- Email: [email protected]
Evolution of the resistivity of single-layer Bi2Sr1.6La0.4CuOy thin films with doping and phase diagram
Physica C 351 (2001) 163±168
www.elsevier.nl/locate/physc
Evolution of the resistivity of single-layer Bi2Sr1:6La0:4CuOy thin ®lms with doping and phase diagram Z. Konstantinovic, Z.Z. Li, H. Ray * Laboratoire de Physique des Solides, B^ at 510, Universit e Paris-Sud, Centre Universitaire, 91405 Orsay C edex, France Received 11 August 2000; accepted 1 November 2000
Abstract The temperature dependence of the in-plane resistivity q(T) is measured on epitaxial c-axis oriented single-layer Bi2 Sr1:6 La0:4 CuOy thin ®lms at various oxygen concentrations. By successive annealing treatments, the oxygen content of the same ®lm is changed from maximally overdoped to strongly underdoped non-superconducting state, passing through the optimal state with Tc max 30 K. The underdoped states show a downturn of the resistivity from the high T-linear behavior below a characteristic temperature T*, signature of the pseudogap eect. T* appears near optimally doped state and increases sharply with decreasing carrier concentration. Two other characteristic temperatures are observed in q(T) for underdoped states: the temperature TI of the in¯ection point in q(T) (TI 0:5T ) and the temperature TM corresponding to the onset of localization eects. A phase diagram T versus doping is established. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.72.Hs; 74.76.Bz; 74.25.Fy; 74.62.Dh Keywords: Bi-based cuprates; High-Tc ®lms; Electric conductivity; Doping
1. Introduction The evolution with hole doping of the normal state electronic properties of cuprates is considered to be a principal line of research for understanding the underlying mechanism of high-temperature superconductivity (HTSC). Depending on temperature and doping, the electronic properties change from those of an antiferromagnetic insulator to those of a metal, what motivates detailed investigations of the rich phase diagram of cuprates.
* Corresponding author. Tel.: +33-1-69155338; fax: +33-1691-56086. E-mail address: ra[email protected] (H. Ray).
One striking phenomena is the pseudogap which opens in the electronic excitations [1±8]. This eect, observed in underdoped HTSC, has been the center of investigations for many years without consensus about its nature and its relation with superconductivity. The pseudogap eect was ®rst observed in CuO2 bilayer YBa2 Cu3 O6x (YBCO) [9] and single-layer La2 x Srx CuO4 (LSCO) [10] cuprates, although certain dierences between these two materials [11] have lead to controversial conclusions regarding the existence of this eect in systems with one CuO2 plane per cell [12]. Recently, the existence of the pseudogap was con®rmed in single-layer systems by NMR measurements on HgBa2 CuO4d (HgBaCuO) [13] and by photoemission measurements
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 0 ) 0 1 7 3 3 - 0
164
Z. Konstantinovic et al. / Physica C 351 (2001) 163±168
on Bi2 Sr2 x Lax CuOy (BSLCO) [14]. More recently, a pseudogap eect was reported from transport measurements on single-layer Bi2 Sr2 x Lax CuO6 crystals, where the carrier concentration was changed by changing La doping x [15]. On the other hand, at low doping level and lowtemperature localization eects compete with the observed pseudogap eect. Onset of localization eects was investigated recently by suppressing superconductivity with 60-T pulsed magnetic ®elds [16,17]. It was reported that the metal±insulator (MI) crossover takes place at optimum doping in LSCO compound, i.e. at the same doping where pseudogap opens [16]. However, recent results in BSLCO indicate that the MI crossover is not universal for all cuprates [17]. The other way for inducing a MI crossover is by decreasing the carrier concentration or by increasing disorder by chemical substitution [18±20]. Here, we present results obtained by measuring the in-plane resistivity of Bi2 Sr1:6 La0:4 CuOy (Bi(La)-2201) thin ®lms as a function of temperature, over a wide range of carrier concentration. The oxygen content is changed on the same ®lm by annealing treatments, which permitted to investigate almost all the phase diagram, from strongly overdoped to strongly underdoped. By reducing the carrier concentration, the superconductivity is suppressed and the MI crossover is induced. 2. Experimental details The c-axis oriented epitaxial Bi2 Sr1:6 La0:4 CuOy thin ®lms, with thickness between 1000 and 2000 are grown in situ by RF magnetron sputtering A, on SrTiO3 substrates [21]. The ®lms are chemically patterned and equipped with gold sputtered contact pads. The temperature dependence of the in-plane resistivity is measured at dierent oxygen doping levels using a standard four-probe dc method. The oxygen content of a single sample is changed by repeated annealing treatments in a controlled atmosphere going from the maximally overdoped state (Tc (R 0) 17 K) to the strongly underdoped non-superconducting states (Tc 0). The change in Hall coecient, measured at room temperature in a magnetic ®eld of 1 T, con®rms
the change in carrier concentration after each annealing procedure. The transport properties of states obtained in this way are reproducible. The partial substitution of Sr by La increases the optimum Tc max from 18 K for pure Bi2 Sr2 CuOy (Bi2201) to 30 K for Bi2 Sr1:6 La0:4 CuOy , which also increases the width of the underdoped region. The number of holes per Cu, p, is calculated from the empirical parabolic function Tc =Tc max 1 82:6 2 p 0:16 [22]. 3. Experimental results Fig. 1 shows three typical sets of curves representing the temperature dependence of q(T) obtained on the same ®lm in (a) the overdoped, (b) the underdoped and (c) the strongly underdoped non-superconducting region (Tc 0). The conductivity at room temperature decreases monotonically with decreasing oxygen content in the sample and it has been used to characterize the carrier concentration. It is to be noted that while in pure Bi-2201 ®lms the non-superconducting metallic state (Tc 0) can be reached [23], the minimal critical temperature value of our Bi(La)-2201 ®lms is Tc (R 0) 17 K. In the overdoped region (Fig. 1(a)), q(T) develops a positive curvature and can be described by the phenomenological law q T q0 aT m with m mmax 1:3 for the maximally overdoped state. It appears that mmax has the same characteristic value for all overdoped Bi-2201 [23] and is lower than in LSCO and Tl2 Ba2 CuO6d (Tl-2201) compounds (mmax 1:5 and 1.8 respectively [24,25]). This low mmax value can be related to the low Tc max value in Bi(La)2201 compared to those in the other two singlelayer compounds (Tc max 35 and 85 K in LSCO and Tl-2201 respectively). The exponent m decreases with decreasing doping down to 1, which corresponds to the optimally doped state (inset of the same ®gure). The resistivity at optimal doping shows a T-linear behavior above 55 K (top curve in Fig. 1(a) and bottom curve in Fig. 1(b)). In the underdoped states (Fig. 1(b)), q(T) deviates downwards from this linear high-T behavior below T*, attributed to the pseudogap opening [9]. Another characteristic temperature corresponding to
Z. Konstantinovic et al. / Physica C 351 (2001) 163±168
165
Fig. 2. Doping dependence of (a) the Hall number nH and of (b) the c-axis lattice constant, c0 (the dashed line is a guide to the eye) for the same ®lm as in Fig. 1. The upper horizontal axis indicates the normalized conductivity r=rop 300 K .
Fig. 1. The temperature dependence of the in-plane resistivity in the (a) overdoped region, (b) underdoped region, and (c) strongly underdoped region with Tc 0. The increase of the oxygen concentration y is indicated by the right long vertical arrow. Other characteristic temperatures indicated by dierent type of arrows are explained in the text.
a change of curvature in q(T), labeled TI , is pointed in Fig. 1(b). Additional removing of oxygen out of the ®lm leads to the loss of superconductivity and the occurrence of insulating behavior starting at the temperature TM , where q(T) is minimum (Fig. 1(c)). All above characteristic behaviors are also found in bilayer Bi-2212 thin ®lms and a comparison between both phases in the pseudogap region is done in Ref. [26,28]. Fig. 2a shows the doping dependence of the Hall number nH , measured at 300 K, for the same ®lm as in Fig. 1. The upper horizontal axis gives also the conductivity at room temperature normalized by
its value at optimally doped state r=rop 300 K . The critical temperature Tc is also a parabolic function of r=rop 300 K , parameter previously used to characterize the oxygen doping in the case of Bi2 Sr2 CaCu2 Oy (Bi-2212) ®lms [27]. This quantity is used here in the same manner in order to parameterize the doping of the strongly underdoped states (Tc 0) where the above parabolic function cannot be applied (see further Fig. 3). The decrease of nH with reducing carrier concentration indicates a total decrease of carriers by a factor of the order of 4, which is in good agreement with the corresponding decrease of p from 0.24 to 0.06. Moreover, it is shown that nH varies nearly linearly with p and r=rop 300 K which con®rms that the latter can be used to characterize doping. Another quantity which allows to characterize the doping level is the c-axis lattice constant, c0 , obtained from X-ray diraction spectra. The doping dependence of c0 for some characteristic states for the same ®lm
166
Z. Konstantinovic et al. / Physica C 351 (2001) 163±168
Fig. 3. (a) Plot of q T q0 =aT versus T for states near optimal doping (overdoped OD, optimally doped OP and underdoped UD) with arrows indicating the beginning of the deviation from T-linear behavior at T*. (b) dq=dT versus T for some doping states in the superconducting region with bold arrows pointing to the maximum of the curves dq=dT at TI (in¯ection point) and light arrows pointing to T*. (c) Logarithmic plot of q(T) for strongly underdoped states. Arrows show the beginning of insulating behaviors (minimum of q(T)) at TM . The right vertical axis shows (kF l) 1 values evaluated from the resistance per CuO2 layer (see text).
is shown in Fig. 2(b): c0 decreases monotonically with increasing p. In order to show the determination of the temperature T*, where resistivity displays a downturn from high-T-linear behavior, the quantity q T q0 =aT is plotted versus T for optimal and neighboring doping states (Fig. 3(a)). The parameters q0 and a are obtained from the linear ®t to the high temperature part of q(T). The values of T*, indicated by arrows in Fig. 3(a), coincide with the low-temperature limit of the constant part of the ®rst derivative dq=dT (dashed line in Fig. 3(b)) which con®rms as-determined values of T*. One typical overdoped state is also represented in Fig. 3(a) to underline its dierent behavior (upward deviation). The ®rst derivative of the overdoped states is naturally described by dq=dT amT m 1 (solid line in Fig. 3(b)).
Another characteristic temperature TI is de®ned by the maximum value of the ®rst derivative dq=dT in the underdoped region (arrows pointing downward in Fig. 3(b)). This in¯ection point coordinate TI has the same doping dependence as T*, and they are related by: TI T =2 [28], relation earlier found in YBCO [29] and BSLCO [30] compounds. This observation has permitted to determine T* values when they exceed room temperature. For strongly underdoped states, the temperature TM below which the insulating behavior begins is extracted from the minimum of the resistivity versus temperature (Fig. 3(c)). The insulating behavior is a manifestation of localization eects, which suppress the observed pseudogap eect. Moreover, the crossover from superconducting to insulating behavior occurs at qSI 0 1:1 0:1 mX cm. This value corresponds to a resistance per square per CuO2 plane qSI 0 = c0 =2 9 kX, where c0 =2 is the interlayer distance (see Fig. 3(c)). The normalized resistivity values in (kF l) 1 units are plotted on the right vertical axis (same 2 ®gure), given by qSI 0 = c0 =2 h=e = kF l, where kF is the Fermi wave vector and l the mean free path between scattering events. The observed crossover value qSI 0 = c0 =2 is higher than that of conventional 2D superconductors, equal to h= 2e2 6:5 kX kF l 4 [31,32]. However, it is in very good agreement with the value estimated from h=0:69 2e2 9:4 kX, established for 2D disordered systems with Coulomb interactions [33]. This comparison suggests that, although disorder plays an important role in these materials, one cannot neglect Coulomb interactions between carriers, which increase with the decreasing carrier concentration, shown in Fig. 2(a). Note also in Fig. 3(c) that a log 1=T behavior of q(T) is only observed for the state close to the MI transition (third state from bottom curve) and for T 6 20 K. This insulating behavior was previously observed in both underdoped superconducting LSCO [16] and BSLCO [17] under a 60 T magnetic ®eld. However, q(T) for all others states [34] are in good agreement with a thermally activated conduction behavior just below TM and with 2D Mott variable-range hopping at lower temperature observed in LSCO system and associated
Z. Konstantinovic et al. / Physica C 351 (2001) 163±168
167
with phonon assisted impurity scattering [35]. The observed logarithmic behavior close to the superconducting±insulating transition and then 2D Mott variable-range hopping at low temperature are also in agreement with previous results on underdoped non-superconducting Bi-2201 single crystals [36]. 4. Phase diagram The doping dependence of all characteristic temperatures introduced above are shown in Fig. 4 for two dierent thin ®lms (solid and open symbols). All three temperatures, T*, TI and TM , increase with decreasing carrier concentrations and their doping dependence is the same for all examined samples. Note also the parabolic behavior of Tc as a function of normalized conductivity r=rop 300 K , without suppression of the critical temperature near p 1=8 (``1/8'' anomaly), as observed previously in La2 x Bax CuO4 compound [37] and recently mentioned in BSLCO single crystals [38]. The values of T* in Bi(La)-2201 are of the same order of magnitude as in the case of BSLCO single crystals compared for the same ratio Tc =Tc max [15] and smaller than the values reported in LSCO compounds [10]. The change in slope of TI (p) coinciding with the beginning of localization eects could induce a systematic error in T (p) 2TI (p) behavior in the strongly underdoped region (T* values deduced from TI could be overestimated). The doping dependence of T*(p) around optimally doped states presents a steep decrease towards the curve Tc (p). By extrapolating T*(p) to zero, we ®nd that T 0 for p 0:17 0:01 hole per Cu, which is considered as a possible quantum critical point [39,40]. The variation of the third characteristic temperature, TM (p), provides the low-temperature boundary of the pseudogap region, as it was proposed theoretically earlier [39]. The extrapolated value at zero temperature of TM (p) lies well inside the underdoped regime for BSLCO (p 0:07 0:01) which is in good agreement with the MI boundary deduced from q(T) behavior of BSLCO single crystal under 60 T [17]. The only dierence between the two results arises from dierent eval-
Fig. 4. Phase diagram of Bi2 Sr1:6 La0:4 CuOy ®lms as a function of the parameter r=rop 300 K (see text). Some characteristic p values are indicated on the upper horizontal axis. Marks 1(a), 1(b) and 1(c) indicate the corresponding regions of in-plane resistivities (see Fig. 1). The open symbols correspond to the results obtained for the ®lm of Fig. 1, while the solid symbols are for another sample. The hatched area indicates the pseudogap region (PG). T*, TM and TI are de®ned in Figs. 1 and 3.
uated hole concentration values, but still it appears that the MI boundary cut Tc (p) at the same ratio Tc =Tc max 0:4. The situation is quite dierent in LSCO compounds, where the onset of the localization behavior extends up to optimum doping [16]. So the low T beginning of the MI boundary in Bi(La)-2201 deeply in the underdoped region indicates that it depends on the cuprate family and it does not show a visible link with pseudogap eect occurring near optimum doping. Finally, a schematic phase diagram was proposed in Ref. [41]. There the pseudogap phase is associated with 1D stripe formation, while at the MI boundary disorder disrupts the 1D stripes restoring a 2D regime for transport with
168
Z. Konstantinovic et al. / Physica C 351 (2001) 163±168
q T log 1=T [42]. Although this insulating behavior log (1/T) that we have seen in one state close the MI crossover might be associated with low dimensionality imposed by charge con®nement into stripes as indicated in Ref. [17], it is dicult to understand why this behavior is observed in just a very narrow doping window. Moreover, until now there is no direct evidence, as in neutron scattering data on LSCO compound [43], of the existence of the stripe formation in Bi(La)-2201 which might help to clarify this issue. 5. Summary To summarize, we have studied the evolution of the temperature dependence of the in-plane resistivity over a wide range of doping levels, from overdoped to strongly underdoped. We show that the behavior of the resistivity changes strongly with the oxygen content in the ®lm, from metallic to semiconducting behavior. From this analysis, we have established a very detailed unique phase diagram of the single-layer Bi2 Sr1:6 La0:4 CuOy phase. The upper boundary of the pseudogap region is given by the temperature T*(p) and the lower boundary by the temperature TM (p), where localization eects occur. The extrapolation to zero of T*(p) around p 0:17 may possibly indicate the existence of a quantum critical point. Moreover, our data indicate that there is no obvious relation between the onset of localization eects and the pseudogap opening occurring around optimal doping. References [1] [2] [3] [4] [5] [6]
R.E. Walstedt, et al., Phys. Rev. B 41 (1990) 9574. M. Takigawa, et al., Phys. Rev. B 43 (1991) 247. H. Alloul, et al., Phys. Rev. Lett. 67 (1991) 3140. J. Rossat-Mignod, et al., Physica B 169 (1991) 58. J.M. Tranquada, et al., Phys. Rev. B 46 (1992) 5561. C.C. Homes, et al., Phys. Rev. Lett. 71 (1993) 1645.
[7] J.W. Loram, et al., Phys. Rev. Lett. 71 (1993) 1740. [8] T. Timusk, B. Statt, Rep. Prog. Phys. 62 (1999) 61. [9] T. Ito, K. Takenaka, S. Uchida, Phys. Rev. Lett. 70 (1993) 3995. [10] B. Batlogg, et al., Physica C 235-240 (1994) 130. [11] D.N. Basov, H.A. Mook, B. Dabrowski, T. Timusk, Phys. Rev. B 52 (1995) 13141. [12] B.L. Altshuler, L.B. Ioe, A.J. Millis, Phys. Rev. B 53 (1996) 415. [13] J. Bobro, et al., Phys. Rev. Lett. 78 (1997) 3757. [14] J.M. Harris, et al., Phys. Rev. Lett. 79 (1997) 143. [15] Y. Ando, T. Murayama, S. Ono, J. Low Temp. Phys. 117 (1999) 1117. [16] G.S. Boebinger, et al., Phys. Rev. Lett. 77 (1996) 5417. [17] S. Ono, et al., Phys. Rev. Lett. 85 (2000) 638. [18] Y. Iye, Physical Properties of High Temperature Superconductors III, in: D.M. Ginsberg (Ed.), World Scienti®c, Singapore, 1991. [19] Y. Fukuzumi, K. Mizuhashi, K. Takenaka, S. Uchida, Phys. Rev. Lett. 76 (1996) 684. [20] D.J.C. Walker, A.P. Mackenzie, J.R. Cooper, Phys. Rev. B 51 (1995) 15653. [21] Z.Z. Li, H. Ray, to be published. [22] M.R. Presland, et al., Physica C 176 (1991) 95. [23] H. Ri®, Thesis, University of Orsay (1996), unpublished. [24] Y. Kubo, et al., Phys. Rev. B 43 (1991) 7875. [25] H. Takagi, et al., Phys. Rev. Lett. 69 (1992) 2975. [26] Z. Konstantinovic, Z.Z. Li, H. Ray, in preparation. [27] Z. Konstantinovic, Z.Z. Li, H. Ray, Physica B 259±261 (1999) 567. [28] Z. Konstantinovic, Z.Z. Li, H. Ray, Physica C 341±348 (2000) 859. [29] B. Wuyts, V.V. Moshchalkov, Y. Bruynseraede, Phys. Rev. B 53 (1996) 9418. [30] Y. Ando, T. Murayama, Phys. Rev. B 60 (1999) 6991. [31] T. Pang, Phys. Rev. Lett. 62 (1989) 2176. [32] M.P.A. Fisher, G. Grinstein, S.M. Girvin, Phys. Rev. Lett. 64 (1990) 587. [33] I. Herbut, Phys. Rev. Lett. 81 (1998) 3916. [34] Z. Konstantinovic, Z.Z. Li, H. Ray, unpublished. [35] E. Lai, R.J. Gooding, Phys. Rev. B 57 (1998) 1498. [36] A.T. Fiory, et al., Phys. Rev. B 41 (1990) 2627. [37] A.R. Moodenbaugh, et al., Phys. Rev. B 38 (1988) 4596. [38] W.L. Yang, H.H. Wen, Z.X. Zhao, Phys. Rev. B 62 (2000) 1361. [39] C.M. Varma, Phys. Rev. B 55 (1997) 14554. [40] S. Sachdev, Physics World, April (1999) 33. [41] V.V. Moshchalkov, L. Trappeniers, J. Vanacken, J. Low Temp. Phys. 117 (1999) 1283. [42] L. Trappeniers, et al., J. Low Temp. Phys. 117 (1999) 681. [43] K. Yamada, et al., Phys. Rev. B 57 (1998) 6165.
www.elsevier.nl/locate/physc
Evolution of the resistivity of single-layer Bi2Sr1:6La0:4CuOy thin ®lms with doping and phase diagram Z. Konstantinovic, Z.Z. Li, H. Ray * Laboratoire de Physique des Solides, B^ at 510, Universit e Paris-Sud, Centre Universitaire, 91405 Orsay C edex, France Received 11 August 2000; accepted 1 November 2000
Abstract The temperature dependence of the in-plane resistivity q(T) is measured on epitaxial c-axis oriented single-layer Bi2 Sr1:6 La0:4 CuOy thin ®lms at various oxygen concentrations. By successive annealing treatments, the oxygen content of the same ®lm is changed from maximally overdoped to strongly underdoped non-superconducting state, passing through the optimal state with Tc max 30 K. The underdoped states show a downturn of the resistivity from the high T-linear behavior below a characteristic temperature T*, signature of the pseudogap eect. T* appears near optimally doped state and increases sharply with decreasing carrier concentration. Two other characteristic temperatures are observed in q(T) for underdoped states: the temperature TI of the in¯ection point in q(T) (TI 0:5T ) and the temperature TM corresponding to the onset of localization eects. A phase diagram T versus doping is established. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.72.Hs; 74.76.Bz; 74.25.Fy; 74.62.Dh Keywords: Bi-based cuprates; High-Tc ®lms; Electric conductivity; Doping
1. Introduction The evolution with hole doping of the normal state electronic properties of cuprates is considered to be a principal line of research for understanding the underlying mechanism of high-temperature superconductivity (HTSC). Depending on temperature and doping, the electronic properties change from those of an antiferromagnetic insulator to those of a metal, what motivates detailed investigations of the rich phase diagram of cuprates.
* Corresponding author. Tel.: +33-1-69155338; fax: +33-1691-56086. E-mail address: ra[email protected] (H. Ray).
One striking phenomena is the pseudogap which opens in the electronic excitations [1±8]. This eect, observed in underdoped HTSC, has been the center of investigations for many years without consensus about its nature and its relation with superconductivity. The pseudogap eect was ®rst observed in CuO2 bilayer YBa2 Cu3 O6x (YBCO) [9] and single-layer La2 x Srx CuO4 (LSCO) [10] cuprates, although certain dierences between these two materials [11] have lead to controversial conclusions regarding the existence of this eect in systems with one CuO2 plane per cell [12]. Recently, the existence of the pseudogap was con®rmed in single-layer systems by NMR measurements on HgBa2 CuO4d (HgBaCuO) [13] and by photoemission measurements
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 0 ) 0 1 7 3 3 - 0
164
Z. Konstantinovic et al. / Physica C 351 (2001) 163±168
on Bi2 Sr2 x Lax CuOy (BSLCO) [14]. More recently, a pseudogap eect was reported from transport measurements on single-layer Bi2 Sr2 x Lax CuO6 crystals, where the carrier concentration was changed by changing La doping x [15]. On the other hand, at low doping level and lowtemperature localization eects compete with the observed pseudogap eect. Onset of localization eects was investigated recently by suppressing superconductivity with 60-T pulsed magnetic ®elds [16,17]. It was reported that the metal±insulator (MI) crossover takes place at optimum doping in LSCO compound, i.e. at the same doping where pseudogap opens [16]. However, recent results in BSLCO indicate that the MI crossover is not universal for all cuprates [17]. The other way for inducing a MI crossover is by decreasing the carrier concentration or by increasing disorder by chemical substitution [18±20]. Here, we present results obtained by measuring the in-plane resistivity of Bi2 Sr1:6 La0:4 CuOy (Bi(La)-2201) thin ®lms as a function of temperature, over a wide range of carrier concentration. The oxygen content is changed on the same ®lm by annealing treatments, which permitted to investigate almost all the phase diagram, from strongly overdoped to strongly underdoped. By reducing the carrier concentration, the superconductivity is suppressed and the MI crossover is induced. 2. Experimental details The c-axis oriented epitaxial Bi2 Sr1:6 La0:4 CuOy thin ®lms, with thickness between 1000 and 2000 are grown in situ by RF magnetron sputtering A, on SrTiO3 substrates [21]. The ®lms are chemically patterned and equipped with gold sputtered contact pads. The temperature dependence of the in-plane resistivity is measured at dierent oxygen doping levels using a standard four-probe dc method. The oxygen content of a single sample is changed by repeated annealing treatments in a controlled atmosphere going from the maximally overdoped state (Tc (R 0) 17 K) to the strongly underdoped non-superconducting states (Tc 0). The change in Hall coecient, measured at room temperature in a magnetic ®eld of 1 T, con®rms
the change in carrier concentration after each annealing procedure. The transport properties of states obtained in this way are reproducible. The partial substitution of Sr by La increases the optimum Tc max from 18 K for pure Bi2 Sr2 CuOy (Bi2201) to 30 K for Bi2 Sr1:6 La0:4 CuOy , which also increases the width of the underdoped region. The number of holes per Cu, p, is calculated from the empirical parabolic function Tc =Tc max 1 82:6 2 p 0:16 [22]. 3. Experimental results Fig. 1 shows three typical sets of curves representing the temperature dependence of q(T) obtained on the same ®lm in (a) the overdoped, (b) the underdoped and (c) the strongly underdoped non-superconducting region (Tc 0). The conductivity at room temperature decreases monotonically with decreasing oxygen content in the sample and it has been used to characterize the carrier concentration. It is to be noted that while in pure Bi-2201 ®lms the non-superconducting metallic state (Tc 0) can be reached [23], the minimal critical temperature value of our Bi(La)-2201 ®lms is Tc (R 0) 17 K. In the overdoped region (Fig. 1(a)), q(T) develops a positive curvature and can be described by the phenomenological law q T q0 aT m with m mmax 1:3 for the maximally overdoped state. It appears that mmax has the same characteristic value for all overdoped Bi-2201 [23] and is lower than in LSCO and Tl2 Ba2 CuO6d (Tl-2201) compounds (mmax 1:5 and 1.8 respectively [24,25]). This low mmax value can be related to the low Tc max value in Bi(La)2201 compared to those in the other two singlelayer compounds (Tc max 35 and 85 K in LSCO and Tl-2201 respectively). The exponent m decreases with decreasing doping down to 1, which corresponds to the optimally doped state (inset of the same ®gure). The resistivity at optimal doping shows a T-linear behavior above 55 K (top curve in Fig. 1(a) and bottom curve in Fig. 1(b)). In the underdoped states (Fig. 1(b)), q(T) deviates downwards from this linear high-T behavior below T*, attributed to the pseudogap opening [9]. Another characteristic temperature corresponding to
Z. Konstantinovic et al. / Physica C 351 (2001) 163±168
165
Fig. 2. Doping dependence of (a) the Hall number nH and of (b) the c-axis lattice constant, c0 (the dashed line is a guide to the eye) for the same ®lm as in Fig. 1. The upper horizontal axis indicates the normalized conductivity r=rop 300 K .
Fig. 1. The temperature dependence of the in-plane resistivity in the (a) overdoped region, (b) underdoped region, and (c) strongly underdoped region with Tc 0. The increase of the oxygen concentration y is indicated by the right long vertical arrow. Other characteristic temperatures indicated by dierent type of arrows are explained in the text.
a change of curvature in q(T), labeled TI , is pointed in Fig. 1(b). Additional removing of oxygen out of the ®lm leads to the loss of superconductivity and the occurrence of insulating behavior starting at the temperature TM , where q(T) is minimum (Fig. 1(c)). All above characteristic behaviors are also found in bilayer Bi-2212 thin ®lms and a comparison between both phases in the pseudogap region is done in Ref. [26,28]. Fig. 2a shows the doping dependence of the Hall number nH , measured at 300 K, for the same ®lm as in Fig. 1. The upper horizontal axis gives also the conductivity at room temperature normalized by
its value at optimally doped state r=rop 300 K . The critical temperature Tc is also a parabolic function of r=rop 300 K , parameter previously used to characterize the oxygen doping in the case of Bi2 Sr2 CaCu2 Oy (Bi-2212) ®lms [27]. This quantity is used here in the same manner in order to parameterize the doping of the strongly underdoped states (Tc 0) where the above parabolic function cannot be applied (see further Fig. 3). The decrease of nH with reducing carrier concentration indicates a total decrease of carriers by a factor of the order of 4, which is in good agreement with the corresponding decrease of p from 0.24 to 0.06. Moreover, it is shown that nH varies nearly linearly with p and r=rop 300 K which con®rms that the latter can be used to characterize doping. Another quantity which allows to characterize the doping level is the c-axis lattice constant, c0 , obtained from X-ray diraction spectra. The doping dependence of c0 for some characteristic states for the same ®lm
166
Z. Konstantinovic et al. / Physica C 351 (2001) 163±168
Fig. 3. (a) Plot of q T q0 =aT versus T for states near optimal doping (overdoped OD, optimally doped OP and underdoped UD) with arrows indicating the beginning of the deviation from T-linear behavior at T*. (b) dq=dT versus T for some doping states in the superconducting region with bold arrows pointing to the maximum of the curves dq=dT at TI (in¯ection point) and light arrows pointing to T*. (c) Logarithmic plot of q(T) for strongly underdoped states. Arrows show the beginning of insulating behaviors (minimum of q(T)) at TM . The right vertical axis shows (kF l) 1 values evaluated from the resistance per CuO2 layer (see text).
is shown in Fig. 2(b): c0 decreases monotonically with increasing p. In order to show the determination of the temperature T*, where resistivity displays a downturn from high-T-linear behavior, the quantity q T q0 =aT is plotted versus T for optimal and neighboring doping states (Fig. 3(a)). The parameters q0 and a are obtained from the linear ®t to the high temperature part of q(T). The values of T*, indicated by arrows in Fig. 3(a), coincide with the low-temperature limit of the constant part of the ®rst derivative dq=dT (dashed line in Fig. 3(b)) which con®rms as-determined values of T*. One typical overdoped state is also represented in Fig. 3(a) to underline its dierent behavior (upward deviation). The ®rst derivative of the overdoped states is naturally described by dq=dT amT m 1 (solid line in Fig. 3(b)).
Another characteristic temperature TI is de®ned by the maximum value of the ®rst derivative dq=dT in the underdoped region (arrows pointing downward in Fig. 3(b)). This in¯ection point coordinate TI has the same doping dependence as T*, and they are related by: TI T =2 [28], relation earlier found in YBCO [29] and BSLCO [30] compounds. This observation has permitted to determine T* values when they exceed room temperature. For strongly underdoped states, the temperature TM below which the insulating behavior begins is extracted from the minimum of the resistivity versus temperature (Fig. 3(c)). The insulating behavior is a manifestation of localization eects, which suppress the observed pseudogap eect. Moreover, the crossover from superconducting to insulating behavior occurs at qSI 0 1:1 0:1 mX cm. This value corresponds to a resistance per square per CuO2 plane qSI 0 = c0 =2 9 kX, where c0 =2 is the interlayer distance (see Fig. 3(c)). The normalized resistivity values in (kF l) 1 units are plotted on the right vertical axis (same 2 ®gure), given by qSI 0 = c0 =2 h=e = kF l, where kF is the Fermi wave vector and l the mean free path between scattering events. The observed crossover value qSI 0 = c0 =2 is higher than that of conventional 2D superconductors, equal to h= 2e2 6:5 kX kF l 4 [31,32]. However, it is in very good agreement with the value estimated from h=0:69 2e2 9:4 kX, established for 2D disordered systems with Coulomb interactions [33]. This comparison suggests that, although disorder plays an important role in these materials, one cannot neglect Coulomb interactions between carriers, which increase with the decreasing carrier concentration, shown in Fig. 2(a). Note also in Fig. 3(c) that a log 1=T behavior of q(T) is only observed for the state close to the MI transition (third state from bottom curve) and for T 6 20 K. This insulating behavior was previously observed in both underdoped superconducting LSCO [16] and BSLCO [17] under a 60 T magnetic ®eld. However, q(T) for all others states [34] are in good agreement with a thermally activated conduction behavior just below TM and with 2D Mott variable-range hopping at lower temperature observed in LSCO system and associated
Z. Konstantinovic et al. / Physica C 351 (2001) 163±168
167
with phonon assisted impurity scattering [35]. The observed logarithmic behavior close to the superconducting±insulating transition and then 2D Mott variable-range hopping at low temperature are also in agreement with previous results on underdoped non-superconducting Bi-2201 single crystals [36]. 4. Phase diagram The doping dependence of all characteristic temperatures introduced above are shown in Fig. 4 for two dierent thin ®lms (solid and open symbols). All three temperatures, T*, TI and TM , increase with decreasing carrier concentrations and their doping dependence is the same for all examined samples. Note also the parabolic behavior of Tc as a function of normalized conductivity r=rop 300 K , without suppression of the critical temperature near p 1=8 (``1/8'' anomaly), as observed previously in La2 x Bax CuO4 compound [37] and recently mentioned in BSLCO single crystals [38]. The values of T* in Bi(La)-2201 are of the same order of magnitude as in the case of BSLCO single crystals compared for the same ratio Tc =Tc max [15] and smaller than the values reported in LSCO compounds [10]. The change in slope of TI (p) coinciding with the beginning of localization eects could induce a systematic error in T (p) 2TI (p) behavior in the strongly underdoped region (T* values deduced from TI could be overestimated). The doping dependence of T*(p) around optimally doped states presents a steep decrease towards the curve Tc (p). By extrapolating T*(p) to zero, we ®nd that T 0 for p 0:17 0:01 hole per Cu, which is considered as a possible quantum critical point [39,40]. The variation of the third characteristic temperature, TM (p), provides the low-temperature boundary of the pseudogap region, as it was proposed theoretically earlier [39]. The extrapolated value at zero temperature of TM (p) lies well inside the underdoped regime for BSLCO (p 0:07 0:01) which is in good agreement with the MI boundary deduced from q(T) behavior of BSLCO single crystal under 60 T [17]. The only dierence between the two results arises from dierent eval-
Fig. 4. Phase diagram of Bi2 Sr1:6 La0:4 CuOy ®lms as a function of the parameter r=rop 300 K (see text). Some characteristic p values are indicated on the upper horizontal axis. Marks 1(a), 1(b) and 1(c) indicate the corresponding regions of in-plane resistivities (see Fig. 1). The open symbols correspond to the results obtained for the ®lm of Fig. 1, while the solid symbols are for another sample. The hatched area indicates the pseudogap region (PG). T*, TM and TI are de®ned in Figs. 1 and 3.
uated hole concentration values, but still it appears that the MI boundary cut Tc (p) at the same ratio Tc =Tc max 0:4. The situation is quite dierent in LSCO compounds, where the onset of the localization behavior extends up to optimum doping [16]. So the low T beginning of the MI boundary in Bi(La)-2201 deeply in the underdoped region indicates that it depends on the cuprate family and it does not show a visible link with pseudogap eect occurring near optimum doping. Finally, a schematic phase diagram was proposed in Ref. [41]. There the pseudogap phase is associated with 1D stripe formation, while at the MI boundary disorder disrupts the 1D stripes restoring a 2D regime for transport with
168
Z. Konstantinovic et al. / Physica C 351 (2001) 163±168
q T log 1=T [42]. Although this insulating behavior log (1/T) that we have seen in one state close the MI crossover might be associated with low dimensionality imposed by charge con®nement into stripes as indicated in Ref. [17], it is dicult to understand why this behavior is observed in just a very narrow doping window. Moreover, until now there is no direct evidence, as in neutron scattering data on LSCO compound [43], of the existence of the stripe formation in Bi(La)-2201 which might help to clarify this issue. 5. Summary To summarize, we have studied the evolution of the temperature dependence of the in-plane resistivity over a wide range of doping levels, from overdoped to strongly underdoped. We show that the behavior of the resistivity changes strongly with the oxygen content in the ®lm, from metallic to semiconducting behavior. From this analysis, we have established a very detailed unique phase diagram of the single-layer Bi2 Sr1:6 La0:4 CuOy phase. The upper boundary of the pseudogap region is given by the temperature T*(p) and the lower boundary by the temperature TM (p), where localization eects occur. The extrapolation to zero of T*(p) around p 0:17 may possibly indicate the existence of a quantum critical point. Moreover, our data indicate that there is no obvious relation between the onset of localization eects and the pseudogap opening occurring around optimal doping. References [1] [2] [3] [4] [5] [6]
R.E. Walstedt, et al., Phys. Rev. B 41 (1990) 9574. M. Takigawa, et al., Phys. Rev. B 43 (1991) 247. H. Alloul, et al., Phys. Rev. Lett. 67 (1991) 3140. J. Rossat-Mignod, et al., Physica B 169 (1991) 58. J.M. Tranquada, et al., Phys. Rev. B 46 (1992) 5561. C.C. Homes, et al., Phys. Rev. Lett. 71 (1993) 1645.
[7] J.W. Loram, et al., Phys. Rev. Lett. 71 (1993) 1740. [8] T. Timusk, B. Statt, Rep. Prog. Phys. 62 (1999) 61. [9] T. Ito, K. Takenaka, S. Uchida, Phys. Rev. Lett. 70 (1993) 3995. [10] B. Batlogg, et al., Physica C 235-240 (1994) 130. [11] D.N. Basov, H.A. Mook, B. Dabrowski, T. Timusk, Phys. Rev. B 52 (1995) 13141. [12] B.L. Altshuler, L.B. Ioe, A.J. Millis, Phys. Rev. B 53 (1996) 415. [13] J. Bobro, et al., Phys. Rev. Lett. 78 (1997) 3757. [14] J.M. Harris, et al., Phys. Rev. Lett. 79 (1997) 143. [15] Y. Ando, T. Murayama, S. Ono, J. Low Temp. Phys. 117 (1999) 1117. [16] G.S. Boebinger, et al., Phys. Rev. Lett. 77 (1996) 5417. [17] S. Ono, et al., Phys. Rev. Lett. 85 (2000) 638. [18] Y. Iye, Physical Properties of High Temperature Superconductors III, in: D.M. Ginsberg (Ed.), World Scienti®c, Singapore, 1991. [19] Y. Fukuzumi, K. Mizuhashi, K. Takenaka, S. Uchida, Phys. Rev. Lett. 76 (1996) 684. [20] D.J.C. Walker, A.P. Mackenzie, J.R. Cooper, Phys. Rev. B 51 (1995) 15653. [21] Z.Z. Li, H. Ray, to be published. [22] M.R. Presland, et al., Physica C 176 (1991) 95. [23] H. Ri®, Thesis, University of Orsay (1996), unpublished. [24] Y. Kubo, et al., Phys. Rev. B 43 (1991) 7875. [25] H. Takagi, et al., Phys. Rev. Lett. 69 (1992) 2975. [26] Z. Konstantinovic, Z.Z. Li, H. Ray, in preparation. [27] Z. Konstantinovic, Z.Z. Li, H. Ray, Physica B 259±261 (1999) 567. [28] Z. Konstantinovic, Z.Z. Li, H. Ray, Physica C 341±348 (2000) 859. [29] B. Wuyts, V.V. Moshchalkov, Y. Bruynseraede, Phys. Rev. B 53 (1996) 9418. [30] Y. Ando, T. Murayama, Phys. Rev. B 60 (1999) 6991. [31] T. Pang, Phys. Rev. Lett. 62 (1989) 2176. [32] M.P.A. Fisher, G. Grinstein, S.M. Girvin, Phys. Rev. Lett. 64 (1990) 587. [33] I. Herbut, Phys. Rev. Lett. 81 (1998) 3916. [34] Z. Konstantinovic, Z.Z. Li, H. Ray, unpublished. [35] E. Lai, R.J. Gooding, Phys. Rev. B 57 (1998) 1498. [36] A.T. Fiory, et al., Phys. Rev. B 41 (1990) 2627. [37] A.R. Moodenbaugh, et al., Phys. Rev. B 38 (1988) 4596. [38] W.L. Yang, H.H. Wen, Z.X. Zhao, Phys. Rev. B 62 (2000) 1361. [39] C.M. Varma, Phys. Rev. B 55 (1997) 14554. [40] S. Sachdev, Physics World, April (1999) 33. [41] V.V. Moshchalkov, L. Trappeniers, J. Vanacken, J. Low Temp. Phys. 117 (1999) 1283. [42] L. Trappeniers, et al., J. Low Temp. Phys. 117 (1999) 681. [43] K. Yamada, et al., Phys. Rev. B 57 (1998) 6165.