Enhanced three-dimensional excess conductivity in Be-doped Cu 0.5 Tl 0.5 Ba 2 Ca 3 −x Be x Cu 4 O 12 − δ ( x = 0 , 0.5 , 0.75 , 1.0 , 1.25 , 1.5 ) superconductorsM. Irfan, Najmul Hassan, Syed Asad Manzoor, Babar Shabbir, and Nawazish Ali Khan Citation: Journal of Applied Physics 106, 113913 (2009); doi: 10.1063/1.3266008 View online: http://dx.doi.org/10.1063/1.3266008 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/106/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Fluctuation induced conductivity analysis of Mn doped Cu0.5Tl0.5Ba2Ca2Cu3−xMnxO10−δ (x=0, 0.1, 0.15)superconductors J. Appl. Phys. 116, 103904 (2014); 10.1063/1.4894151 Inter-plane coupling and fluctuation induced conductivity analysis of Cu0.5Tl0.5Ba2Ca2−xYxCu3O10−δsuperconductors J. Appl. Phys. 114, 083908 (2013); 10.1063/1.4819485 Effect of Sn substitution on the para-conductivity of polycrystalline Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3 − y Sn y O 10 −δ superconductors J. Appl. Phys. 107, 083910 (2010); 10.1063/1.3357278 Excess-conductivity analysis of Mg- and Be-doped polycrystalline Cu 0.5 Tl 0.5 Ba 2 Ca 1.5 M 1.5 Cu 4 O 12 − δ( M = 0 , Be, Mg) superconductors J. Appl. Phys. 105, 083926 (2009); 10.1063/1.3116725 Fluctuation-induced conductivity of polycrystalline Ni doped Cu 0.5 Tl 0.5 Ba 2 Ca 2 Cu 3 − y Ni y O 10 − δ ( y =0 , 0.5, 1.0, 1.5) superconductors J. Appl. Phys. 104, 103902 (2008); 10.1063/1.3000477

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Enhanced three-dimensional excess conductivity in Be-dopedCu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� „x=0,0.5,0.75,1.0,1.25,1.5… superconductors

M. Irfan, Najmul Hassan, Syed Asad Manzoor, Babar Shabbir, and Nawazish Ali Khana�

Department of Physics, Materials Science Laboratory, Quaid-i-Azam University, Islamabad 45320,Pakistan

�Received 2 June 2009; accepted 27 October 2009; published online 8 December 2009�

We report the enhanced fluctuation-induced conductivity of Be-doped Cu0.5Tl0.5Ba2Ca3−xBex

Cu4O12−� �x=0,0.5,0.75,1.0,1.25,1.5� samples. The analysis has been done with partialsubstitution of Be in place of Ca. In each case excess conductivity has been analyzed and we triedto make a fit with the Aslamasov–Larkin �AL� and Lawrence–Doniach equations. It is observed thatour data fit well with the three-dimensional �3D� AL equation, and a crossover from two dimensionsto three dimensions has been found in our samples. We have also employed this transition toestimate the Josephson coupling strength in our samples. This interlayer coupling strength J, whichcontrols the superconducting transition, has been found to improve with increased Be content. TheGinzburg–Landau coherence lengths �c�0� for all cases have also been calculated. The Fouriertransform infrared spectroscopy �FTIR� absorption measurements also provide a clue for theenhanced 3D fluctuations. The higher electronegativity, as well as smaller ionic size, of Becompared to Ca is suggested to be the possible source of promoting enhanced 3D character inBe-doped samples. © 2009 American Institute of Physics. �doi:10.1063/1.3266008�

I. INTRODUCTION

High-Tc cuprate superconductors are unique in many as-pects. They are hard type-II superconductors with a verysmall coherence length and anisotropic in many physicalproperties, such as thermal and electrical conductivities.1–7

These have great effects on superconducting order parameterfluctuation �SCOPF�. The excess conductivity analyses inhigh-Tc cuprate superconductors by different groups8–12 re-veal the contribution due to Gaussian fluctuation in themean-field regime as well as the critical-fluctuation regime.In the case of the Y–Ba–Cu–O system, the SCOPF is threedimensional �3D� in the mean-field regime. There is a cross-over from two-dimensional �2D� to 3D conductivity. But inthe case of the Bi–Sr–Ca–Cu–O system, it is essentially2D.13 Often, the crossover is masked by the critical-fluctuation regime setting on before the crossover.13 The be-havior in the SCOPF is affected by intrinsic factors in vari-ous systems, such as the extent of anisotropy in theconductivity �the Bi–Sr–Ca–Cu–O system is more aniso-tropic than Y–Ba–Cu–O�, as well as by nonintrinsic factorssuch as crystallinity, intergranular links, etc.13

The normal pressure synthesizedCu1−xTlxBa2Can−1CunO2n+4−� �n=2, 3, 4, and 5� supercon-ductors are promising candidates in cuprate families due totheir easy and reproducible synthesis route equipped withlow anisotropy ��=�ab /�c�.

14 We have earlier synthesizedCu0.5Tl0.5Ba2Ca4−xMgxCu5O14−� �x=1,2� and Ni-dopedCu0.5Tl0.5Ba2Ca2Cu3−yNiyO10−� �y=0,0.5,1.0,1.5� super-conductors at normal pressure and studied their and fluctua-tion induced conductivity.15,16 In the former, the excess con-ductivity data of sample fitted well with 2D, 3D Aslamasov–

Larkin �AL� equations in oxygen annealed samples, whichhave also shown improved weak link behavior.15 The Fluc-tuation induced conductivity �FIC� investigation of the latterrevealed that Ni doping resulted in shifting of the crossovertemperature to lower values through the scattering ofthe carriers by remnant spins of Ni atoms.16 Many investiga-tions have shown that the superconducting properties ofCu1−xTlxBa2Can−1CunO2n+4−� �n=2, 3, 4, and 5� are usuallyhighly sensitive to different annealing atmospheres andtemperatures.17–19

In this article we report the effect of Be doping on theFIC of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0,0.5,0.75,1.0,1.25,1.5� superconductors. Substitution of Be at the interpla-nar sites possibly changes the carrier concentration in theconducting CuO2 planes. Therefore Be substitution is ex-pected to modify the fluctuation behavior. We have restrictedour analysis to the mean-field regime and tried to extract theinterlayer coupling strength from there.

The excess conductivity �� in the lower anisotropyCu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0,0.5,0.75,1.0,1.25,1.5� superconductors has been calculated using AL model20

involving microscopic approach in the mean-field region.According to this approach the excess conductivities in twodimensions �2D� and three dimensions �3D� are given byformula

��2D = �e2/16�d��−1, �1�

��3D = �e2/32��c�0���−1/2, �2�

where �c�0� and d are the coherence length along the c-axisat 0 K and the interlayer separation, respectively. � is thereduced temperature and given by the relation

a�Electronic mail: nawazishalik@yahoo.com. Tel.: �92-51-2601056. FAX:�92-51-90642240.

JOURNAL OF APPLIED PHYSICS 106, 113913 �2009�

0021-8979/2009/106�11�/113913/7/$25.00 © 2009 American Institute of Physics106, 113913-1

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� = �T − Tcmf�/Tc

mf,

where Tcmf is the mean-field critical temperature obtained

from the point of inflection of versus T curve in our case.The dimensional exponent is found from the slope of

the ln���� versus ln��� plot. All physical parameters dependon the critical-fluctuation dimensionality �D�, which is ex-pressed as

D = 2�2 + � .

It is seen that the 2D to 3D crossover is mainly foundabove the critical temperature at a particular temperature To,which is different for different samples. Lawrence and Doni-ach introduced the concept of interlayer coupling in the vi-cinity of the critical temperature via Josephson coupling J.21

The FIC �� is expressed as

�� = �e2/16�d��−1�1 + �2�c�0�/d�2�−1/2,

where �c�0� and d are the coherence length along the c-axisand the interlayer separation, respectively. The above equa-tion reduces to the AL equation with the approximations�c����d and �c����d in 2D and 3D regions, respectively. Acharacteristic temperature T0 is obtained, which is called acrossover temperature. Below and above this temperature thesystem has 3D and 2D fluctuations, which can be describedby the relevant AL equations. The expression for crossovertemperature according to the Lawrence–Doniach �LD� modelis22,23

To = Tc�1 + �2�c�0�/d�2� . �3�

We have employed the above formulation to interpret thedata on FIC of our samples.

II. EXPERIMENTAL

The samples were prepared by solid-state reactionmethod accomplished in two stages. At the first stageCu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0,0.5,0.75,1.0,1.25,1.5� precursor material was synthesized using Ba�NO3�2

�99%, Merck�, Ca�NO3�2 �99%, Merck�, Cu�CN� �99%,BDH Chemicals Ltd., Poole, England�, KI �99%, BDHChemical Ltd., Poole, England�, and BeO �99%� as startingcompounds. These compounds were mixed in an appropriateratio in a quartz mortar and pestle. Thoroughly mixed mate-rial was fired in air in a quartz boat at 860 °C for 24 hfollowed by furnace cooling to room temperature. The pre-cursor material was then ground for about 1 h and mixedwith Tl2O3 �99%, Merck� to give Cu0.5Tl0.5Ba2Ca3−xBex

Cu4O12−� �x=0,0.5,0.75,1.0,1.25,1.5� as a final reactantcomposition. Thallium mixed material was then pelletizedunder 0.37 GPa pressure and pellets were wrapped in a goldcapsule. A pellet containing gold capsule was heated at860 °C for 10 min and quenched to room temperature afterthe heat treatment. The samples were cut into the shape ofrectangular plates of dimensions 10 8 2.5 mm3. Usingsilver paste, we fixed four linear probes on the surface of oneof the samples for transport resistivity measurements by thestandard dc four-probe technique. The resistivity temperaturecharacteristics in the 80–270 K range and the critical tem-peratures for each sample were determined using the four-

probe method. Constant currents of 1 mA were appliedthrough the outer probes with a current source, and the volt-age drops were measured through the inner probes with ananovoltmeter “Keithley 182.” The samples were cooled in aliquid nitrogen cryostat, which allowed temperature controlbetter to within 0.2 K. The structure of material was deter-mined by using x-ray diffraction scan �D/Max IIIC Rigaku�with a Cu K� source of wavelength 1.540 56 Å and cellparameters by using a check cell computer program. TheFTIR absorption measurements were done by a spectrometerfrom Nickolet™ 5700. The measurements were carried out atthe spectral resolution of 4 cm−1. The background spectrumwas taken with a KBr pellet. The sample was prepared bymixing 5 mg of the sample with 1 g of KBr, and the materialwas pelletized under 0.37 GPa pressure. The background andsample spectrum were taken by applying 200 scans.

III. RESULTS AND DISCUSSIONS

The x-ray diffraction scans of Cu0.5Tl0.5Ba2Ca3−xBex

Cu4O12−� �x=0,0.5,1.25,1.5� superconductor samples, pre-pared at 860 °C, are shown in Figs. 1�a� and 1�b�, respec-tively. Most of the diffraction lines could be indexed accord-ing to the tetragonal structure following P4/mmm spacegroup; the nominal impurity phases are also marked in thediffraction scans. For these samples, there is no remarkablestructural transition with increased Be content. The “c” lat-tice parameter of the samples decreases monotonously withincreasing Be concentration presumably due to the lowerionic size of Be+2 �0.31 Å� as compared to Ca+2 �0.99 Å�.

The resistivity measurements of Cu0.5Tl0.5Ba2Ca3−xBex

Cu4O12−� �x=0,0.5,0.75,1.0,1.25,1.5� samples are shownin the insets of Figs. 2–7, respectively. The resistivity varia-tions are metallic from room temperature down to the onsetof superconductivity. In the inset of these figures, the peakcurves show the derivatives of the resistivities in the regionof transition for all the samples. The peak position of eachsample on temperature axis provides Tc

mf�K�; To�K� is thetemperature at which a crossover in the fluctuations to theorder parameter from 2D to 3D takes place.24 All the sampleshave shown linear dependence of resistivities ��T�=�+�T� with the linear fits to the data at high temperatures, andare shown by the straight lines. The values of � and � andthe aforementioned temperatures for all the samples are in-cluded in Table I. T��K� is the temperature related topseudogap regime where onset of fluctuations in the orderparameter of superconductors sets in. Our samples showbroad transitions, which lead to quite higher values of T��K�above Tc

mf. However, despite the considerable number ofpapers devoted to this problem, there is still no clarity onthe question of whether the excess conductivity in high tem-perature superconductors �HTSCs� at T�Tc

mf is entirelyfluctuation conductivity. Quite higher values of T��K��160�30 K for optimally doped YBCO films25 and singlecrystals26,27 have been observed and reported to be increasedrapidly to T��K��250 K,28 with decreasing oxygen contentin the samples.29 The possibility that paired holes exist inHTSCs at T�Tc

mf has also been widely discussed.30–33 Theobservation of a coherent-boson current at T�120 K �Ref.

113913-2 Irfan et al. J. Appl. Phys. 106, 113913 �2009�

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33� and the findings of magnetoresistance described by thefluctuation theories all the way to T�230 K �Ref. 30� hasbeen reported for nearly optimally doped YBCO systems. Ithas been shown theoretically34–36 that pair correlations in

HTSCs above Tc can give rise to a highly anisotropicpseudogap in the spectrum of electronic states and lead todistortion of the Fermi surface.37,31 Studies of Bi-2212 com-pounds by the method of angle-resolved photoemission

FIG. 1. �a� X-ray diffraction pattern of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0,0.5� samples. The solid squares represent the unknown impurities. �b� X-raydiffraction pattern of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=1.25,1.5� samples. The solid squares represent the unknown impurities.

FIG. 2. ln���� vs ln��� plot of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0�sample. The scattered points are experimentally found FIC. The solid anddashed lines show the 3D AL and 2D AL fitting with a distinct crossovertemperature. The inset shows the resistivity measurement with extrapolatedlinear fit and its derivative curve.

FIG. 3. ln���� vs ln��� plot of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0.5�sample. The scattered points are experimentally found FIC. The solid anddashed lines show the 3D AL and 2D AL fitting with a distinct crossovertemperature. The inset shows the resistivity measurement with extrapolatedlinear fit and its derivative curve.

113913-3 Irfan et al. J. Appl. Phys. 106, 113913 �2009�

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spectroscopy38 and by resistivity39 and tunnelingconductivity40 measurements have shown the presence ofsuch a pseudogap in samples at temperatures Tc�T�T�

�170 K. Thus the presence of fluctuational pairs in HTSCs,at least up to T�200�20 K, seems extremely likely. Thusat sufficiently high temperatures there is a strong possibilityof fluctuational pairing and we can expect the existence oftwo types of carriers �normal holes and fluctuational pairs� ina HTSC at T�200 K. In this scenario though the contribu-tion of extrinsic factors to fluctuations might exist but therole of superconducting fluctuational pairs even at highertemperatures seems to be dominant. In case of these samplesthe AL theory is also applicable at T�Tc

mf as it has beenalready reported by Ghosh et al.41,42 for Bi-2212 and �Y,Ca�-123 samples.

A. Fluctuations induce conductivities anddimensional exponents

The excess conductivity has been estimated as ��= �N�T�−�T�� / �N�T��T��, where �T� is the actuallymeasured resistivity and N�T�=�+�T is the extrapolatednormal resistivity from room temperature to 0 K as seen inFigs. 2–7. N�T� is the sum total of the resistive contributionof the grains and of the links connecting the grains, the latterassumed to be independent of temperature. The intergrainparameter is included in �, and the values of � at 0 K havebeen obtained from the intercepts. The lower values of �suggest improved intergrain coupling.42 We see an increasein the value of � in the Be-doped samples, which indicatesdegradation in the intergrain connectivity of the samples.

FIG. 4. ln���� vs ln��� plot of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0.75�sample. The scattered points are experimentally found FIC. The solid anddashed lines show the 3D AL and 2D AL fitting with a distinct crossovertemperature. The inset shows the resistivity measurement with extrapolatedlinear fit and its derivative curve.

FIG. 5. ln���� vs ln��� plot of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=1.0�sample. The scattered points are experimentally found FIC. The solid anddashed lines show the 3D AL and 2D AL fitting with a distinct crossovertemperature. The inset shows the resistivity measurement with extrapolatedlinear fit and its derivative curve.

FIG. 6. ln���� vs ln��� plot of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=1.25�sample. The scattered points are experimentally found FIC. The solid anddashed lines show the 3D AL and 2D AL fitting with a distinct crossovertemperature. The inset shows the resistivity measurement with extrapolatedlinear fit and its derivative curve.

FIG. 7. ln���� vs ln��� plot of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=1.5�sample. The scattered points are experimentally found FIC. The solid anddashed lines show the 3D AL and 2D AL fitting with a distinct crossovertemperature. The inset shows the resistivity measurement with extrapolatedlinear fit and its derivative curve.

113913-4 Irfan et al. J. Appl. Phys. 106, 113913 �2009�

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In order to compare the experimental data with the the-oretical expressions for superconducting fluctuating behav-ior, we have plotted ln���� versus ln��� for the undoped andBe-doped samples, Figs. 2–7. ��2D and ��3D have beencalculated by using �c�0�=4 Å and �ab�0�=16 Å forCu0.5Tl0.5Ba2Ca3Cu4O10−� sample.43 We have taken d, the ef-fective separation between the CuO2 layers, to be equal to3.1 Å for this analysis.44 Like all HTSCs, most of oursamples have shown 2D character at higher temperature and3D behavior at lower temperatures �closer to the transitiontemperature regions�.

From these figures, it is evident that there are two dis-tinct changes in slope in each plot, the slope gradually in-creasing from the low to the high temperature side. The tem-perature corresponding to the change in slope is designatedas To. We have used the general fitting of the excess conduc-tivity with the equation ��=A�− for the temperature rangeconcerned. In the log-log plot of the excess conductivity ver-sus the reduced temperature, different values, or the expo-nents corresponding to various samples above and below thecrossover temperature, are listed in Table I �1 referring tothe exponent below To, 2 to that above To�. The followingthings are evident from the analysis of the plots of all thesamples.

Except x=0.75 the exponent 1 is found to be around 0.5in all the samples. The exponent values seem to fit well with3D AL theory showing 3D conductivity. For x=0.75 sample,the exponent 1 is found to be 0.36, and the value of 1 isless than 0.5; therefore, excess conductivity below crossovertemperature does not fit well with 3D AL theory. This region�−4.85� ln����−3.75� is known as dynamic scaling regionin accordance with Lobb’s prediction.45 This apparent ab-sence of 3D behavior in the conductivity may be due to the

transition from mean-field to critical-fluctuation regime be-fore the transformation from 2D to 3D conductivity. Thismay be because of the small mean free path of the chargecarriers and the small coherence length of the order of 2 Å.

The temperature ranges corresponding to 3D behaviorare given in Table II, which shows that the width of thetemperature window for 3D conductivity continuously in-creases with enhanced Be concentration �except x=0.75,which does not show 3D character�. The expansion of 3Dtemperature region with Be doping seems to be promoteddue to improved interlayer coupling. Since the ionic size ofthe Be ion is smaller than that of the Ca; therefore, its sub-stitution at the Ca sites lowers the size of the unit cell andreduces the distance among the CuO2 planes. This reducesthe anisotropy and enhances the coherence length along thec-axis, thereby improving the 3D character of the order pa-rameter of the carriers.

The exponent 2 above the crossover temperature To forthe Be free sample is �0.69 in the region −3.44� ln����

−1.4; this value corresponds to the static scaling region. Inthe x=0.5 sample the exponent 2 is found to be 0.97, in theregion −2.8� ln����−0.87. Mostly this exponent is near to1.0, which is the characteristic of 2D conductivity �2D AL�.The exponent 2, in the high temperature region, is 0.74 forthe x=0.75 sample in the region −3.75� ln����−1.6; thisvalue corresponds to the static scaling region. In sampleswith x=1.0 and x=1.5 the values of 2 are 1.14 and 1.1,respectively, which are reminiscent of 2D AL conductivity.On the other hand for x=1.25 the exponent value is 1.32,which may be due to the superposition of different dimen-sional fluctuations. This was also observed by Vidal et al.,13

and they attributed this to the formation of a higher-Tc phase.

TABLE I. Various parameters obtained from the resistivity vs temperature data and ln���� vs ln��� plots of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0,0.5,0.75,1.0,1.25,1.5� samples.

SamplesTc

�K�Tp

�K�T�

�K� �=n�0� 1 2

To

�K��o

�� J= �2��0��2 /d2

x=0 99 106 183 0.000 5 �0.47 �0.67 109 1.50 0.104x=0.5 103 109 198 0.23 �0.49 �0.97 116 1.65 0.126x=0.75 105 117 180 0.000 18 �0.36 �0.74 120 1.75 0.141x=1.0 107 112 184 0.073 �0.45 �1.14 123 1.79 0.148x=1.25 110 111 180 0.100 �0.47 �1.32 127 1.82 0.153x=1.5 114 127 193 0.06 �0.52 �1.10 137 2.09 0.202

TABLE II. Temperature ranges for 3D and 2D FIC behaviors of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0,0.5,0.75,1.0,1.25,1.5� samples.

SamplesTemperature range for 3D behavior

�K�Temperature range for 2D behavior

�K�

x=0 107.47–109.4 109.4–132.2x=0.5 110–116 116–155x=0.75 ¯ 120.2–141x=1.0 108.5–123.4 123.4–155x=1.25 107.4–127.4 127.4–144x=1.5 115.4–137 137–177

113913-5 Irfan et al. J. Appl. Phys. 106, 113913 �2009�

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B. Coherence length, crossover temperature, andinterlayer coupling strength

At the crossover temperature To, fluctuations of lowerdimension are converted into 3D or critical fluctuations. Ithas lower values for undoped sample as compared to Be-doped samples. At the crossover temperature To, we can findout coherence length along the c-axis using LD model

To = Tc1 + 2�c�0�d

�2� ,

where d is the thickness of superconducting layers. The val-ues of �c�0� of all the samples are listed in Table I. It isevident from the table that the value of coherence length is�1.5 Å in the undoped sample and gradually increases withBe doping and finally approaches 2.09 Å for x=1.5 concen-tration. In cuprate HTSCs, the two major constituents ofunit cell22 are MBa2O4−�, a charge reservoir layer �M=Cu,Tl,Hg,Bi,C�, and the conducting nCuO2 planes �n=2,3 ,4 ,5 ,6�. The Ca atoms separate the CuO2 planes, andthe wave function of the Ca atoms develops a correlationamong the carriers in various CuO2 planes. In previous stud-ies the substitution of Mg+2 or Be+2 at the Ca+2 site in�Cu0.5Tl0.5�Ba2Ca2Cu3O10−� has been found to improve theinterplane coupling due its the smaller ionic size �Ca�Mg�Be�, which in turn can increase the interactions among thecharge carriers in various conducting CuO2 planes.46,47 It canbe seen that the length of the a- and c-axes decreases with theincrease in Mg or Be content in the final compound. Thedecrease in length of the c-axis is a direct evidence of de-creased bond lengths between copper atoms and improvedinterplane couplings. The decrease in axis lengths suppressthe volume “V” of the unit cell, which increases the Fermivector KF= �3�2N /V�1/3. The increase in Fermi vector pro-motes enhancement of coherence length along the c-axis��c=�2KF /2m��. In oxide HTSCs the value of ab-plane co-herence length is around 16 Å. The dimensionless parameter�=�ab�0� /�c�0� defines the anisotropy of the superconduct-ors, which is 11 for the undoped sample and it becomes 7 forthe x=1.5 sample. The lower anisotropy is possibly reminis-cence of enhanced interplane coupling, which is possibly dueto increased coherence length along the c-axis.

Lawrence and Doniach21 introduced the concept of inter-layer coupling in the vicinity of the critical temperature viaJosephson coupling �i.e., J�. The FIC ���� is expressed as

�� = e2

16�d��−11 + 2�c�0�

d�2�−1/2

, �4�

where �c�0� and d are the coherence length along the c-axisand the interlayer separation, respectively. The above equa-tion reduces to the AL equation with the approximations�c����d and �c����d in 2D and 3D regions, respectively.

The values of interlayer coupling strength J and �c�0� ofvarious samples are listed in Table I. The J values of thesamples clearly show an increasing trend with Be doping.Be, being smaller in size as compared to Ca, improves inter-plane coupling that results in lower anisotropy and longercoherence length along the c-axis.

C. Fourier transform IR studies

Figure 8 shows the FTIR spectra ofCu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0,0.5,0.75,1.0,1.25�samples. Here we will discuss oxygen related phonon modes,which are observed above 300 cm−1.48 In the previous stud-ies on the cuprate superconductors the phonon modes of api-cal oxygen of types Cu�1�–OA–Cu�2� and Tl–OA–Cu�2�are observed around 534 and 485 cm−1, respectively.49–52

The apical oxygen related mode Tl–O–Cu can be seen hard-ening from 459 to 505 cm−1 with increased Be doping. An-other apical oxygen mode of type Cu�1�–O–Cu�2� has showna softening trend in x=0.5 and x=0.75 samples, while in theremaining samples it is found almost constant around524 cm−1. The planar oxygen modes appear to be undis-turbed with Be doping with a fixed value around 585 cm−1.These observations indicate that improved interplane cou-pling, due to Be doping at the Ca site, has a major impact onthe bond lengths involving Tl ions in the charge reservoirlayer. It can be inferred that the higher electronegative Be+2

�1.5 Paulings� interacts more strongly with Tl as compared tothe Ca2+ ion �1.0 Paulings�, thereby introducing a strong in-teraction causing the shrinking of the bond lengths. Since Tlin the charge reservoir layer plays a vital role in the flow ofcharge carriers to the conducting CuO2 planes, the stronginfluence of the Be on the Tl somehow promotes the smoothcharge transfer between the charge reservoir layer and theconducting planes that is witnessed in enhanced supercon-ductivity and expansion of the 3D fluctuation temperaturerange with increased Be concentration

FIG. 8. FTIR absorption spectra of Cu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0,0.5,0.75,1.0,1.25� samples.

113913-6 Irfan et al. J. Appl. Phys. 106, 113913 �2009�

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IV. CONCLUSION

Electrical resistivity measurements of theCu0.5Tl0.5Ba2Ca3−xBex Cu4O12−� �x=0,0.5,0.75,1.0,1.25,1.5� superconductor samples have shown two distinct re-gions in the �T� versus T plots. One of them is ascribed tothe normal state resistivity where the metallic fit �N�T�=�+�T� is satisfactory, and the other is the characteristic super-conducting fluctuation region where the fit deviates from lin-earity. The origin of this deviation has been traced to theformation of cooper pairs �even above T0�. We have ana-lyzed the excess conductivity data of samples. In most of thesamples one crossover temperature and two distinct expo-nents have been observed and the excess conductivity dataseem to fit well with 2D, 3D AL equations. The analysisshows an increasing trend in the 3D FIC character with in-creased Be content, which can be attributed to the improvedinterplane coupling. Further FTIR analysis shows significanthardening of the Tl–O–Cu�2� modes, indicating a strong in-teraction between Be and Tl atoms. This interaction is mostlikely causing a smooth flow of charge along the c-axis ofthe unit cell, which can be a source of increased coherencelength along the c-axis as well as enhanced 3D character offluctuations.

ACKNOWLEDGMENTS

The Higher Education Commission, Pakistan is ac-knowledged for scholarships and research funding. We alsoacknowledge the International Center for Theoretical Physics�ICTP� for their financial support through Project No. PRJ-27.

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