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Charge carrier localization and metal to insulator transition in cerium substituted (Bi,Pb)-2212 superconductor
Journal of Alloys and Compounds 493 (2010) 11–16
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Charge carrier localization and metal to insulator transition in cerium substituted (Bi,Pb)-2212 superconductor R. Shabna, P.M. Sarun, S. Vinu, U. Syamaprasad ∗ National Institute for Interdisciplinary Science and Technology (CSIR), Trivandrum 695019, India
a r t i c l e
i n f o
Article history: Received 31 August 2009 Received in revised form 7 December 2009 Accepted 8 December 2009 Available online 16 December 2009 PACS: 74.72.Hs 71.30.+h 72.20.Ee 74.62.C 74.62.Dh
a b s t r a c t We report on the details of carrier localization and metal to insulator transition in (Bi,Pb)-2212 by substituting Ce at its Sr site (0.2 ≤ x ≤ 1.0). Structural and compositional analysis confirm good homogeneity of Ce distribution in the (Bi,Pb)-2212 matrix. The resistivity measurements show that x = 0.2 sample is a superconductor while those with x > 0.2 are insulators. Resistivity in the insulating regime (0.4 ≤ x ≤ 1.0) is analyzed using a generalized hopping approach. The increase in normal state resistivity and disorder of the samples leads to a metal to insulator transition at 0.2 < x ≤ 0.4 and the insulating phases exhibit Mott’s variable range hopping phenomenon. Around the transition, a dimensional change over from two to three dimensions is observed in the variable range hopping regime. Results show that substitution reduces the carrier concentration of (Bi,Pb)-2212, leads to suppression of superconductivity and metal to insulator transition in the system by localizing the electronic states at the Fermi level. © 2009 Elsevier B.V. All rights reserved.
Keywords: Bi-2212 superconductor Metal insulator transition Variable range hopping
1. Introduction The interplay of localization and superconductivity is of fundamental interest in the physics of electrons in strongly correlated and disordered systems such as the high temperature superconductors (HTSCs). Disorder in a metallic system can cause localization of the electronic states in the vicinity of the Fermi level and therefore lead to a metal to insulator transition (MIT), known as the Anderson’s MIT [1]. Several authors have theoretically shown that the Anderson localization and superconductivity are not mutually exclusive and that the Anderson’s theorem is still valid in a narrow region, around the mobility edge [2–4]. Although the electronic density of states at the Fermi level remains finite, the ground state of a disordered system is an insulator due to the spatial localization of the electronic wave functions. On the other hand, a metallic system can become superconducting if there exists a finite attractive interaction among the electrons. In the original BCS theory, the itinerant electrons form a macroscopic wave function, = (nc )1/2 ei , where nc is the Cooper pair
∗ Corresponding author at: National Institute for Interdisciplinary Science and Technology, Council of Scientific and Industrial Research, Trivandrum 695019, India. Tel.: +91 471 2515373; fax: +91 471 2491712. E-mail address: [email protected] (U. Syamaprasad). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.12.047
density and is the macroscopic phase. This superconducting ground state can be changed to an insulating ground state either through the disorder induced localization which causes a decrease of carrier density or by the spatial inhomogeneity which causes a loss of macroscopic phase. It has been reported that intra-grain disorder induced by doping or by elements deficiency [5,6] reduces the effective coupling strength of cuprate superconductors and results in smaller carrier density whereas inter-grain disorder arising from grain boundary defects, reduces the coupling between grains and thus destroys the phase . As a consequence, the electrical properties of cuprates change from insulating (d/dT < 0) to metallic (d/dT > 0) due to the fact that all high-TC cuprates lie close to a metal–insulator transition [7,8]. A coexistence of superconductivity and localization has previously been observed for the latter case in granular superconductors in which small, metallic clusters become superconducting and are coupled through Josephson junctions [9]. The former case occurs in homogeneous systems by a decrease of critical temperature, TC with increase of disorder. HTSCs are examples of homogeneous systems and in recent years the rare-earth (RE) substitution studies in HTSCs have attracted considerable attention. It has been reported that different aliovalent substitutions or changes in the oxygen stoichiometry can effectively alter the concentration of carriers in the HTSC systems, resulting in a MIT [8,10–12]. MIT can also be caused by photo-induced laser treatment in which the photo-induced
12
R. Shabna et al. / Journal of Alloys and Compounds 493 (2010) 11–16
electron–phonon anharmonicity plays a crucial role in the transition [13]. The interplay near the MIT between randomness, Coulomb repulsion and the pairing mechanism that creates superconductivity is a topic of intense debate. In two dimensions, this interplay becomes particularly interesting, since the lower critical dimension for both the localization and superconductivity is two. A number of previous studies of ultra thin film superconductors have established that increasing the disorder by increasing the sheet resistance results in the suppression of superconductivity in two dimensions [14]. Bi2 Sr2 CaCu2 O8 [Bi-2212] is a HTSC and the presence of Cu–O planes in this system, strongly suggests the presence of two dimensional (2D), physical and electronic properties which makes it suitable for the above investigations. So, in the present work, we report the effect of disorder and localization on the MIT and superconducting properties of Bi1.7 Pb0.4 Sr2 Ca1.1 Cu2.1 O8+ı [(Bi,Pb)2212] system which is a HTSC, through the substitution of a rare-earth, cerium (Ce) at its Sr site. Ce is substituted in this material over a wide range (0.2 ≤ x ≤ 1), to explore both the superconducting and insulating regions in the temperature doping phase diagram of (Bi,Pb)-2212 system. Here Pb is also substituted in the Bi-2212 system due to the established beneficial effects of Pb, like its role in the homogenization and stabilization of the Bi-2212 phase and also in increasing its TC , and therefore makes the system more useful for the above investigations [15,16]. Detailed evaluation of the structural and resistivity parameters of the insulating phases in Bi1.7 Pb0.4 Sr2−x Cex Ca1.1 Cu2.1 O8+ı system is also explored which provide an excellent insight and understanding about the electronic conduction and the variable range hopping (VRH) mechanism in this material. 2. Materials and methods Bi1.7 Pb0.4 Sr2−x Cex Ca1.1 Cu2.1 O8+ı (0.2 ≤ x ≤ 1) samples were prepared by solid state synthesis route, using high purity chemicals of Bi2 O3 , PbO, SrCO3 , CaCO3 , CuO and CeO2 (Aldrich >99.9%). Stoichiometric amounts of the ingredients were accurately weighed using an electronic balance (Mettler AE 240), thoroughly mixed and ground using an agate mortar and pestle, and then subjected to a three stage calcination process in air at temperatures, 800 ◦ C/15 h, 820 ◦ C/30 h, and 840 ◦ C/60 h with a heating rate of 3 ◦ C/min. Intermediate wet grinding was done between each stages of calcination. After calcination, the samples were pelletized using a cylindrical die of 12 mm diameter, under a force of 80 kN. The pellets were then heat treated at 885 ◦ C for 120 h (60 + 60) in two stages, with one intermediate re-pressing under the same stress. Phase analysis of the samples was done using X-ray diffraction (XRD) (Philips X’pert Pro) employing an X’celerator and monochromator at the diffracted beam side. Phase identification was performed using X’Pert High score software, in support with ICDD-PDF 2 database. Microstructural examinations of the samples were done using scanning electron microscopy (JEOL JSM 5600 LV). Elemental analyses of the samples were done using energy dispersive X-ray analysis attached to the SEM. The electrical transport properties of the samples from 64 K to 300 K were measured using the four probe method. A Lakeshore temperature controller (Model: 340) was used to accurately monitor the temperature.
Fig. 1. XRD pattern of samples after final stage sintering process.
that the solubility limit of Ce in (Bi,Pb)-2212 system is around, x = 0.4. The SEM micrographs of the fractured samples after the last stage sintering process are shown in Fig. 2. It is found that the grain morphology is not much affected by the substitution of Ce. All the samples contain long and flaky grains that characterize the (Bi,Pb)-2212 system. But with the increase in Ce content, presence of small, rounded secondary phase is also observed in samples with x > 0.6. The secondary phase and (Bi,Pb)-2212 grains were analyzed through EDAX and Fig. 3 shows the EDAX spectra of (Bi,Pb)-2212 grains of the pure and a typical Ce substituted (Bi,Pb)-2212 [Ce10] samples. Presence of Ce is detected in the (Bi,Pb)-2212 grains of Ce substituted samples with a corresponding reduction in Sr. This indicates that the Ce atoms are successfully substituted in place of Sr site of the (Bi,Pb)-2212 system. The relative concentration of Ce and Sr are evaluated as a function of the nominal doping value x and the results are shown in Table 1. From the EDAX analysis, it is identified that the rounded phase which is observed between the flaky grains of (Bi,Pb)-2212 system in the SEM micrographs corresponds to the CeO2 . This indicates that beyond the solubility limit, CeO2 remains as such in the system and this was already confirmed from the XRD pattern of the Ce10 sample. From the XRD patterns, the lattice parameters are calculated using the d values and (h k l) parameters by assuming an orthorhombic symmetry for (Bi,Pb)-2212. The variation of lattice parameters against actual Ce concentration is shown in Fig. 4 with an accuracy of (±0.002). The c axis length decreases with the dopant concentration. This decrease in c lattice parameter can arise due to (i) the increase in oxygen content of the system, (ii) the substitution of higher valence cation Ce4+ with an ionic radius smaller than that
3. Results and discussion The samples are labelled as Ce2, Ce4, Ce6, Ce8 and Ce10, initially with respect to the nominal x values (0.2, 0.4, 0.6, 0.8 and 1.0, respectively) and later on with respect to the actual Ce concentrations (0.19, 0.38, 0.56, 0.72 and 0.85, respectively), obtained from the EDAX analysis. The normalized XRD patterns of the samples after sintering at 855 ◦ C/120 h are shown in Fig. 1. In all samples, the major phase detected is (Bi,Pb)-2212. But from x = 0.6 onwards, some additional peaks are also observed along with the (Bi,Pb)-2212. By analyzing the patterns using X’pert high score software, it has been found that these peaks correspond to that of CeO2 [34-0394], as referred in the database. The absence of any Ce containing phase up to x = 0.4 shows
Table 1 Quantitative EDX results of cation stoichiometry of Ce substituted (Bi,Pb)-2212 grains (standardized with respect to Ca). Sample
Stoichiometry
(Bi,Pb)
Sr
Cu
Ce
Ce2
Initial From EDX Initial From EDX Initial From EDX Initial From EDX Initial From EDX
2.10 2.00 2.10 1.99 2.10 2.00 2.10 1.98 2.10 1.99
1.80 1.78 1.60 1.59 1.40 1.38 1.20 1.16 1.00 0.97
2.10 2.00 2.10 1.99 2.10 2.00 2.10 2.00 2.10 2.00
0.20 0.19 0.40 0.38 0.60 0.56 0.80 0.72 1.00 0.85
Ce4 Ce6 Ce8 Ce10
R. Shabna et al. / Journal of Alloys and Compounds 493 (2010) 11–16
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Fig. 2. SEM micrographs of fractured surfaces of Ce substituted (Bi,Pb)-2212 samples.
of Sr2+ . The a axis length increases up to Ce6. This can be ascribed to the change in the planar Cu–O bond distance due to hole compensation in the system. The b lattice parameter gradually decreases in all samples. From Ce6 onwards, the a axis parameter decreases and the difference between a and b lattice parameters becomes very small. This indicates the structural change of the system from the orthorhombic symmetry to the tetragonal. In order to show the gross feature of the successive phase changes of the system with Ce concentration, the temperature dependence of resistivity of the samples is given in Fig. 5. The resistivity changes systematically with doping which reflects the well controlled stoichiometry of these samples. The sample Ce2 is a superconductor with TC -onset of 83.38 K. The temperature coefficient of resistivity of the Ce2 sample is positive for temperatures above TC with (d/dt) > 0, and this shows that Ce2 is metallic in the normal state. But, when the Ce concentration is increased beyond 0.2, the normal state resistivity of the samples increases sharply
with the doping concentration, x and no superconducting transition could be observed. All the samples from Ce4 to Ce10 show the negative temperature coefficient of resistivity with (d/dt) < 0, indicating the insulating behavior. This indicates that the metal to insulator transition takes place in between x = 0.2 and x = 0.4. From the resistivity analysis, we found that none of the insulating phases satisfy either the thermally activated conductivity [ln vs 1/T behavior] or the mechanism of hopping conductivity in a system of localized electrons with long range coulomb interaction (ln vs (1/T)1/2 ). However, they all satisfy the Mott’s variable range hopping equation (VRH): (T ) = 0 exp
T n 0
T
,
(1)
which in general indicates conduction by polarons [17]. Here 0 and T0 are constants characterizing a given material. The exponent ‘n’ in the above equation depends crucially on the behavior of the
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R. Shabna et al. / Journal of Alloys and Compounds 493 (2010) 11–16 Table 2 Hopping parameters. Sample
1/n
Localization length (Å)
R (Å)
T0 (K)
Ce4 Ce6 Ce8 Ce10
3 3 4 4
0.008 0.0008 20 17.6
0.01 0.001 21.29 18.14
2.96 285 1790 2990
the Bi-2212 system on a flat band along the –M–Z direction. They report that the FL is pinned close to a VHS in Bi-2212 system. For an (E–EF ) dependence of DOS on the energy [20], n=
m+1 , m+d+1
(2)
where ‘m’ is the constant representing the behavior of DOS and ‘d’ is the dimensionality of the hopping process. For VRH in two dimension, d = 2 and for VRH in three dimension, d = 3. When the DOS remains finite at the FL, m = 0 and the value of n becomes either 1/3 or 1/4 depending on whether the hopping is in two or three dimensions, respectively. We fit the –T curve of the insulating samples (Ce4 to Ce10) to Eq. (1) and Fig. 6 shows the best fit [ln vs (1/T)n ] of the samples. It is found that the resistivity data of the insulating samples Ce4, and Ce6 fit well to the Eq. (1) with n = 1/3 while that for Ce8 and Ce10 with n = 1/4. This suggests that the electronic conduction in samples Ce4 and Ce6 take place by the two dimensional (2D) variable range hopping mechanism and that in Ce8 and Ce10 by the three dimensional (3D) VRH. Moreover, the systematic increase in normal state resistivity of samples with the Ce content also shows that the system enters the variable range hopping regime, indicating a metal to insulator transition in the system. The parameters used for fitting are given in Table 2. The system exhibits a dimensionality crossover, while passing from Ce6 to Ce8. The characteristic temperature T0 is related to the N(EF ), Boltzmann constant (KB ) and to the radius of the localized states or the localization length (˛) by the following relations. In 2D: Fig. 3. EDAX patterns of (Bi,Pb)-2212 grains of pure and Ce10 sample.
density of states (DOS) with energy (E) near the Fermi level (FL) and on the dimensionality of the hopping process. The Van Hove singularity (VHS) provides a paradigm for the study of the role of peaks in the DOS on electronic properties. The Van Hove scenario is based on the assumption that in HTSC, the Fermi level lies close to such a singularity [18]. Dessau et al. [19] provided a report for
T0 =
27 , 4˛2 KB N(EF )
and In 3D: T0 =
16 . [˛3 KB N(EF )]
(4)
At any temperature, the transition probability for the occurrence of a hop to a state at a distance R from the initial state and separated by an energy W is given by
p∼ exp −2aR −
Fig. 4. Variation of lattice parameters with Ce content.
(3)
W kT
.
(5)
The term exp(−2aR) denotes the probability of finding an electron at a distance R from its initial state and a is the inverse localization length [˛−1 ] [22]. Fisher et al. [21] measured specific heat in the Bi-2:2:1:2 system and obtained a value of 11 mJ mol−1 K−2 which corresponds to N(EF )∼1.1 states/eV Cu spin. We have estimated the localization length and most probable hopping distance (R) [22] of the insulating samples, by making use of Eqs. (3)–(5). The values of R given in Table 2 were estimated at temperatures corresponding to T < T0 /27 (for samples Ce4 and Ce6) and T < T0 /50 (for samples Ce8 and Ce10) because the temperature range where the localization length is lower than the most probable hopping distance is T < T0 /50 for VRH in 3D and T < T0 /27 for VRH in 2D. Since, it is clear from the table that the hopping length of the insulating Ce samples in the said temperature range is larger than the localization length, we conclude that our interpretation of the resistivity data are in agreement
R. Shabna et al. / Journal of Alloys and Compounds 493 (2010) 11–16
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Fig. 5. Variation of resistivity of the samples with temperature.
with the conditions for Mott VRH behavior. It is found that within a particular dimension, the localization length decreases with x. This shows that the substituted Ce atoms localize the holes in the system and lead to the observed MIT. The VRH mechanism of conduction is best described at low temperatures where the thermal energy for the charge transport is insufficient to excite the carriers across the mobility gap. In such a system, contribution to the electrical conduction is possible only by the hopping process, mediated by phonons from one filled state to an empty state. Crystalline materials generally exhibit this phenomenon due to the absence of long range order. Mott has experimentally verified the VRH mechanism
at low temperatures, in a class of systems and treatise his observations. Such trends have been reported in the insulating phases of high-TC materials too, like the GdBa2 Cu3−x Crx O7+ı system [10]. The XRD pattern, lattice parameter calculations and elemental analysis have shown that the substituted Ce atoms are successfully entering into the crystal structure of (Bi,Pb)-2212 system. When Ce is substituted in place of Sr, each replacement compensates two holes and decreases the hole concentration in the Cu–O planes of (Bi,Pb)-2212 system. Since, Ce possess different charge, ionic radius and electronic structure in comparison with Sr, the replacement of each Sr2+ by Ce4+ in (Bi,Pb)-2212 leads to
Fig. 6. Best fit of ln vs (1/T(K))1/n [EXP denotes the experimental data and GEN denotes generated data].
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R. Shabna et al. / Journal of Alloys and Compounds 493 (2010) 11–16
disorder in the system along with the electronic/chemical inhomogeneity of the charge reservoir (Bi–O) layers. The intrinsic defects produced by the substitution of Ce in (Bi,Pb)-2212 also play a decisive role in the electronic structure of the system because disorder in condensed matter is generally associated with the presence of zero-to-three dimensional defects in crystalline and semi crystalline materials, impurities and distortions coming from the meta-stability of the structures. It has been reported that the small changes in the composition or structure of cuprates by doping provokes both inter-grain and intra-grain disorder due to crystalline structural defects and grain boundary defects, respectively [5,6]. Hence, superconductivity is suppressed by either inter-grain disorder or intra-grain disorder. The localization length which represents the exponential decay of the electronic wave functions at large distances depends on the extent of disorder present in a system. It is interesting to note that from Ce4 to Ce10, the localization length decreases in a systematic way. This shows that disorder in the system increases with Ce content. The disorder tends to slow down or localize a carrier at the lattice sites, resulting in the formation of polarons [23]. Moreover, it breaks the symmetry of the ordered system at the molecular scale and consequently affects the extended states of valence and conduction bands forming the localized states [1,17] which concentrate in band tails. As the conduction process is very dependent on the spatial and energy densities of these localized states, the energy required for the conduction process increases with increase in disorder. Since, the local activation energy [24] in a disordered system is calculated from the slope of the ln vs (1/T) curve, the systematic increase in T0 values of samples with respect to x implies that the disorder in the (Bi,Pb)-2212 system increases with Ce concentration. The metal to insulator transition usually takes place when the density of carriers decreases; the latter necessarily leading to an increase of the effective strength of e–e interaction. On the other hand, the decrease in the carrier density is accompanied by an increase in the effective disorder, particularly, due to the weakening of the screening of potential fluctuations. Thus, the properties of the samples are strongly influenced by both the electronic interaction and randomness. Hence, in the present system, both the Coulomb correlations (Mott transition) and disorder (Anderson transition) are the driving forces behind the MIT. Most existing theories are not able to combine these two fundamental processes within the same framework, and this conceptual difficulty has provided the essential pitfall in the understanding of the MIT. At higher doping levels (x > 0.2), supplied carriers tend to be localized at low temperatures as indicated by the variable range hopping type resistivity behavior and this disorder induced transition leads to a localization of states in the vicinity of Fermi level and in a finite density of states at the Fermi level. The localized electronic states are randomly distributed in energy as well as in space, with a uniform distribution given by N(EF ), which is the density of states per unit volume per unit energy. The conduction takes place by the variable range hoping mechanism which involves hopping of carriers between the various localized states. Thus the satisfactory
agreement between the theory and the experimental data implies that in the Ce substituted (Bi,Pb)-2212 system, the depletion of charge carriers induces disorder, leads to localization of states in the vicinity of Fermi level and thus drives a MIT. 4. Conclusions In summary, we have investigated the metal to insulator transition and charge carrier localization effects in (Bi,Pb)-2212 superconductor through Ce substitution. The TC suppression is due to the reduction of hole concentration in the Cu–O planes of (Bi,Pb)-2212 system and the electronic transport in the insulating samples can be explained using the Mott’s variable range hopping mechanism. A Mott–Anderson MIT takes place at 0.2 < x ≤ 0.4 due to depletion and disorder induced localization of charge carriers. Acknowledgements The authors, Mrs. R. Shabna, Mr. P.M. Sarun and Mr. S. Vinu acknowledge the KSCSTE, CSIR and U. G. C. India, respectively, for providing their Senior Research Fellowships. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13] [14] [15] [16] [17] [18] [19]
[20] [21] [22] [23] [24]
P.W. Anderson, Phys. Rev. 109 (1958) 1492. L.N. Bulaevskii, M.V. Sadovski, J. Low Temp. Phys. 59 (1985) 89. M. Ma, P. Lee, Phys. Rev. B 32 (1985) 5658. A. Kapitulnik, G. Kotliar, Phys. Rev. Lett. 54 (1985) 473. C.H. Booth, F. Bridges, J.B. Boyee, T. Claeson, Z.X. Zhao, P. Cervantes, Phys. Rev. B 49 (1994) 3432. R. Buhleir, S.D. Brorson, I.E. Trofimo, J.O. White, H.U. Habermeier, J. Kuhl, Phys. Rev. B 50 (1994) 9672. J.C. Philips, Phys. Rev. B 39 (1989) 7536. R. Shabna, P.M. Sarun, S. Vinu, A. Biju, P. Guruswamy, U. Syamaprasad, J. Appl. Phys. 104 (2008) 013919. Y. Imry, M. Strongin, C.C. Homes, Physica C 468 (2008) 288. S. Bazargan, H. Javanmard, M. Akhavan, Physica C 466 (2007) 157. G.I. Harus, A.I. Ponomarev, T.B. Charikova, A.N. Ignatenkov, L.D. Sabirzjanova, N.G. Shelushinina, V.F. Elesin, A.A. Ivanov, I.A. Rudnev, Physica C 383 (2002) 207. P. Starowicz, J. Sokowski, M. Balanda, A. Szytua, Physica C 363 (2001) 80. I.V. Kityk, J. Phys. Condens. Matter 6 (1994) 4119. A.F. Hebard, Strongly Correlated Electronic Materials: The Los Alamos Symposium, Addison Wesley, Reading, 1993. P.M. Sarun, S. Vinu, R. Shabna, A. Biju, U. Syamaprasad, J. Alloys Compd. 472 (2009) 13. S. Vinu, P.M. Sarun, R. Shabna, A. Biju, U. Syamaprasad, Supercond. Sci. Technol. 21 (2008) 085010. N.F. Mott, E.A. Davis, Electronic Processes in Noncrystalline Materials, Clarendon Press, Oxford, 1979. J. Bok, J. Bouvier, Physica C 460–462 (2007) 1010. D.S. Dessau, Z.X. Shen, D.M. King, D.S. Marshall, L.W. Lombardo, P.H. Dickinson, A.G. Loeser, J. DiCarlo, C.-H. Park, A. Kapitulink, W.E. Spicer, Phys. Rev. Lett. 71 (1993) 2781. I.P. Zvygin, in: M. Pollak, B. Shklovskii (Eds.), Hopping Conduction in Solids, North Holland, Amsterdam, 1991. R.A. Fisher, S. Kim, S.E. Lacy, N.E. Phillips, D.E. Morris, A.G. Markelz, J.Y.T. Wei, D.S. Ginley, Phys. Rev. B 38 (1988) 11942. R. Zallen, The Physics of Amorphous Solids, Wiley Classics Library, 1998. B.I. Shklovskii, A.L. Efros, Electronic Properties of Doped Semiconductors, Springer, Berlin, 1984. J. Tateno, Physica C 214 (1993) 377.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Charge carrier localization and metal to insulator transition in cerium substituted (Bi,Pb)-2212 superconductor R. Shabna, P.M. Sarun, S. Vinu, U. Syamaprasad ∗ National Institute for Interdisciplinary Science and Technology (CSIR), Trivandrum 695019, India
a r t i c l e
i n f o
Article history: Received 31 August 2009 Received in revised form 7 December 2009 Accepted 8 December 2009 Available online 16 December 2009 PACS: 74.72.Hs 71.30.+h 72.20.Ee 74.62.C 74.62.Dh
a b s t r a c t We report on the details of carrier localization and metal to insulator transition in (Bi,Pb)-2212 by substituting Ce at its Sr site (0.2 ≤ x ≤ 1.0). Structural and compositional analysis confirm good homogeneity of Ce distribution in the (Bi,Pb)-2212 matrix. The resistivity measurements show that x = 0.2 sample is a superconductor while those with x > 0.2 are insulators. Resistivity in the insulating regime (0.4 ≤ x ≤ 1.0) is analyzed using a generalized hopping approach. The increase in normal state resistivity and disorder of the samples leads to a metal to insulator transition at 0.2 < x ≤ 0.4 and the insulating phases exhibit Mott’s variable range hopping phenomenon. Around the transition, a dimensional change over from two to three dimensions is observed in the variable range hopping regime. Results show that substitution reduces the carrier concentration of (Bi,Pb)-2212, leads to suppression of superconductivity and metal to insulator transition in the system by localizing the electronic states at the Fermi level. © 2009 Elsevier B.V. All rights reserved.
Keywords: Bi-2212 superconductor Metal insulator transition Variable range hopping
1. Introduction The interplay of localization and superconductivity is of fundamental interest in the physics of electrons in strongly correlated and disordered systems such as the high temperature superconductors (HTSCs). Disorder in a metallic system can cause localization of the electronic states in the vicinity of the Fermi level and therefore lead to a metal to insulator transition (MIT), known as the Anderson’s MIT [1]. Several authors have theoretically shown that the Anderson localization and superconductivity are not mutually exclusive and that the Anderson’s theorem is still valid in a narrow region, around the mobility edge [2–4]. Although the electronic density of states at the Fermi level remains finite, the ground state of a disordered system is an insulator due to the spatial localization of the electronic wave functions. On the other hand, a metallic system can become superconducting if there exists a finite attractive interaction among the electrons. In the original BCS theory, the itinerant electrons form a macroscopic wave function, = (nc )1/2 ei , where nc is the Cooper pair
∗ Corresponding author at: National Institute for Interdisciplinary Science and Technology, Council of Scientific and Industrial Research, Trivandrum 695019, India. Tel.: +91 471 2515373; fax: +91 471 2491712. E-mail address: [email protected] (U. Syamaprasad). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.12.047
density and is the macroscopic phase. This superconducting ground state can be changed to an insulating ground state either through the disorder induced localization which causes a decrease of carrier density or by the spatial inhomogeneity which causes a loss of macroscopic phase. It has been reported that intra-grain disorder induced by doping or by elements deficiency [5,6] reduces the effective coupling strength of cuprate superconductors and results in smaller carrier density whereas inter-grain disorder arising from grain boundary defects, reduces the coupling between grains and thus destroys the phase . As a consequence, the electrical properties of cuprates change from insulating (d/dT < 0) to metallic (d/dT > 0) due to the fact that all high-TC cuprates lie close to a metal–insulator transition [7,8]. A coexistence of superconductivity and localization has previously been observed for the latter case in granular superconductors in which small, metallic clusters become superconducting and are coupled through Josephson junctions [9]. The former case occurs in homogeneous systems by a decrease of critical temperature, TC with increase of disorder. HTSCs are examples of homogeneous systems and in recent years the rare-earth (RE) substitution studies in HTSCs have attracted considerable attention. It has been reported that different aliovalent substitutions or changes in the oxygen stoichiometry can effectively alter the concentration of carriers in the HTSC systems, resulting in a MIT [8,10–12]. MIT can also be caused by photo-induced laser treatment in which the photo-induced
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R. Shabna et al. / Journal of Alloys and Compounds 493 (2010) 11–16
electron–phonon anharmonicity plays a crucial role in the transition [13]. The interplay near the MIT between randomness, Coulomb repulsion and the pairing mechanism that creates superconductivity is a topic of intense debate. In two dimensions, this interplay becomes particularly interesting, since the lower critical dimension for both the localization and superconductivity is two. A number of previous studies of ultra thin film superconductors have established that increasing the disorder by increasing the sheet resistance results in the suppression of superconductivity in two dimensions [14]. Bi2 Sr2 CaCu2 O8 [Bi-2212] is a HTSC and the presence of Cu–O planes in this system, strongly suggests the presence of two dimensional (2D), physical and electronic properties which makes it suitable for the above investigations. So, in the present work, we report the effect of disorder and localization on the MIT and superconducting properties of Bi1.7 Pb0.4 Sr2 Ca1.1 Cu2.1 O8+ı [(Bi,Pb)2212] system which is a HTSC, through the substitution of a rare-earth, cerium (Ce) at its Sr site. Ce is substituted in this material over a wide range (0.2 ≤ x ≤ 1), to explore both the superconducting and insulating regions in the temperature doping phase diagram of (Bi,Pb)-2212 system. Here Pb is also substituted in the Bi-2212 system due to the established beneficial effects of Pb, like its role in the homogenization and stabilization of the Bi-2212 phase and also in increasing its TC , and therefore makes the system more useful for the above investigations [15,16]. Detailed evaluation of the structural and resistivity parameters of the insulating phases in Bi1.7 Pb0.4 Sr2−x Cex Ca1.1 Cu2.1 O8+ı system is also explored which provide an excellent insight and understanding about the electronic conduction and the variable range hopping (VRH) mechanism in this material. 2. Materials and methods Bi1.7 Pb0.4 Sr2−x Cex Ca1.1 Cu2.1 O8+ı (0.2 ≤ x ≤ 1) samples were prepared by solid state synthesis route, using high purity chemicals of Bi2 O3 , PbO, SrCO3 , CaCO3 , CuO and CeO2 (Aldrich >99.9%). Stoichiometric amounts of the ingredients were accurately weighed using an electronic balance (Mettler AE 240), thoroughly mixed and ground using an agate mortar and pestle, and then subjected to a three stage calcination process in air at temperatures, 800 ◦ C/15 h, 820 ◦ C/30 h, and 840 ◦ C/60 h with a heating rate of 3 ◦ C/min. Intermediate wet grinding was done between each stages of calcination. After calcination, the samples were pelletized using a cylindrical die of 12 mm diameter, under a force of 80 kN. The pellets were then heat treated at 885 ◦ C for 120 h (60 + 60) in two stages, with one intermediate re-pressing under the same stress. Phase analysis of the samples was done using X-ray diffraction (XRD) (Philips X’pert Pro) employing an X’celerator and monochromator at the diffracted beam side. Phase identification was performed using X’Pert High score software, in support with ICDD-PDF 2 database. Microstructural examinations of the samples were done using scanning electron microscopy (JEOL JSM 5600 LV). Elemental analyses of the samples were done using energy dispersive X-ray analysis attached to the SEM. The electrical transport properties of the samples from 64 K to 300 K were measured using the four probe method. A Lakeshore temperature controller (Model: 340) was used to accurately monitor the temperature.
Fig. 1. XRD pattern of samples after final stage sintering process.
that the solubility limit of Ce in (Bi,Pb)-2212 system is around, x = 0.4. The SEM micrographs of the fractured samples after the last stage sintering process are shown in Fig. 2. It is found that the grain morphology is not much affected by the substitution of Ce. All the samples contain long and flaky grains that characterize the (Bi,Pb)-2212 system. But with the increase in Ce content, presence of small, rounded secondary phase is also observed in samples with x > 0.6. The secondary phase and (Bi,Pb)-2212 grains were analyzed through EDAX and Fig. 3 shows the EDAX spectra of (Bi,Pb)-2212 grains of the pure and a typical Ce substituted (Bi,Pb)-2212 [Ce10] samples. Presence of Ce is detected in the (Bi,Pb)-2212 grains of Ce substituted samples with a corresponding reduction in Sr. This indicates that the Ce atoms are successfully substituted in place of Sr site of the (Bi,Pb)-2212 system. The relative concentration of Ce and Sr are evaluated as a function of the nominal doping value x and the results are shown in Table 1. From the EDAX analysis, it is identified that the rounded phase which is observed between the flaky grains of (Bi,Pb)-2212 system in the SEM micrographs corresponds to the CeO2 . This indicates that beyond the solubility limit, CeO2 remains as such in the system and this was already confirmed from the XRD pattern of the Ce10 sample. From the XRD patterns, the lattice parameters are calculated using the d values and (h k l) parameters by assuming an orthorhombic symmetry for (Bi,Pb)-2212. The variation of lattice parameters against actual Ce concentration is shown in Fig. 4 with an accuracy of (±0.002). The c axis length decreases with the dopant concentration. This decrease in c lattice parameter can arise due to (i) the increase in oxygen content of the system, (ii) the substitution of higher valence cation Ce4+ with an ionic radius smaller than that
3. Results and discussion The samples are labelled as Ce2, Ce4, Ce6, Ce8 and Ce10, initially with respect to the nominal x values (0.2, 0.4, 0.6, 0.8 and 1.0, respectively) and later on with respect to the actual Ce concentrations (0.19, 0.38, 0.56, 0.72 and 0.85, respectively), obtained from the EDAX analysis. The normalized XRD patterns of the samples after sintering at 855 ◦ C/120 h are shown in Fig. 1. In all samples, the major phase detected is (Bi,Pb)-2212. But from x = 0.6 onwards, some additional peaks are also observed along with the (Bi,Pb)-2212. By analyzing the patterns using X’pert high score software, it has been found that these peaks correspond to that of CeO2 [34-0394], as referred in the database. The absence of any Ce containing phase up to x = 0.4 shows
Table 1 Quantitative EDX results of cation stoichiometry of Ce substituted (Bi,Pb)-2212 grains (standardized with respect to Ca). Sample
Stoichiometry
(Bi,Pb)
Sr
Cu
Ce
Ce2
Initial From EDX Initial From EDX Initial From EDX Initial From EDX Initial From EDX
2.10 2.00 2.10 1.99 2.10 2.00 2.10 1.98 2.10 1.99
1.80 1.78 1.60 1.59 1.40 1.38 1.20 1.16 1.00 0.97
2.10 2.00 2.10 1.99 2.10 2.00 2.10 2.00 2.10 2.00
0.20 0.19 0.40 0.38 0.60 0.56 0.80 0.72 1.00 0.85
Ce4 Ce6 Ce8 Ce10
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Fig. 2. SEM micrographs of fractured surfaces of Ce substituted (Bi,Pb)-2212 samples.
of Sr2+ . The a axis length increases up to Ce6. This can be ascribed to the change in the planar Cu–O bond distance due to hole compensation in the system. The b lattice parameter gradually decreases in all samples. From Ce6 onwards, the a axis parameter decreases and the difference between a and b lattice parameters becomes very small. This indicates the structural change of the system from the orthorhombic symmetry to the tetragonal. In order to show the gross feature of the successive phase changes of the system with Ce concentration, the temperature dependence of resistivity of the samples is given in Fig. 5. The resistivity changes systematically with doping which reflects the well controlled stoichiometry of these samples. The sample Ce2 is a superconductor with TC -onset of 83.38 K. The temperature coefficient of resistivity of the Ce2 sample is positive for temperatures above TC with (d/dt) > 0, and this shows that Ce2 is metallic in the normal state. But, when the Ce concentration is increased beyond 0.2, the normal state resistivity of the samples increases sharply
with the doping concentration, x and no superconducting transition could be observed. All the samples from Ce4 to Ce10 show the negative temperature coefficient of resistivity with (d/dt) < 0, indicating the insulating behavior. This indicates that the metal to insulator transition takes place in between x = 0.2 and x = 0.4. From the resistivity analysis, we found that none of the insulating phases satisfy either the thermally activated conductivity [ln vs 1/T behavior] or the mechanism of hopping conductivity in a system of localized electrons with long range coulomb interaction (ln vs (1/T)1/2 ). However, they all satisfy the Mott’s variable range hopping equation (VRH): (T ) = 0 exp
T n 0
T
,
(1)
which in general indicates conduction by polarons [17]. Here 0 and T0 are constants characterizing a given material. The exponent ‘n’ in the above equation depends crucially on the behavior of the
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R. Shabna et al. / Journal of Alloys and Compounds 493 (2010) 11–16 Table 2 Hopping parameters. Sample
1/n
Localization length (Å)
R (Å)
T0 (K)
Ce4 Ce6 Ce8 Ce10
3 3 4 4
0.008 0.0008 20 17.6
0.01 0.001 21.29 18.14
2.96 285 1790 2990
the Bi-2212 system on a flat band along the –M–Z direction. They report that the FL is pinned close to a VHS in Bi-2212 system. For an (E–EF ) dependence of DOS on the energy [20], n=
m+1 , m+d+1
(2)
where ‘m’ is the constant representing the behavior of DOS and ‘d’ is the dimensionality of the hopping process. For VRH in two dimension, d = 2 and for VRH in three dimension, d = 3. When the DOS remains finite at the FL, m = 0 and the value of n becomes either 1/3 or 1/4 depending on whether the hopping is in two or three dimensions, respectively. We fit the –T curve of the insulating samples (Ce4 to Ce10) to Eq. (1) and Fig. 6 shows the best fit [ln vs (1/T)n ] of the samples. It is found that the resistivity data of the insulating samples Ce4, and Ce6 fit well to the Eq. (1) with n = 1/3 while that for Ce8 and Ce10 with n = 1/4. This suggests that the electronic conduction in samples Ce4 and Ce6 take place by the two dimensional (2D) variable range hopping mechanism and that in Ce8 and Ce10 by the three dimensional (3D) VRH. Moreover, the systematic increase in normal state resistivity of samples with the Ce content also shows that the system enters the variable range hopping regime, indicating a metal to insulator transition in the system. The parameters used for fitting are given in Table 2. The system exhibits a dimensionality crossover, while passing from Ce6 to Ce8. The characteristic temperature T0 is related to the N(EF ), Boltzmann constant (KB ) and to the radius of the localized states or the localization length (˛) by the following relations. In 2D: Fig. 3. EDAX patterns of (Bi,Pb)-2212 grains of pure and Ce10 sample.
density of states (DOS) with energy (E) near the Fermi level (FL) and on the dimensionality of the hopping process. The Van Hove singularity (VHS) provides a paradigm for the study of the role of peaks in the DOS on electronic properties. The Van Hove scenario is based on the assumption that in HTSC, the Fermi level lies close to such a singularity [18]. Dessau et al. [19] provided a report for
T0 =
27 , 4˛2 KB N(EF )
and In 3D: T0 =
16 . [˛3 KB N(EF )]
(4)
At any temperature, the transition probability for the occurrence of a hop to a state at a distance R from the initial state and separated by an energy W is given by
p∼ exp −2aR −
Fig. 4. Variation of lattice parameters with Ce content.
(3)
W kT
.
(5)
The term exp(−2aR) denotes the probability of finding an electron at a distance R from its initial state and a is the inverse localization length [˛−1 ] [22]. Fisher et al. [21] measured specific heat in the Bi-2:2:1:2 system and obtained a value of 11 mJ mol−1 K−2 which corresponds to N(EF )∼1.1 states/eV Cu spin. We have estimated the localization length and most probable hopping distance (R) [22] of the insulating samples, by making use of Eqs. (3)–(5). The values of R given in Table 2 were estimated at temperatures corresponding to T < T0 /27 (for samples Ce4 and Ce6) and T < T0 /50 (for samples Ce8 and Ce10) because the temperature range where the localization length is lower than the most probable hopping distance is T < T0 /50 for VRH in 3D and T < T0 /27 for VRH in 2D. Since, it is clear from the table that the hopping length of the insulating Ce samples in the said temperature range is larger than the localization length, we conclude that our interpretation of the resistivity data are in agreement
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Fig. 5. Variation of resistivity of the samples with temperature.
with the conditions for Mott VRH behavior. It is found that within a particular dimension, the localization length decreases with x. This shows that the substituted Ce atoms localize the holes in the system and lead to the observed MIT. The VRH mechanism of conduction is best described at low temperatures where the thermal energy for the charge transport is insufficient to excite the carriers across the mobility gap. In such a system, contribution to the electrical conduction is possible only by the hopping process, mediated by phonons from one filled state to an empty state. Crystalline materials generally exhibit this phenomenon due to the absence of long range order. Mott has experimentally verified the VRH mechanism
at low temperatures, in a class of systems and treatise his observations. Such trends have been reported in the insulating phases of high-TC materials too, like the GdBa2 Cu3−x Crx O7+ı system [10]. The XRD pattern, lattice parameter calculations and elemental analysis have shown that the substituted Ce atoms are successfully entering into the crystal structure of (Bi,Pb)-2212 system. When Ce is substituted in place of Sr, each replacement compensates two holes and decreases the hole concentration in the Cu–O planes of (Bi,Pb)-2212 system. Since, Ce possess different charge, ionic radius and electronic structure in comparison with Sr, the replacement of each Sr2+ by Ce4+ in (Bi,Pb)-2212 leads to
Fig. 6. Best fit of ln vs (1/T(K))1/n [EXP denotes the experimental data and GEN denotes generated data].
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disorder in the system along with the electronic/chemical inhomogeneity of the charge reservoir (Bi–O) layers. The intrinsic defects produced by the substitution of Ce in (Bi,Pb)-2212 also play a decisive role in the electronic structure of the system because disorder in condensed matter is generally associated with the presence of zero-to-three dimensional defects in crystalline and semi crystalline materials, impurities and distortions coming from the meta-stability of the structures. It has been reported that the small changes in the composition or structure of cuprates by doping provokes both inter-grain and intra-grain disorder due to crystalline structural defects and grain boundary defects, respectively [5,6]. Hence, superconductivity is suppressed by either inter-grain disorder or intra-grain disorder. The localization length which represents the exponential decay of the electronic wave functions at large distances depends on the extent of disorder present in a system. It is interesting to note that from Ce4 to Ce10, the localization length decreases in a systematic way. This shows that disorder in the system increases with Ce content. The disorder tends to slow down or localize a carrier at the lattice sites, resulting in the formation of polarons [23]. Moreover, it breaks the symmetry of the ordered system at the molecular scale and consequently affects the extended states of valence and conduction bands forming the localized states [1,17] which concentrate in band tails. As the conduction process is very dependent on the spatial and energy densities of these localized states, the energy required for the conduction process increases with increase in disorder. Since, the local activation energy [24] in a disordered system is calculated from the slope of the ln vs (1/T) curve, the systematic increase in T0 values of samples with respect to x implies that the disorder in the (Bi,Pb)-2212 system increases with Ce concentration. The metal to insulator transition usually takes place when the density of carriers decreases; the latter necessarily leading to an increase of the effective strength of e–e interaction. On the other hand, the decrease in the carrier density is accompanied by an increase in the effective disorder, particularly, due to the weakening of the screening of potential fluctuations. Thus, the properties of the samples are strongly influenced by both the electronic interaction and randomness. Hence, in the present system, both the Coulomb correlations (Mott transition) and disorder (Anderson transition) are the driving forces behind the MIT. Most existing theories are not able to combine these two fundamental processes within the same framework, and this conceptual difficulty has provided the essential pitfall in the understanding of the MIT. At higher doping levels (x > 0.2), supplied carriers tend to be localized at low temperatures as indicated by the variable range hopping type resistivity behavior and this disorder induced transition leads to a localization of states in the vicinity of Fermi level and in a finite density of states at the Fermi level. The localized electronic states are randomly distributed in energy as well as in space, with a uniform distribution given by N(EF ), which is the density of states per unit volume per unit energy. The conduction takes place by the variable range hoping mechanism which involves hopping of carriers between the various localized states. Thus the satisfactory
agreement between the theory and the experimental data implies that in the Ce substituted (Bi,Pb)-2212 system, the depletion of charge carriers induces disorder, leads to localization of states in the vicinity of Fermi level and thus drives a MIT. 4. Conclusions In summary, we have investigated the metal to insulator transition and charge carrier localization effects in (Bi,Pb)-2212 superconductor through Ce substitution. The TC suppression is due to the reduction of hole concentration in the Cu–O planes of (Bi,Pb)-2212 system and the electronic transport in the insulating samples can be explained using the Mott’s variable range hopping mechanism. A Mott–Anderson MIT takes place at 0.2 < x ≤ 0.4 due to depletion and disorder induced localization of charge carriers. Acknowledgements The authors, Mrs. R. Shabna, Mr. P.M. Sarun and Mr. S. Vinu acknowledge the KSCSTE, CSIR and U. G. C. India, respectively, for providing their Senior Research Fellowships. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
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