink because the extra oxygen resides in the B i - O double layers. This extra oxygen balances the increased valency due to the replacement of Ca 2÷ by Er 3÷. Consequently, the net positive charge in the B i - O layers reduces. Hence, the repulsion between them is reduced and the distance between all the layers in the structure contracts [16]. The contraction of c is consistent with the replacement of the Ca ion by a smaller Er ion. The elongation of b is generally associated with the increase in the C u - O bond length in CuO 2 planes, which controls the dimensions of the basal plane [6].

3.2. Resistivity analysis The variation of electrical resistivity with temperature for the Bi2Sr2Cat_xErxCu208+, ( x = 0 . 0 1.0) composition is shown in Figs. 3a-c. The resistivity behaviour of these samples may be divided into three parts: (a) Samples with x = 0.0 to 0.4 show normal state metallic behaviour followed by superconducting transition with decreasing temperature (Fig. 3a). In the temperature range 120 to 300 K, the resistivity data may be fitted to p(T) = p(O) + bT. (b) For sample x = 0.45, a minimum in resistivity is observed around 100 K. Above this temperature it shows metallic properties and below it behaves semiconducting and then finally goes to the superconducting state (Fig. 3a). This upturn in resistivity may be due to the random distribution of Er at Ca site, i.e., disorder in the system which leads to a logarithmic correction [17] in the conductivity (Fig. 4). This

340

A. Sattar et a l . / Physica C 266 (1996) 335-344 0.010

127.0

(a) x = 0.45

o.oo~

J,.-.. 126.5

o I

o 7 0.006

~

126.0

>

0.004 -

~i 0.002

"

I~

0.000

"''x = 0.1

~=,,,,'~ *

¢,;, 125.5

o.o

*"*"~'*=

o ro

KxxxxxxX ~ x x x x x x x x x x x

x

=

0.2

i

0

100

T (K)

200

(b) t

o ~

0.150

> ..~ 0.100

.....

0.050

.

0.000

IO0

2()0

300

T (K)

(c)

L

3.00

o

4.5

in(T)

4/7

4.9

sample still shows superconductivity because of longer coherence length [18]. It is proper to mention here that the minimum in resistivity as observed by us could not be seen in Y-substituded Bi-2212 system [8]. (c) Samples with Er concentration x > 0.475 show metallic behaviour above 300 K. The decrease in temperature below 300 K eliminates superconductivity and leads to the insulating phase (Fig. 3b, c). The rate of increase of resistivity becomes faster as temperature approaches zero for x > 0.475. The loss of superconductivity may be usually attributed to the introduction of the magnetic ion Er 3+ causing disorder where all the charge carriers become localized. We would also like to report here that the behaviour of T~ with x, as derived from the resistivity data in the present system, is almost similar to that observed in other RE substituted Bi-2212 systems

[5,81.

I

2.00

3.3. Behaviour of charge transport in the insulating state

t. "~

i

4.3

Fig. 4. Conductivity versus In T for the sample x = 0.45 in the temperature region 80-130 K.

0.250

0.200

124.5

300

:

125.0

1.00

The behaviour of charge transport in insulating samples is very important because it provides diverse ,, = o s ~ m , , m . . . . . , . , . ~

0.00

,

~

,

1O0

T

(K)

i

200

,

i

300

Fig. 3, Temperature dependence of electrical resistivity for various Er concentrations in the Bi2SrzCal__xErxCuzOs+ 8 system as shown in (a), (b) and (c).

A. Sattar et al./ Physica C 266 (1996) 335-344

information such as electronic correlation and the density of states [8]. Below about 100 K the conductivity of the insulating sample decreases strongly with decreasing temperature which cannot be described by thermally activated conduction. It can be described by hopping conduction [19] between the localized states. In hopping conduction the temperature dependence is generally weaker than e x p ( - 1 / T ) (thermally activated conduction). The well known examples for hopping conduction are due to Mott and Davis [19] and Shklovskii and Efros [20] where they have given the temperature dependence of conductivity as t r ( T ) = tr0 exp( t~= (n +

To/T )'~,

1)/(n+D+

1),

(1) (2)

where D is the dimensionality of the hopping process and n describes the energy dependence of the density of states near the Fermi energy N(EF), tr0 and To are the model dependent parameters. To depends on the shape of localization of the hopping site, the form of tunneling probability and the energy dependence of the density of states. TO can be expressed as [21] TO= 16/33/kN(EF),

(3)

where /3 is the inverse fall of length of the wave function of a localized state (localization length) near the Fermi level. It is very difficult to determine the unique value of a. However, for energy independent density of states (n = 0) we can write a = 1 / 3 in two dimensions and a = 1 / 4 in three dimensions in the Mott-Davis variable range hopping (VRH) whereas in the Shklovskii and Efros case n = 1 for 2D and n = 2 for 3D which leads to the same exponent, a = 1/2. The electrical conductivity of the Bi2Sr2Cal_ x ErxCu2Os+ 8 system cannot be described by the simple Mott-Davis or Shklovskii-Efros case alone. This is so mainly due to the electronic correlation effect coming in our system. As Er concentration increases, the disorder increases in the system. As a result the Coulomb repulsion between electrons in occupied centres could change the density of states in the vicinity of Fermi level (EF). This will affect the pre-exponential factor tr0. There are different views on the pre-exponential factor tr0. Ortuno and

341

6.0

t~~ ' ~ 4 . 0

v

~

.

,---i

.

2.0

0.0

0.20

0.30 T_~14o.4o

0.50

Fig. 5. l l l ( O ' T 0"42) v e r s u s T- 1/4 for samples x = 0.5, x = 0.6 and x = 0.8. The solid lines are linear fits in t w o separate temperature regions: 15 K < T < 3 8 K a n d 5 0 K < T < 2 0 0 K .

Pollak [22] considered a concave density of states near the Fermi level and gave the following expression for o"0.

cro = 1.7e2vN( EF)°'ss( /3 )-°

7'(kt)-°"2,

(4)

where u is phonon frequency, e is the electronic charge, k is the Boltzmann constant, /3-1 is the localization length and N(E F) is the density of states at the Fermi level. We have tried to estimate N(E F) using both the formulae, the one given by Mott-Davis or Shklovskii-Efros and the other after Ortuno-Pollak. The first formula gives values of the order of 1017 which is far different from those obtained ( ~ 1022) in Bi-2212 systems [23]. On the other hand the use of Ortuno-Pollak formula gives N(E F) values in the range of 1021 which shows the applicability of this formula to our system. In view of this fact we have preferred OrtunoPollak model and plotted our data as ln(trT °'42) versus T- I/4 for the samples x > 0.475 and shown in Fig. 5. Linear fits are obtained for two temperature regions; from 15 to 38 K and from 50 to 200 K. We have used the low temperature region for the estimation of N(EF). We have also used Eqs. (3) and (4) and took v = l013 Hz with allowed uncertainty. There is an indication of the slight upward

342

A. Sattar et a l . / Physica C 266 (1996) 335-344

At low temperature ~ 20 K, it is of the order of 5-20 Mev, PRT < 0.2ll cm and TO is order of 103 to 105 K. So the mechanism appears to involve multiphonon assisted hopping [24].

o

4.75 ,r---

4. Scaling dependence of the conductivity

II X

In doped semiconductors it is well known that the conductivity in the vicinity of MIT obeys a scaling law [20]

"-~.2.75 -.t-

O

or(n) = O-o( ( n - n c ) / n c ) ~, 0.75

04

o.'6

1.b X

Fig. 6. Plot showing the variation of localization length with Er concentration.

trend in the plot at low temperature. This trend is predicted by the theory of Ortuno and Pollak. Thus, the density of states near the Fermi energy is concave in nature. At high temperature, conductivity data follows the thermally activated conduction. In Fig. 5 one can see that the slope of the curves increases with Er concentration. The slope is given by To~ which is related to the localization length /3-1. The exact relation between /3 and TO is known for the simple Mott-Davis (D = 3) and the Shklovskii-Efros cases only. However, in order to estimate the localization length from the experimental a and TO values, we can use the simple formula

[8] aH= (/3-1) ~ T~/(~-t),

(5)

where a possible effect of prefactor is completely ignored. The coefficient of proportionality which may depend weakly upon the details of the density of states in the vicinity of E F is also dropped here. The variation of the localization length a H with Er content is shown in Fig. 6. It diverges at the MIT, indicating that the charge carders are delocalized due to the increasing overlap between wave functions on neighbouring sites. The value of the differential activation energy involved in the hopping process is given by [24]; Ea = k T3/'Td/4

(6)

(7)

where /z, the critical exponent, can be calculated by using the scaling theory of Abrahams et al. [25]. The parameter n is normally taken to be the career concentration in the system. In the following analysis we replace the carrier density by the Er concentration x, as it is well established that doping of the trivalent RE ion at the divalent Ca ion controls the carrier concentration in the metallic regime [8]. Hence, Eqs. (7) can be rewritten as ( x ) = ~o(( go x ) / ( 1 - xc))~.

(8)

The exponent /z is unique to the character of the transition and independent of the specific substance under investigation. Thus, the critical exponent gives us important information about the mechanism inducing the MIT. The scaling behaviour in HTSC's is more complicated than in well known semiconductors because the sample quality is not yet comparable to that of traditional semiconductors. However, we can follow the procedure due to Quitmann et al. [8]. To search the scaling behaviour we can use the conductivity at T = 100 K, as the lowest temperature conductivity because at that temperature the results are not influenced by the superconductivity. The value of xc can be estimated utilizing the fact that the sample with x = 0.45 is metallic and shows superconductivity; and the sample with x = 0.475 is insulating at low temperature. This gives x c = 0.46 + 0.03 whereas for Y substituted Bi-2212 xc = 0.43 [8]. To show the power law behaviour we have plotted a double logarithmic plot as conductivity ( T = 100 K) versus reduced concentration ( x xc)/(1 -Xc), shown in Fig. 7. We get the critical exponent,/z = 0.94 ~ 1 from the plot. Thus, our data also show the universality on the scaling behaviour

A. Sattar et aL / Physica C 266 (1996) 335-344

343

x = x c. It is, therefore, most probably of the Anderson type. 500"

Acknowledgement

T_

3oo

The authors are very much indebted to A.K. Majumdar for providing experimental facilities and taking keen interest in the progress of this work. A. Sattar thanks UGC New Delhi (India) for financial support.

o zoo

b'-

100

,

0.1

0.2

,

,

,

,

0.5

-

,

,

References

1

( xc-x 1

,

)

"Xe

Fig. 7. Double logarithmic plot of conductivity o-(T = 100 K) versus reduced Er concentration.

with / x = l . The value / x = l is the same as is observed in other samples, where the MIT is believed to be disorder induced [8,26]. So, the metal insulator transition may be occuring due to disorder in our system.

5. C o n c l u s i o n

The lattice parameter b increases with doping concentration ( x ) of Er whereas a remains constant and c decreases. Doping of Er leads to a metal-insulator transition above a critical concentration x¢ = 0.46 + 0.03. The suppression of superconductivity occurs due to the disorder in the system. The insulating samples show 3D hopping conduction at low temperatures and the results are best explained in the framework of the Ortuno and Pollak model. From the calculation of differential activation energy it is also evident that hopping is multiphonon assisted between two localized sites at low temperatures. In the metallic regime of this metal-insulator transition, the conductivity obeys a scalling law with a critical exponent /~ = 1. In the insulating regime, the localization length diverges and the separation between localized states and the Fermi energy vanishes for

[1] H. Maeda, T. Tanaka, M. Fukutomi and T. Asano, Jpn. J. Appl. Phys. 27 (1988) L 209. [2] P.W. Anderson, K.A. Muttalib and T.V. Ramakrishnan, Phys. Rev. B 28 (1983) 117. [3] J.M. Tarascon, P. Barboux, G.W. Hull, R. Ramesh, L.H. Greene, M Giroud, M.S. Hedge and W.R. Mckirmon, Phys. Rev. B 39 (1989) 4316. [4] B. Jayaram, P.C. Lanchester and M.T. Weller, Phys. Rev. B 43 (1991) 5444; Physica C 160 (1989) 17. [5] P. Mandal, A. Poddar, B. Ghosh and P. Choudhury, Phys. Rev. B 43 (1991) 13102. [6] E.L. Narsaiah, U.V.S. Rao, O. Pefia and C. Perrin, Solid State Commun. 83 (1992) 689. [7] V.P.S. Awana, S.K. Agarwal, R. Ray, S. Gupta and A.V. Narlikar, Physica C 191 (1992) 43. [8] C. Quitmann, D. Andrich, C. Jarehow, M. Fleuster, B. Beschoten, G. Gfintherodt, V.V. Moshchalkov, G. Mante and R. Manzke, Phys. Rev. B 46 (1992) 11813 and references therein.

[9] J.S. XIIc, M. Reedyk, J.E. Greedan and T. Timusk, J. Solid State Chem. 102 (1993) 492. [10] R.C. Dynes, A.E. White, J.M. Graybeal and J.P. Garno, Phys. Rev. Lett. 57 (1986) 2195. [11] M.A. Subramanian, J.C. Clabrese, C.C. Torardi, J. Gopalkrishnan, T.R. Askew, R.B. Flippen, KJ. Morrissey, U. Chowdhry and A.W. sleight, Nature 332 (1988) 420. [12] Y. Inoue, Y. Shichi, F. Munakata and M. Yamanaka, Phys. Rev. B 40 (1989) 7307. [13] R. Eremina, M. Falin, S. Gudenko, V. Kosynkin, S. Kucheyko, A. Mezhuev, D. Pishagin, A. Yakubovskii and E. 2~eglov, Physica C 185-189 (1991) 849. [14] H. Niu, N. Fukushima, S. Takeno, S. Nakamura and K. Ando, Jpn. J. Appl. Phys. 28 (1989) L 784. [ 15] H.W. Zandbergen, W.A. Groen, F.C. Mijihoff, G. van Tendeloo and S. Arnelinckx, Physica C 156 (1988) 325. [16] Y.Y. Xue, P.H. Hor, Y.Y. Sun, ZJ. Huang, L. Gao, R.L. Meng, C.W. Chu, J.C. Ho and C.Y. Wu, Physica C 158 (1989) 211.

344

A. Sattar et al./Physica C 266 (1996) 335-344

[17] P.A. Lee and T.V. Ramakrishnan, Rev. Mod. Phys. 57 (1985) 287. [18] M. Ma and P.A. Lee, Phys. Rev. B 32 (1985) 5658. [19] N.F. Mott and E.A. Davis, Electronic Processes in NonCrystalline Materials, 2nd Ed. (Clarendon, Oxford, 1979). [20] B.I. Shklovskii and A.L. Efros, in: Elecronic properties of Doped Semi-Conductors, eds. M. Cardona, P. Fulde and H.J. Queisser Springer Series in Solid State Sciences (Springer, Berlin, 1984). [21] V. Ambegaokar, B.I. Halperin and J.S. Langer, Phys. Rev. B 4 (1971) 2612.

[22] M. Ortuno and M. Pollak; Philos. Mag. B 47 (1983) L 93. [23] A. Chakraborty, A.J. Epstein, D.E. Cox, E.M. McCarron and W.E. Fameth, Phys. Rev. B 39 (1989) 12267. [24] M.A. Gomilez, J.L. Vicent, F. Garcia-Alvarado, E. Mor~ and M.A. Alario-Franco, Solid State Commun. 80 (1991) 697. [25] E. Abrahams, P.W. Anderson, D.C. Licciardello and T.V. Ramakrishnan, Phys. Rev. Lett. 42 (1979) 673. [26] G. Hertel, D.J. Bishop, E.G. Spencer, J.M. Rowell and R.C. Dynes, Phys. Rev. Lett. 50 (1983) 743.