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Pseudogap opening, superconducting fluctuation and vortex-like excitation above Tc in slightly overdoped Bi2Sr2CaCu2O8+δ
Physica C 421 (2005) 61–66 www.elsevier.com/locate/physc
Pseudogap opening, superconducting fluctuation and vortex-like excitation above Tc in slightly overdoped Bi2Sr2CaCu2O8+d Z.A. Xu b
a,*
, J.Q. Shen a, S. Ooi b, T. Mochiku b, K. Hirata
b
a Department of Physics, Zhejiang University, Hangzhou 310027, China National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
Received 6 October 2004
Abstract The magnetoresistance, Hall effect and Nernst effect of slightly overdoped Bi2Sr2CaCu2O8+d single crystals were measured for both normal state and mixed state. The superconducting transition temperature (Tc0) and the pseudogap opening temperature (T ) determined from the temperature dependence of resistivity are 86.5 K and 120 K respectively, while the onset temperature (T O) of vortex-like excitation detected by Nernst effect is about 105 K, which is consistent with the onset temperature of superconducting fluctuation determined from magnetoresistance and Hall coefficient measurement. This result indicates that both pseudogap opening and superconducting fluctuation exist above Tc in the slightly overdoped region of electronic phase diagram of cuprates. In contrast to the underdoped case, the narrower temperature range of superconducting fluctuation in the slightly overdoped region could be understood by the Ginzburg–Landau fluctuation theory. 2005 Elsevier B.V. All rights reserved. PACS: 74.72.h; 74.40.+k; 74.25.Fy; 74.72.Hs Keywords: High-Tc compounds; Superconducting fluctuation; Pseudogap, Nernst effect
1. Introduction The superconducting properties of high-Tc superconductors (HTS) exhibit very different nat*
Corresponding author. Tel./fax: +86 571 87953255. E-mail address: [email protected] (Z.A. Xu).
ure compared to conventional BCS-type superconductors and the pairing mechanism is still under debate. On the other hand, their normal-state properties deviate severely from the predictions of Fermi Liquid theory. Especially in the underdoped HTS, a pseuodogap which opens at a certain characteristic temperature T above Tc has
0921-4534/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2005.02.012
62
Z.A. Xu et al. / Physica C 421 (2005) 61–66
been observed in the single-particle excitation spectra [1]. An explanation of the pseudogap phenomenon is regarded as one of the most important unresolved questions in the theory of superconductivity. Due to the extremely complex structural and electronic nature of the cuprates, and the somewhat controversial nature of much of the current experimental data, there are many theoretical attempts to explain pseudogap behavior. Recently Xu et al. and his colleagues [2,3] surprisingly found that the Nernst signals due to vortex-like excitations still persist in the pseudogap region above Tc which is a strong evidence supporting the theoretic model proposed by Emery and Kivelson (EK model) [4] in which the pseudogap state is a precursor to high-Tc superconductivity. However, like other experimental probes, most investigations of Nernst effect have been performed on underdoped cuprates and few studies have been reported for overdoped cuprates. How the T line continues in the overdoped region, i.e., what is the ‘‘real phase diagram’’, is crucial to the theories. For example, EK model which is based on the superconducting phase fluctuations predicts that the T line will merge with Tc line gradually in overdoped region and other theoretic models predict that T line drops abruptly to zero at a quantum critical point (QCP) around x = 0.19 [5,6]. This paper reports the measurements of resistivity, Hall effect, and Nernst effect in the slightly overdoped high-Tc superconducting Bi2Sr2CaCu2O8+d (Bi-2212) single crystals with Tc0 of 86.5 K. It was found that the onset temperature TO of anomalous Nernst signals due to vortex-like excitation is consistent with the onset temperature of superconducting fluctuation determined by the magnetoresistance (MR) and Hall effect. Our results show that T for pseudogap opening is still observable above Tc0 and the onset of vortex-like Nernst signal is between T and Tc0 in the slightly overdoped Bi-2212, which could be understood by the Ginzburg–Landau fluctuation theory.
as grown Bi-2212 crystals are overdoped and the oxygen distribution is not homogenous. The slightly overdoped samples were obtained by annealing the as grown crystals under a suitable oxygen partial pressure at 700 C for about 30 h. Two annealed crystals from the same batch (sample B1 and B2) were chosen for this study. Both Tc0 is 86.5 K and the hole-doping concentration x is about 0.18 ± 0.01 estimated from the drop of Tc0 compared to the optimally doped Bi-2212. Unless emphasized, Bi-2212 in this paper denotes the slightly overdoped Bi2Sr2CaCu2O8+d singlecrystals with Tc0 of 86.5 K. The Bi-2212 crystals were cut into about 3 mm in length and 1 mm in width (the thickness is about 10 lm) by a dicing saw for transport property and Nernst effect measurements. The in-plane resistivity and magnetoresistance were measured by standard four-probe method. The electric contacts were made by using golden paste and the contact resistance was less than 1 X. The sampleÕs resistance was read by a LR 700 AC Resistance Bridge. The (x, y) plane is defined as the conducting ab plane of the flake-like Bi-2212 crystal. In the set-up of Nernst effect measurement, the temperature gradient is applied along longitudinal direction (x-direction), and the magnetic field is applied along z-direction (c-axis of the sample). Thus the Nernst electric field is along y-direction, which was measured by Keithley Model 2182 Nano-voltmeter. The temperature gradient was measured by two small Cernox thermometers (CX-1050-BR from Lake Shore Cryotronics) attached to the two ends of the sample and GE varnish (VGE-7031) was used for good thermal contact. A small heater with a size of 0.5 · 1 mm2 in area was supported by a thin nylon pillar and closely attached to one end of the sample. The heater current was provided by a Keithley 2400 Digital Source-meter and the applied temperature gradient was about 5 K/cm. The Nernst coefficient m is defined as: m¼
2. Experimental The Bi-2212 single-crystals were prepared by traveling solvent floating-zone technique. Usually
Ey j o x T j Bz
ð1Þ
It has already been confirmed that the Nernst signal is highly sensitive to the moving vortices in conventional type-II superconductors and there-
Z.A. Xu et al. / Physica C 421 (2005) 61–66
fore Nernst effect is a good probe of vortex excitations [7].
3. Results and discussion Since both measured Bi-2212 crystals have almost same doping level and the temperature dependences of resistivity and Hall coefficient are nearly same, we only show the resistivity and Hall effect data for one Bi-2212 sample (sample B1) here. Fig. 1 shows the temperature dependence of in-plane resistivity for Bi-2212 without applying magnetic field and under 5 T magnetic field along c-axis. The arrow indicates the position where the resistivity deviates from linear temperature dependence. The inset of Fig. 1 shows the plot of MR, q/q, versus temperature, where Dq/q (q(5 T) q(0 T))/q(0 T). The zero-point superconducting transition temperature Tc0 is 86.5 K and the mid-point transition temperature is 90 K determined from the zero-field resistivity. Similar to other high-Tc superconducting cuprates, the resistivity is linearly dependent on the temperature at high temperatures, then it deviates downwards from the linear dependence at a certain temperature T of about 120 K. This characteristic temper-
Fig. 1. The temperature dependence of in-plane resistivity, q(T), under different magnetic fields for slightly overdoped single-crystal Bi2Sr2CaCu2O8+d. The arrow indicates the position where the resistivity deviates from linear temperature dependence. Inset: magnetoresistance Dq/q versus temperature. The arrow indicates the position where Dq/q increases abruptly, i.e., the onset temperature of superconducting fluctuation.
63
ature T should be related to pseudogap opening [8] instead of superconducting fluctuation. As shown in the inset of Fig. 1, Dq/q is still nearly zero at T , indicating that the downward deviation in resistivity could not be caused by the superconducting fluctuation. Dq/q appears abruptly at about 105 K which is indicated by the arrow in the inset of Fig. 1, corresponding to the onset temperature of superconducting fluctuation, TFL. The temperature dependence of Hall coefficient RH was also measured in order to detect the temperature range of superconducting fluctuation for the Bi-2212 sample. Fig. 2 shows the temperature dependence of Hall coefficient for Bi-2212 (sample B1). The inset of Fig. 2 shows the plot of cotangent of Hall angle, cot h, versus the square of temperature, T2 The Hall angle h is defined as tan h qH(H)/q(H), where qH(H) is Hall resistivity measured at l0H = 5 T. Just below Tc0 the double sign revisals of Hall coefficient are often observed in high-quality Bi-2212 crystals [9]. Several theoretical approaches based on the mechanism of vortex motion, superconducting fluctuations, and/or hydrodynamics interaction between vortices and the charge carriers have been attempted to explain the complex features of Hall effect below Tc0 [10], but we do not attempt to discuss further the anomalous Hall effect in mixed state in this paper. Generally the Hall angle in the normal state of HTS
Fig. 2. The temperature dependence of Hall coefficient RH for single-crystal Bi2Sr2CaCu2O8+d. The Hall coefficient was measured under 5 T magnetic field. The inset shows the cotangent of Hall angle versus the square of temperature. The arrow denotes the onset temperature for superconducting fluctuation.
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satisfies the relation cot h / T2 [11] which can be interpreted in the AndersonÕs spin-charge separation model [12]. Although the Hall coefficient RH deviates downwards from 1/T dependence around T of 120 K, there is no observable change in the cot h / T2 curve as T decreases across T . As T further approaches to superconducting transition temperature Tc0, coth deviates from the T2 dependence due to the strong superconducting fluctuation. From the inset of Fig. 2, it can be seen that the superconducting fluctuation appears at TFL ffi 103 K, consistent with the result of MR measurement from which the onset temperature of superconducting fluctuation is determined as 105 K. Thus it is concluded that the onset temperature of superconducting fluctuation is about 105 K and the temperature of pseudogap opening is about 120 K in our slightly overdoped Bi-2212 samples. Fig. 3 shows the Nernst signal ey Ey/oxT at l0H = 5 T as a function of temperature for the two Bi-2212 samples (samples B1 and B2). The temperature dependence of dc susceptibility (measured at H = 10 Oe) is also plotted for sample B1. Although there is about 20% difference in the magnitude of ey the profile of ey versus T curves of sample B1 and B2 is same. Such an error in the absolute values of ey could be caused by the measurement errors of sampleÕs dimensions and the
Fig. 3. The temperature dependence of Nernst signal ey and dc susceptibility v for Bi-2212 crystals. The solid line denotes the dc susceptibility, the open symbols denote the Nernst signals measured at l0H = 5 T. Number 1 and 2 denote sample B1 and B2.
condition of thermal contacts between temperature sensors and samples. However, this error usually does not change the temperature dependence of ey. The onset transition temperature determined from the susceptibility is about 88 K, consistent with the resistive transition temperature. The Nernst signal ey in high-temperature normal state is small and almost temperature independent, similar to the underdoped HTS. With decreasing temperatures, ey deviates from the high-temperature background and increases sharply at about 105 K, then reaches a maximum around 80 K below Tc0, and finally decreases to zero as T < 40 K. In the temperature range between Tc0 and 105 K there exists anomalously large Nernst signal, indicating that there are vortex-like excitations in this region. We define TO as the onset temperature at which the Nernst signal starts to deviate from the high temperature background. Anomalous Nernst signals due to vortex-like excitations have been observed at temperatures well above Tc0 in underdoped HTS, such as La2xSrxCuO4 (0.05 6 x 6 0.17) [2,3], Bi2Sr2CaCu2Ox (8.05 6 x 6 8.1) [13,14], and YBa2Cu3Ox (6.4 6 x 6 6.9) [14]. According to the general phase diagram of HTS, as the doping concentration decreases from optimally-doping, Tc decreases, but T increases on the contrary in a certain doping range [1]. The varying trend of TO line is similar to that of T line, but opposite to that of Tc0 line in the underdoped region. These results indicate that the anomalous Nernst signals in the pseudogap region of underdopoed HTS can not be understood in the frame of conventional superconducting fluctuations, which implies that the mechanism of HTS is substantially different from the that of conventional superconductors. According to the scenario of precursor pairing proposed in EK model [4], the pairing amplitude jwj is no longer zero when the pseudogap opens as T < T , and the loss of the Meissner effect (flux-expulsion) in the temperature range Tc < T < T corresponds to a loss of long-range phase coherence of Cooper pairs caused by the vortex excitations. The broad range of temperatures above Tc0 in which the vortex signal is observed by the highly sensitive Nernst experiment presents the most compelling evidence for this scenario.
Z.A. Xu et al. / Physica C 421 (2005) 61–66
Corson et al. [15] detected dynamic vortices by high-frequency ac conductivity and found that there exist dynamic vortices in a temperature range above Tc0 in underdoped Bi-2212, in agreement with the Nernst measurements. Existing theories of the pseudogap can be classified broadly into two categories. The first is based on a model of Cooper pair formation at T (well above Tc), with long-range phase coherence appearing at T 6 Tc [4]. The second assumes that the appearance of the pseudogap is due to fluctuations of some other type, such as antiferromagnetic fluctuations, charge density waves, or electronic phase separation (e.g., the stripe scenario), which compete or coexist with superconductivity [16–19]. Within the second category the concept of QCP at xc = 0.19 has been proposed and T line in the phase diagram of HTS should drop to zero abruptly as x > xc = 0.19 [5,6]. However, the experimental results on this issue are still controversial in the literature. For example, STM study by Renner et al. [20] and tunneling spectra study by Matsuda, Sugita and Watanabe [21] found that the pseudogap always opens above Tc in Bi-2212 irrespective of the doping level. Meanwhile, break-junction-type tunneling measurements of Mandrus et al. [22] and Miyakawa et al. [23] show no strong evidence of a pseudogap above Tc in overdoped Bi-2212. The doping level of our samples is close to xc = 0.19, and the temperature dependence of resistivity shows clear evidence of pseudogap opening around 120 K. Moreover, there is another temperature scale (TFL or TO) corresponding to superconducting fluctuation between Tc0 and T from the temperature dependence of the magnetoresistance, Hall angle, and Nernst coefficient. Ong et al. [14] reported that the onset of Nernst coefficient of a more overdoped Bi-2212 with Tc0 of 77 K is at about 100 K, similar to our result. The strength of the fluctuation effect can be given by the Ginzburg criterion G(H) = DT(H)/Tc(H), where DT(H) is the width of the critical region and Tc(H) is the transition temperature in a magnetic field H. In conventional fluctuation theory, GðH Þ ¼ ð8pj2 k B T c H =/0 nc H 2c2 Þ2=3 , where j is the Ginzburg–Landau parameter, nc is the c-axis coherence length and Hc2 is the upper critical field.
65
For conventional superconductors, G(H) is usually very small (the order of magnitude is 0.001). Due to the low dimensionality, small superfluid density (1022/cm3), and short coherence length (nc 6 1 nm) and high temperature scales, the G values of cuprates should be 100–1000 times larger than that in conventional superconductors. Let make a rough estimate of G for Bi-2212. Take Tc 85 K for H = 50 kOe, j 100, nc 5 · 108 cm, Hc2 500 kOe, we get G 0.15, and DT 13 K. The estimated G and DT values are quite close to the experimental results. Therefore, in contrast to the underdoped cuprates, the fluctuation effect revealed by Nernst effect measurements in overdoped Bi-2212 is consistent with the Ginzburg– Landau fluctuation theory. 4. Conclusions The studies of resistivity, Hall effect, and Nernst effect in slightly overdoped Bi-2212 indicate that there exist Nernst signals due to vortex-like excitation in a temperature range from Tc0 of 86.5 K up to TO of 105 K. TO is consistent with the onset temperature of superconducting fluctuations, TFL determined from MR and Hall effect. T of pseudogap opening is determined to be about 120 K from the deviation from linear temperature dependence of resistivity. The results imply that superconducting fluctuations exist well above Tc0 even in overdoped HTS. In contrast to the underdoped cuprates, the superconducting effect revealed by Nernst effect is consistent with the Ginzburg–Landau fluctuation theory. Acknowledgement The project was sponsored by the National Science Foundation of China (NSFC 10225417) and the Ministry of Science and Technology of China (Project: NKBRSF-G1999064602).
References [1] For a review, see T. Timusk, B. Statt, Rep. Prog. Phys. 62 (1999) 61.
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[2] Z.A. Xu et al., Nature (London) 406 (2000) 486. [3] Y. Wang et al., Phys. Rev. B 64 (2001) 224519. [4] V.J. Emery, S.A. Kivelson, Nature (London) 374 (1995) 434. [5] J.L. Tallon et al., Physica C 235–240 (1994) 1821. [6] J.L. Tallon, J.W. Loram, Physica C 349 (2001) 53. [7] F. Vidal, Phys. Rev. B 8 (1973) 1982. [8] T. Ito, K. Takenaka, S. Uchida, Phys. Rev. Lett. 70 (1993) 3995. [9] For example, see A.V. Samoilov, Phys. Rev. Lett. 71 (1993) 617. [10] I. Puica et al., Phys. Rev. B 69 (2004) 104513, and references therein. [11] T.R. Chien et al., Phys. Rev. Lett. 67 (1991) 2088.
[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
P.W. Anderson, Phys. Rev. Lett. 67 (1991) 2092. Y. Wang et al., Science 299 (2003) 86. N.P. Ong et al., Ann. Phys. (Leipzig) 13 (2004) 9. J. Corson et al., Nature (London) 398 (1999) 221. A.P. Kampf, J.R. Schrieffer, Phys. Rev. B 42 (1990) 7967. M. Langer et al., Phys. Rev. Lett. 75 (1995) 4508. J.J. Desz et al., Phys. Rev. Lett. 76 (1996) 1312. J. Schmalian, D. Pines, B. Stojkovic, Phys. Rev. Lett. 80 (1998) 3839. C. Renner et al., Phys. Rev. Lett. 80 (1998) 149. A. Matsuda, S. Sugita, T. Watanabe, Phys. Rev. B 60 (1999) 1377. D. Mandrus et al., Europhys. Lett. 22 (1993) 199. N. Miyakawa et al., Phys. Rev. Lett. 80 (1998) 157.
Pseudogap opening, superconducting fluctuation and vortex-like excitation above Tc in slightly overdoped Bi2Sr2CaCu2O8+d Z.A. Xu b
a,*
, J.Q. Shen a, S. Ooi b, T. Mochiku b, K. Hirata
b
a Department of Physics, Zhejiang University, Hangzhou 310027, China National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
Received 6 October 2004
Abstract The magnetoresistance, Hall effect and Nernst effect of slightly overdoped Bi2Sr2CaCu2O8+d single crystals were measured for both normal state and mixed state. The superconducting transition temperature (Tc0) and the pseudogap opening temperature (T ) determined from the temperature dependence of resistivity are 86.5 K and 120 K respectively, while the onset temperature (T O) of vortex-like excitation detected by Nernst effect is about 105 K, which is consistent with the onset temperature of superconducting fluctuation determined from magnetoresistance and Hall coefficient measurement. This result indicates that both pseudogap opening and superconducting fluctuation exist above Tc in the slightly overdoped region of electronic phase diagram of cuprates. In contrast to the underdoped case, the narrower temperature range of superconducting fluctuation in the slightly overdoped region could be understood by the Ginzburg–Landau fluctuation theory. 2005 Elsevier B.V. All rights reserved. PACS: 74.72.h; 74.40.+k; 74.25.Fy; 74.72.Hs Keywords: High-Tc compounds; Superconducting fluctuation; Pseudogap, Nernst effect
1. Introduction The superconducting properties of high-Tc superconductors (HTS) exhibit very different nat*
Corresponding author. Tel./fax: +86 571 87953255. E-mail address: [email protected] (Z.A. Xu).
ure compared to conventional BCS-type superconductors and the pairing mechanism is still under debate. On the other hand, their normal-state properties deviate severely from the predictions of Fermi Liquid theory. Especially in the underdoped HTS, a pseuodogap which opens at a certain characteristic temperature T above Tc has
0921-4534/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2005.02.012
62
Z.A. Xu et al. / Physica C 421 (2005) 61–66
been observed in the single-particle excitation spectra [1]. An explanation of the pseudogap phenomenon is regarded as one of the most important unresolved questions in the theory of superconductivity. Due to the extremely complex structural and electronic nature of the cuprates, and the somewhat controversial nature of much of the current experimental data, there are many theoretical attempts to explain pseudogap behavior. Recently Xu et al. and his colleagues [2,3] surprisingly found that the Nernst signals due to vortex-like excitations still persist in the pseudogap region above Tc which is a strong evidence supporting the theoretic model proposed by Emery and Kivelson (EK model) [4] in which the pseudogap state is a precursor to high-Tc superconductivity. However, like other experimental probes, most investigations of Nernst effect have been performed on underdoped cuprates and few studies have been reported for overdoped cuprates. How the T line continues in the overdoped region, i.e., what is the ‘‘real phase diagram’’, is crucial to the theories. For example, EK model which is based on the superconducting phase fluctuations predicts that the T line will merge with Tc line gradually in overdoped region and other theoretic models predict that T line drops abruptly to zero at a quantum critical point (QCP) around x = 0.19 [5,6]. This paper reports the measurements of resistivity, Hall effect, and Nernst effect in the slightly overdoped high-Tc superconducting Bi2Sr2CaCu2O8+d (Bi-2212) single crystals with Tc0 of 86.5 K. It was found that the onset temperature TO of anomalous Nernst signals due to vortex-like excitation is consistent with the onset temperature of superconducting fluctuation determined by the magnetoresistance (MR) and Hall effect. Our results show that T for pseudogap opening is still observable above Tc0 and the onset of vortex-like Nernst signal is between T and Tc0 in the slightly overdoped Bi-2212, which could be understood by the Ginzburg–Landau fluctuation theory.
as grown Bi-2212 crystals are overdoped and the oxygen distribution is not homogenous. The slightly overdoped samples were obtained by annealing the as grown crystals under a suitable oxygen partial pressure at 700 C for about 30 h. Two annealed crystals from the same batch (sample B1 and B2) were chosen for this study. Both Tc0 is 86.5 K and the hole-doping concentration x is about 0.18 ± 0.01 estimated from the drop of Tc0 compared to the optimally doped Bi-2212. Unless emphasized, Bi-2212 in this paper denotes the slightly overdoped Bi2Sr2CaCu2O8+d singlecrystals with Tc0 of 86.5 K. The Bi-2212 crystals were cut into about 3 mm in length and 1 mm in width (the thickness is about 10 lm) by a dicing saw for transport property and Nernst effect measurements. The in-plane resistivity and magnetoresistance were measured by standard four-probe method. The electric contacts were made by using golden paste and the contact resistance was less than 1 X. The sampleÕs resistance was read by a LR 700 AC Resistance Bridge. The (x, y) plane is defined as the conducting ab plane of the flake-like Bi-2212 crystal. In the set-up of Nernst effect measurement, the temperature gradient is applied along longitudinal direction (x-direction), and the magnetic field is applied along z-direction (c-axis of the sample). Thus the Nernst electric field is along y-direction, which was measured by Keithley Model 2182 Nano-voltmeter. The temperature gradient was measured by two small Cernox thermometers (CX-1050-BR from Lake Shore Cryotronics) attached to the two ends of the sample and GE varnish (VGE-7031) was used for good thermal contact. A small heater with a size of 0.5 · 1 mm2 in area was supported by a thin nylon pillar and closely attached to one end of the sample. The heater current was provided by a Keithley 2400 Digital Source-meter and the applied temperature gradient was about 5 K/cm. The Nernst coefficient m is defined as: m¼
2. Experimental The Bi-2212 single-crystals were prepared by traveling solvent floating-zone technique. Usually
Ey j o x T j Bz
ð1Þ
It has already been confirmed that the Nernst signal is highly sensitive to the moving vortices in conventional type-II superconductors and there-
Z.A. Xu et al. / Physica C 421 (2005) 61–66
fore Nernst effect is a good probe of vortex excitations [7].
3. Results and discussion Since both measured Bi-2212 crystals have almost same doping level and the temperature dependences of resistivity and Hall coefficient are nearly same, we only show the resistivity and Hall effect data for one Bi-2212 sample (sample B1) here. Fig. 1 shows the temperature dependence of in-plane resistivity for Bi-2212 without applying magnetic field and under 5 T magnetic field along c-axis. The arrow indicates the position where the resistivity deviates from linear temperature dependence. The inset of Fig. 1 shows the plot of MR, q/q, versus temperature, where Dq/q (q(5 T) q(0 T))/q(0 T). The zero-point superconducting transition temperature Tc0 is 86.5 K and the mid-point transition temperature is 90 K determined from the zero-field resistivity. Similar to other high-Tc superconducting cuprates, the resistivity is linearly dependent on the temperature at high temperatures, then it deviates downwards from the linear dependence at a certain temperature T of about 120 K. This characteristic temper-
Fig. 1. The temperature dependence of in-plane resistivity, q(T), under different magnetic fields for slightly overdoped single-crystal Bi2Sr2CaCu2O8+d. The arrow indicates the position where the resistivity deviates from linear temperature dependence. Inset: magnetoresistance Dq/q versus temperature. The arrow indicates the position where Dq/q increases abruptly, i.e., the onset temperature of superconducting fluctuation.
63
ature T should be related to pseudogap opening [8] instead of superconducting fluctuation. As shown in the inset of Fig. 1, Dq/q is still nearly zero at T , indicating that the downward deviation in resistivity could not be caused by the superconducting fluctuation. Dq/q appears abruptly at about 105 K which is indicated by the arrow in the inset of Fig. 1, corresponding to the onset temperature of superconducting fluctuation, TFL. The temperature dependence of Hall coefficient RH was also measured in order to detect the temperature range of superconducting fluctuation for the Bi-2212 sample. Fig. 2 shows the temperature dependence of Hall coefficient for Bi-2212 (sample B1). The inset of Fig. 2 shows the plot of cotangent of Hall angle, cot h, versus the square of temperature, T2 The Hall angle h is defined as tan h qH(H)/q(H), where qH(H) is Hall resistivity measured at l0H = 5 T. Just below Tc0 the double sign revisals of Hall coefficient are often observed in high-quality Bi-2212 crystals [9]. Several theoretical approaches based on the mechanism of vortex motion, superconducting fluctuations, and/or hydrodynamics interaction between vortices and the charge carriers have been attempted to explain the complex features of Hall effect below Tc0 [10], but we do not attempt to discuss further the anomalous Hall effect in mixed state in this paper. Generally the Hall angle in the normal state of HTS
Fig. 2. The temperature dependence of Hall coefficient RH for single-crystal Bi2Sr2CaCu2O8+d. The Hall coefficient was measured under 5 T magnetic field. The inset shows the cotangent of Hall angle versus the square of temperature. The arrow denotes the onset temperature for superconducting fluctuation.
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satisfies the relation cot h / T2 [11] which can be interpreted in the AndersonÕs spin-charge separation model [12]. Although the Hall coefficient RH deviates downwards from 1/T dependence around T of 120 K, there is no observable change in the cot h / T2 curve as T decreases across T . As T further approaches to superconducting transition temperature Tc0, coth deviates from the T2 dependence due to the strong superconducting fluctuation. From the inset of Fig. 2, it can be seen that the superconducting fluctuation appears at TFL ffi 103 K, consistent with the result of MR measurement from which the onset temperature of superconducting fluctuation is determined as 105 K. Thus it is concluded that the onset temperature of superconducting fluctuation is about 105 K and the temperature of pseudogap opening is about 120 K in our slightly overdoped Bi-2212 samples. Fig. 3 shows the Nernst signal ey Ey/oxT at l0H = 5 T as a function of temperature for the two Bi-2212 samples (samples B1 and B2). The temperature dependence of dc susceptibility (measured at H = 10 Oe) is also plotted for sample B1. Although there is about 20% difference in the magnitude of ey the profile of ey versus T curves of sample B1 and B2 is same. Such an error in the absolute values of ey could be caused by the measurement errors of sampleÕs dimensions and the
Fig. 3. The temperature dependence of Nernst signal ey and dc susceptibility v for Bi-2212 crystals. The solid line denotes the dc susceptibility, the open symbols denote the Nernst signals measured at l0H = 5 T. Number 1 and 2 denote sample B1 and B2.
condition of thermal contacts between temperature sensors and samples. However, this error usually does not change the temperature dependence of ey. The onset transition temperature determined from the susceptibility is about 88 K, consistent with the resistive transition temperature. The Nernst signal ey in high-temperature normal state is small and almost temperature independent, similar to the underdoped HTS. With decreasing temperatures, ey deviates from the high-temperature background and increases sharply at about 105 K, then reaches a maximum around 80 K below Tc0, and finally decreases to zero as T < 40 K. In the temperature range between Tc0 and 105 K there exists anomalously large Nernst signal, indicating that there are vortex-like excitations in this region. We define TO as the onset temperature at which the Nernst signal starts to deviate from the high temperature background. Anomalous Nernst signals due to vortex-like excitations have been observed at temperatures well above Tc0 in underdoped HTS, such as La2xSrxCuO4 (0.05 6 x 6 0.17) [2,3], Bi2Sr2CaCu2Ox (8.05 6 x 6 8.1) [13,14], and YBa2Cu3Ox (6.4 6 x 6 6.9) [14]. According to the general phase diagram of HTS, as the doping concentration decreases from optimally-doping, Tc decreases, but T increases on the contrary in a certain doping range [1]. The varying trend of TO line is similar to that of T line, but opposite to that of Tc0 line in the underdoped region. These results indicate that the anomalous Nernst signals in the pseudogap region of underdopoed HTS can not be understood in the frame of conventional superconducting fluctuations, which implies that the mechanism of HTS is substantially different from the that of conventional superconductors. According to the scenario of precursor pairing proposed in EK model [4], the pairing amplitude jwj is no longer zero when the pseudogap opens as T < T , and the loss of the Meissner effect (flux-expulsion) in the temperature range Tc < T < T corresponds to a loss of long-range phase coherence of Cooper pairs caused by the vortex excitations. The broad range of temperatures above Tc0 in which the vortex signal is observed by the highly sensitive Nernst experiment presents the most compelling evidence for this scenario.
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Corson et al. [15] detected dynamic vortices by high-frequency ac conductivity and found that there exist dynamic vortices in a temperature range above Tc0 in underdoped Bi-2212, in agreement with the Nernst measurements. Existing theories of the pseudogap can be classified broadly into two categories. The first is based on a model of Cooper pair formation at T (well above Tc), with long-range phase coherence appearing at T 6 Tc [4]. The second assumes that the appearance of the pseudogap is due to fluctuations of some other type, such as antiferromagnetic fluctuations, charge density waves, or electronic phase separation (e.g., the stripe scenario), which compete or coexist with superconductivity [16–19]. Within the second category the concept of QCP at xc = 0.19 has been proposed and T line in the phase diagram of HTS should drop to zero abruptly as x > xc = 0.19 [5,6]. However, the experimental results on this issue are still controversial in the literature. For example, STM study by Renner et al. [20] and tunneling spectra study by Matsuda, Sugita and Watanabe [21] found that the pseudogap always opens above Tc in Bi-2212 irrespective of the doping level. Meanwhile, break-junction-type tunneling measurements of Mandrus et al. [22] and Miyakawa et al. [23] show no strong evidence of a pseudogap above Tc in overdoped Bi-2212. The doping level of our samples is close to xc = 0.19, and the temperature dependence of resistivity shows clear evidence of pseudogap opening around 120 K. Moreover, there is another temperature scale (TFL or TO) corresponding to superconducting fluctuation between Tc0 and T from the temperature dependence of the magnetoresistance, Hall angle, and Nernst coefficient. Ong et al. [14] reported that the onset of Nernst coefficient of a more overdoped Bi-2212 with Tc0 of 77 K is at about 100 K, similar to our result. The strength of the fluctuation effect can be given by the Ginzburg criterion G(H) = DT(H)/Tc(H), where DT(H) is the width of the critical region and Tc(H) is the transition temperature in a magnetic field H. In conventional fluctuation theory, GðH Þ ¼ ð8pj2 k B T c H =/0 nc H 2c2 Þ2=3 , where j is the Ginzburg–Landau parameter, nc is the c-axis coherence length and Hc2 is the upper critical field.
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For conventional superconductors, G(H) is usually very small (the order of magnitude is 0.001). Due to the low dimensionality, small superfluid density (1022/cm3), and short coherence length (nc 6 1 nm) and high temperature scales, the G values of cuprates should be 100–1000 times larger than that in conventional superconductors. Let make a rough estimate of G for Bi-2212. Take Tc 85 K for H = 50 kOe, j 100, nc 5 · 108 cm, Hc2 500 kOe, we get G 0.15, and DT 13 K. The estimated G and DT values are quite close to the experimental results. Therefore, in contrast to the underdoped cuprates, the fluctuation effect revealed by Nernst effect measurements in overdoped Bi-2212 is consistent with the Ginzburg– Landau fluctuation theory. 4. Conclusions The studies of resistivity, Hall effect, and Nernst effect in slightly overdoped Bi-2212 indicate that there exist Nernst signals due to vortex-like excitation in a temperature range from Tc0 of 86.5 K up to TO of 105 K. TO is consistent with the onset temperature of superconducting fluctuations, TFL determined from MR and Hall effect. T of pseudogap opening is determined to be about 120 K from the deviation from linear temperature dependence of resistivity. The results imply that superconducting fluctuations exist well above Tc0 even in overdoped HTS. In contrast to the underdoped cuprates, the superconducting effect revealed by Nernst effect is consistent with the Ginzburg–Landau fluctuation theory. Acknowledgement The project was sponsored by the National Science Foundation of China (NSFC 10225417) and the Ministry of Science and Technology of China (Project: NKBRSF-G1999064602).
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