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Characterization of intrinsic Josephson junctions for La2−xSrxCuO4 single crystals
Physica C 367 (2002) 382±387
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Characterization of intrinsic Josephson junctions for La2 x SrxCuO4 single crystals Y. Uematsu a,b,*, Y. Mizugaki a,b, K. Nakajima a,b, T. Yamashita b,c, S. Watauchi b,d, I. Tanaka b,d a
Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan b CREST, Japan Science and Technology Corporation, Japan c New Industry Creation Hatchery Center, Tohoku University, Sendai 980-8579, Japan d Faculty of Engineering, Yamanashi University, Kofu 400-8511, Japan
Abstract We have fabricated c-axis micro-bridges of La2 x Srx CuO4 (LSCO) single crystals in order to characterize the LSCO intrinsic Josephson junctions (IJJs). The current±voltage characteristics of the micro-bridges exhibited a large hysteresis with a voltage jump of the order 0.5±3 V and no multiple branching structures. A superconducting energy gap was clearly observed on the quasi-particle branch and showed BCS-like temperature dependence. In addition, the temperature dependence of the critical current of the IJJ was in good agreement with the theoretical curves for superconductor±insulator±superconductor (SIS) Josephson junctions. These results demonstrate that the IJJs of LSCO are characterized as stacked series SIS junctions. Ó 2002 Published by Elsevier Science B.V. PACS: 74.72.Dn; 74.80.Dm; 74.50.r; 74.25.Jb Keywords: La2 x Srx CuO4 ; Intrinsic Josephson eect
1. Introduction Since the discovery of the intrinsic Josephson eect (IJE) for high-Tc superconducting cuprates (HTSCs) by Kleiner et al. [1,2] a decade ago, there have been numerous breakthroughs that exhibit the exotic features of this phenomenon. Demonstrating the IJE, high-frequency responses, such as those shown by the Fiske steps [3] or the Shapiro steps [4], magnetic ®eld properties, shown by the * Corresponding author. Address: Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan. Tel.: +81-22-217-5474; fax: +81-22-217-5473. E-mail address: [email protected] (Y. Uematsu).
Fraunhofer-like critical current modulation [5,6] and Josephson vortex ¯ow behavior [7], were clearly observed in the current±voltage characteristics (IVCs) of the intrinsic Josephson junctions (IJJs). These experiments have been performed using highly anisotropic HTSCs such as Bi2 Sr2 CaCu2 O8d (BSCCO), whose IJJs are characterized as types of superconductor±insulator±superconductor (SIS) Josephson junctions (JJs). On the other hand, the demonstrations of IVCs for the IJJs in HTSCs with lower anisotropy, such as La2 x Srx CuO4 (LSCO), are still inadequate, although the Josephson plasma phenomena related to IJE have been studied in depth [8±10]. LSCO is an attractive material for investigation of the IJE from several points of view. First, large
0921-4534/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 1 0 3 6 - X
Y. Uematsu et al. / Physica C 367 (2002) 382±387
and high-quality single crystals are relatively easy to synthesize [11]; as a result, the IJJs can be free of imperfections. Second, the anisotropy can be controlled by changing Sr dopant contents unequivocally, i.e., junction properties can be modi®ed nonstoichiometrically. Furthermore, the superconducting layer for LSCO IJJs consists of a single CuO2 plane. This may account for the dierence in the properties of the stacked junction from those of BSCCO, which have a double CuO2 plane in one superconducting layer. Finally, LSCO has a relatively high Josephson plasma frequency due to the low anisotropy, and the frequency range is just in the THz region. This is quite interesting from the point of view of its application for a THz wave-band high-frequency oscillator based on Josephson plasma excitation [12±14]. This paper is a presentation of the details of the IVCs for the IJJs of LSCO. In order to characterize the LSCO IJJs, we have fabricated c-axis micro-bridges of LSCO single crystals using a focused ion beam (FIB) technique, which is proper to fabricate three-dimensional micro-structures [15]. The fundamental IVCs for these c-axis microbridges and the temperature dependence of some parameters on IVCs (critical current, gap voltage, and jump voltage) will be discussed in detail. We will demonstrate that the IJJs of LSCO are characterized as stacked series SIS junctions. 2. Experimental We used high-quality single crystals of underdoped (x 0:09, Tc 22 K) LSCO grown by the traveling-solvent ¯oating-zone (TSFZ) method [11]. Needle-like small LSCO pieces were cut from the TSFZ crystals using a diamond saw. The sizes of these LSCO pieces were typically about 40 40 lm2 in area for the ab-plane and about 500 lm in length along the c-axis. The small LSCO pieces were ®xed onto quartz substrates by silver epoxy and annealed in an oxygen atmosphere at 400 °C for 10 min. The silver epoxy also worked as an electrode at the measurement. By using the FIB etching technique, we fabricated c-axis micro-bridges at the center of each LSCO piece, forming the devices shown in Fig. 1.
383
Fig. 1. Schematic view of the LSCO c-axis micro-bridge.
Hundreds of IJJs were included in the bridges, which were about 1 lm in length (L) along the caxis. The area of the bridge was determined by width (W) and thickness (T). The deviation angle of the bridge direction from the c-axis was less than a few degrees. The electrical measurements were carried out with a standard four-probe method of the Physical Property Measurement System of the Quantum Design Co. Dierential conductance properties (DCPs) were obtained numerically from measured IVCs. 3. Experimental results and discussion Fig. 2(a)±(c) shows the IVCs and DCPs for Sample A (W 20 lm, T 1 lm, L 1 lm) at dierent temperatures (4.2, 18 and 19 K, respectively). These show typical IVCs for SIS-type JJs with low subgap resistance. However, two unconventional features should be noted. First, the IVCs in Fig. 2(a) show negative dynamic resistance on the resistive branch. This is probably the result of the superconducting gap suppression caused by the nonequilibrium superconductivity eect due to quasi-particle injection [16].
384
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Fig. 2. IVCs and DCPs of the LSCO c-axis micro-bridge at dierent temperatures: (a) 4.2 K, (b) 18 K, and (c) 19 K.
Secondly, we observed only one voltage jump, Vj with volt order, i.e., no multiple branching. This feature suggests that all IJJs in the bridges switched simultaneously into a resistive state. Such a collective transition also occurs in oxygen-annealed or Pb-doped Bi-cuprate superconductors, which reveal lower anisotropy (higher Jc and smaller hysteresis) than the typical ones [2,17]. The triggering of the collective transition can be assigned to
a strong interaction between the dierent intrinsic junctions in the array and a modi®cation of the conductance of the barrier [17]. It is suggested that the strength of the interaction between the intrinsic junctions is determined by a critical current density and the thickness of the superconducting layer of the IJJs [18]. In the case of LSCO IJJs, high critical current density due to low anisotropy and a very thin superconducting layer consisting of a single CuO2 layer eciently produce an exceedingly strong interaction; thus, the strong interaction facilitates the driving of the collective transition of the entire array by the switching of one junction. We also designate the eect of the modi®cation of the conductance of the barrier against the collective transition. The higher conductivity of the barrier serves as a matched resistive load [17] as well as the external resistive load that is utilized for the sake of a stabilization of the in-phase locking of the Josephson oscillation for arti®cial junction arrays [19]. Fig. 2 shows a lower hysteretic behavior for LSCO than for the Bi-cuprate superconductor; this denotes the small McCumber parameter value (bc 9), which indicates the higher conductivity of the barrier for IJJs of LSCO. This high conductivity stimulates the phase-locking state for the entire LSCO IJJ array, and, thus, global switching is expected [17]. Judging from the above, it appears that the collective transition could be attributed to the superconducting phase-lock switching of the entire IJJ originating from the essential properties of LSCO IJJs. It is necessary to con®rm that the gap structures on IVCs come from a superconducting energy gap of LSCO, DLSCO . Next, the changes in the gap structures will be examined in the IVCs at dierent temperatures. As shown in Fig. 2(b) and (c), by increasing the temperature, the critical current, Ic decreases, and the quasi-particle injection eect becomes weaker. Thus, the gap suppression decreases, and the gap structure becomes more apparent. In this temperature region (T > 18 K), clear temperature dependence of gap structures can be observed. At higher temperatures, the gap voltage decreases, and the subgap conductance increases. The gap structure disappears slightly
Y. Uematsu et al. / Physica C 367 (2002) 382±387
385
Fig. 3. IVS and DCP of an LSCO c-axis micro-bridge at 10.7.
above Tc . This behavior is very similar to that of a superconducting gap structure. A larger dierence between VG and Vj comes from the dierent temperature dependence at higher temperature for these parameters: VG T is determined by DLSCO T , and Vj T is determined by Ic T . Fig. 3 shows the IVC and DCP for another sample (Sample B, W 20 lm, T 1 lm, L 1 lm) at 10.7 K. For this sample, although a clear gap structure is not seen on the IVCs, a gap structure can be clearly seen on the DCP without a gap suppression. Hence, we can investigate the temperature dependence of the gap voltage in a wide temperature region. Fig. 4 shows the temperature dependence of the DCPs for Sample B. With increasing temperature, the voltage of the gap structure decreases gradually. At a higher temperature, it rapidly decreases, and the structure becomes weak and invisible. For further analysis of the gap structure, the gap voltage vs. the temperature is plotted in Fig. 5. In order to compare the experimental data to the theory, the temperature is normalized by the critical temperature, Tc . The gap voltages at dierent temperatures are normalized by the value at 4.2 K and displayed as squares. As seen in Fig. 5, the temperature dependence of the gap voltage is well ®tted by the BCS theory, which is drawn as a broken line in the ®gure. This behavior strongly suggests that the observed gap structures are the result of a superconducting energy gap. In addition to the gap
Fig. 4. DCPs at dierent temperatures for the sample shown in Fig. 3.
Fig. 5. Temperature dependence of the gap voltage, VG jump voltage, Vj and critical current, Ic . The temperature is normalized by the critical temperature, Tc . VG T ), Vj T , and Ic T are each normalized by the value at low temperature. The broken line, the dotted line, and the solid line represent a theoretical curve for temperature dependence of the superconducting energy gap based on the BCS theory, the A±B relation, and the T±K relation based on the temperature dependence of the gap voltage of our experimental data, respectively. The marks () and ( ) next to the parameters indicate that the values for the parameters are for positive and negative bias, respectively.
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structure, a multiple dierential conductance peak structure can be seen below the gap voltage in the DCP. In our opinion, this characteristic structure may be derived from the Josephson plasma oscillation of the LSCO single crystal. Since this structure is irrelevant to the main subject of this paper, it will be presented in detail in another paper [20]. We also analyzed the temperature dependence of the jump voltage, Vj and the critical current, Ic The jump voltages and the critical current at different temperatures are plotted in Fig. 5. These parameters are normalized by the values at 4.2 K. As shown in Fig. 5, Vj and Ic are well ®tted by the dotted line, which represents the Ambegaokar± Barato (A±B) relation [21]. Considering the pairing symmetry of LSCO, we adopted the Tanaka± Kashiwaya (T±K) theory [22], which describes the temperature dependence of the Josephson critical current for SIS-type coupling of a d-wave superconductor along the c-axis, as well. The solid line in Fig. 5 indicates the T±K ®tting based on the gap values of experimental data and assumes a twodimensional limit. As shown in the ®gure, the T±K curve seems to ®t the experimental data better than the A±B ®tting. Because we have only limited and unpersuasive information to con®rm the pairing symmetry of LSCO, we cannot treat the subject here in detail. Consequently, there is considerable validity to the concept that the IJJs of LSCO are SIS-type JJs. Finally, the number of IJJs in the c-axis microbridge are discussed. Usually, the number of IJJs in the c-axis micro-bridges is estimated from the number of quasi-particle branches on the IVCs or from the length of the IJJ stacks. For our LSCO sample, multiple branches corresponding to the number of IJJs were not observed. In this case, the number of IJJs (N) was estimated from the total gap voltage VG (or total jump voltage Vj ) at low temperature (e.g., at 4.2 K). We can say that VG (or Vj ) at low temperature is N times of gap voltage for the elementary junction, Vg . Previously, we reported that a Vg of about 3.5kB Tc =e could be obtained for LSCO IJJs using mesa-type devices [23]. Consequently, the number of IJJs could be obtained by simply dividing VG (or Vj ) by Vg 3:5kB Tc =e. The calculations show a value of about
150±1000 for our samples. These values are several times smaller than the numbers expected from the bridge length (L 1 lm), NL L=s of about 1500, is the spacing between the CuO2 where s 6:6 A layers for LSCO. This dierence seems reasonable considering the reduction in the junction number derived from the angular deviations of the bridges from the c-axis of LSCO. The maximum angle deviation estimated from the dierence in the junction number was less than a few degrees.
4. Conclusion We studied the IVCs of the FIB-patterned caxis micro-bridges of LSCO single crystals in order to characterize the junction properties of LSCO IJJs. The IVCs of the c-axis micro-bridges exhibited a hysteresis with a large single-voltage jump of the ``volt'' order. Gap structures were also observed and showed BCS-like temperature dependence. The temperature dependence of the critical current was in good agreement with the theoretical curves for both s- and d-wave type SIS JJs. These results demonstrate that the intrinsic Josephson junctions of LSCO are characterized as stacked series SIS junctions.
Acknowledgements The authors are thankful to Dr. S.-J. Kim, Dr. T. Tachiki, and Dr. J. Chen for their valuable technical support and participation in fruitful discussions. Y. Uematsu also wishes to thank Dr. C. Buzea for her critical reading of the manuscript.
References [1] R. Kleiner, F. Steinmeyer, G. Kunkel, P. M uller, Phys. Rev. Lett. 68 (1992) 2394. [2] R. Kleiner, P. M uller, H. Kohlstedt, N.F. Pedersen, S. Sakai, Phys. Rev. B 50 (1994) 3942. [3] H.B. Wang, Y. Aruga, J. Chen, K. Nakajima, T. Yamashita, P.H. Wu, Appl. Phys. Lett. 77 (2000) 1017. [4] V.M. Krasnov, N. Mros, A. Yurgens, D. Winkler, Phys. Rev. B 59 (1999) 8463.
Y. Uematsu et al. / Physica C 367 (2002) 382±387 [5] Yu.I. Latyshev, V.N. Pavlenko, S.-J. Kim, Y. Yamashita, Adv. Supercond. 12 (2000) 47. [6] A. Irie, S. Heim, S. Schromm, M. M oûole, T. Nachtrab, M. G odo, R. Kleiner, P. M uller, G. Oya, Phys. Rev. B 62 (2000) 6681. [7] J.U. Lee, J.E. Nordman, G. Hohenwarter, Appl. Phys. Lett. 67 (1995) 1471. [8] K. Tamasaku, Y. Nakamura, S. Uchida, Phys. Rev. Lett. 70 (1992) 3995. [9] S. Uchida, K. Tamasaku, Physica C 293 (1997) 1. [10] P.J.M. van Bentum, A. Wittlin, M.E.J. Boonman, M. Gross, S. Uchida, Physica C 293 (1997) 136. [11] I. Tanaka, H. Kojima, Nature 337 (1989) 21. [12] M. Tachiki, T. Koyama, S. Takahashi, Phys. Rev. B 50 (1994) 7065. [13] T. Koyama, M. Tachiki, Solid State Commun. 96 (1995) 367. [14] S. Shafranjuk, M. Tachiki, Phys. Rev. B 59 (1999) 14087.
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[15] S.-J. Kim, Yu.I. Latyshev, T. Yamashita, Supercond. Sci. Technol. 12 (1999) 729. [16] M. Suzuki, K. Tanabe, Jpn. J. Appl. Phys. 35 (1996) L482. [17] F.X. Regi, J. Schneck, J.F. Palmier, H. Savaty, J. Appl. Phys. 76 (1994) 4426. [18] M. Sakai, A. Odagawa, H. Adachi, K. Setsune, Physica C 299 (1998) 31. [19] K.Y. Tsang, K. Wiesen®eld, J. Appl. Phys. 70 (1991) 1075. [20] Y. Uematsu, N. Sasaki, Y. Mizugaki, K. Nakajima, T. Yamashita, S. Watauchi, I. Tanaka, Physica C 362 (2001) 290. [21] V. Ambegaokar, A. Barato, Phys. Rev. Lett. 10 (1963) 486. [22] Y. Tanaka, S. Kashiwaya, Phys. Rev. B 56 (1997) 892. [23] Y. Uematsu, Y. Mizugaki, K. Nakajima, T. Yamashita, I. Tanaka, H. Kojima, Intrinsic Josephson eect in LSCO single crystal, Extended Abstracts (The 46th Spring Meeting, 1999); The Japan Society of Applied Physics (in Japanese).
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Characterization of intrinsic Josephson junctions for La2 x SrxCuO4 single crystals Y. Uematsu a,b,*, Y. Mizugaki a,b, K. Nakajima a,b, T. Yamashita b,c, S. Watauchi b,d, I. Tanaka b,d a
Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan b CREST, Japan Science and Technology Corporation, Japan c New Industry Creation Hatchery Center, Tohoku University, Sendai 980-8579, Japan d Faculty of Engineering, Yamanashi University, Kofu 400-8511, Japan
Abstract We have fabricated c-axis micro-bridges of La2 x Srx CuO4 (LSCO) single crystals in order to characterize the LSCO intrinsic Josephson junctions (IJJs). The current±voltage characteristics of the micro-bridges exhibited a large hysteresis with a voltage jump of the order 0.5±3 V and no multiple branching structures. A superconducting energy gap was clearly observed on the quasi-particle branch and showed BCS-like temperature dependence. In addition, the temperature dependence of the critical current of the IJJ was in good agreement with the theoretical curves for superconductor±insulator±superconductor (SIS) Josephson junctions. These results demonstrate that the IJJs of LSCO are characterized as stacked series SIS junctions. Ó 2002 Published by Elsevier Science B.V. PACS: 74.72.Dn; 74.80.Dm; 74.50.r; 74.25.Jb Keywords: La2 x Srx CuO4 ; Intrinsic Josephson eect
1. Introduction Since the discovery of the intrinsic Josephson eect (IJE) for high-Tc superconducting cuprates (HTSCs) by Kleiner et al. [1,2] a decade ago, there have been numerous breakthroughs that exhibit the exotic features of this phenomenon. Demonstrating the IJE, high-frequency responses, such as those shown by the Fiske steps [3] or the Shapiro steps [4], magnetic ®eld properties, shown by the * Corresponding author. Address: Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan. Tel.: +81-22-217-5474; fax: +81-22-217-5473. E-mail address: [email protected] (Y. Uematsu).
Fraunhofer-like critical current modulation [5,6] and Josephson vortex ¯ow behavior [7], were clearly observed in the current±voltage characteristics (IVCs) of the intrinsic Josephson junctions (IJJs). These experiments have been performed using highly anisotropic HTSCs such as Bi2 Sr2 CaCu2 O8d (BSCCO), whose IJJs are characterized as types of superconductor±insulator±superconductor (SIS) Josephson junctions (JJs). On the other hand, the demonstrations of IVCs for the IJJs in HTSCs with lower anisotropy, such as La2 x Srx CuO4 (LSCO), are still inadequate, although the Josephson plasma phenomena related to IJE have been studied in depth [8±10]. LSCO is an attractive material for investigation of the IJE from several points of view. First, large
0921-4534/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 1 0 3 6 - X
Y. Uematsu et al. / Physica C 367 (2002) 382±387
and high-quality single crystals are relatively easy to synthesize [11]; as a result, the IJJs can be free of imperfections. Second, the anisotropy can be controlled by changing Sr dopant contents unequivocally, i.e., junction properties can be modi®ed nonstoichiometrically. Furthermore, the superconducting layer for LSCO IJJs consists of a single CuO2 plane. This may account for the dierence in the properties of the stacked junction from those of BSCCO, which have a double CuO2 plane in one superconducting layer. Finally, LSCO has a relatively high Josephson plasma frequency due to the low anisotropy, and the frequency range is just in the THz region. This is quite interesting from the point of view of its application for a THz wave-band high-frequency oscillator based on Josephson plasma excitation [12±14]. This paper is a presentation of the details of the IVCs for the IJJs of LSCO. In order to characterize the LSCO IJJs, we have fabricated c-axis micro-bridges of LSCO single crystals using a focused ion beam (FIB) technique, which is proper to fabricate three-dimensional micro-structures [15]. The fundamental IVCs for these c-axis microbridges and the temperature dependence of some parameters on IVCs (critical current, gap voltage, and jump voltage) will be discussed in detail. We will demonstrate that the IJJs of LSCO are characterized as stacked series SIS junctions. 2. Experimental We used high-quality single crystals of underdoped (x 0:09, Tc 22 K) LSCO grown by the traveling-solvent ¯oating-zone (TSFZ) method [11]. Needle-like small LSCO pieces were cut from the TSFZ crystals using a diamond saw. The sizes of these LSCO pieces were typically about 40 40 lm2 in area for the ab-plane and about 500 lm in length along the c-axis. The small LSCO pieces were ®xed onto quartz substrates by silver epoxy and annealed in an oxygen atmosphere at 400 °C for 10 min. The silver epoxy also worked as an electrode at the measurement. By using the FIB etching technique, we fabricated c-axis micro-bridges at the center of each LSCO piece, forming the devices shown in Fig. 1.
383
Fig. 1. Schematic view of the LSCO c-axis micro-bridge.
Hundreds of IJJs were included in the bridges, which were about 1 lm in length (L) along the caxis. The area of the bridge was determined by width (W) and thickness (T). The deviation angle of the bridge direction from the c-axis was less than a few degrees. The electrical measurements were carried out with a standard four-probe method of the Physical Property Measurement System of the Quantum Design Co. Dierential conductance properties (DCPs) were obtained numerically from measured IVCs. 3. Experimental results and discussion Fig. 2(a)±(c) shows the IVCs and DCPs for Sample A (W 20 lm, T 1 lm, L 1 lm) at dierent temperatures (4.2, 18 and 19 K, respectively). These show typical IVCs for SIS-type JJs with low subgap resistance. However, two unconventional features should be noted. First, the IVCs in Fig. 2(a) show negative dynamic resistance on the resistive branch. This is probably the result of the superconducting gap suppression caused by the nonequilibrium superconductivity eect due to quasi-particle injection [16].
384
Y. Uematsu et al. / Physica C 367 (2002) 382±387
Fig. 2. IVCs and DCPs of the LSCO c-axis micro-bridge at dierent temperatures: (a) 4.2 K, (b) 18 K, and (c) 19 K.
Secondly, we observed only one voltage jump, Vj with volt order, i.e., no multiple branching. This feature suggests that all IJJs in the bridges switched simultaneously into a resistive state. Such a collective transition also occurs in oxygen-annealed or Pb-doped Bi-cuprate superconductors, which reveal lower anisotropy (higher Jc and smaller hysteresis) than the typical ones [2,17]. The triggering of the collective transition can be assigned to
a strong interaction between the dierent intrinsic junctions in the array and a modi®cation of the conductance of the barrier [17]. It is suggested that the strength of the interaction between the intrinsic junctions is determined by a critical current density and the thickness of the superconducting layer of the IJJs [18]. In the case of LSCO IJJs, high critical current density due to low anisotropy and a very thin superconducting layer consisting of a single CuO2 layer eciently produce an exceedingly strong interaction; thus, the strong interaction facilitates the driving of the collective transition of the entire array by the switching of one junction. We also designate the eect of the modi®cation of the conductance of the barrier against the collective transition. The higher conductivity of the barrier serves as a matched resistive load [17] as well as the external resistive load that is utilized for the sake of a stabilization of the in-phase locking of the Josephson oscillation for arti®cial junction arrays [19]. Fig. 2 shows a lower hysteretic behavior for LSCO than for the Bi-cuprate superconductor; this denotes the small McCumber parameter value (bc 9), which indicates the higher conductivity of the barrier for IJJs of LSCO. This high conductivity stimulates the phase-locking state for the entire LSCO IJJ array, and, thus, global switching is expected [17]. Judging from the above, it appears that the collective transition could be attributed to the superconducting phase-lock switching of the entire IJJ originating from the essential properties of LSCO IJJs. It is necessary to con®rm that the gap structures on IVCs come from a superconducting energy gap of LSCO, DLSCO . Next, the changes in the gap structures will be examined in the IVCs at dierent temperatures. As shown in Fig. 2(b) and (c), by increasing the temperature, the critical current, Ic decreases, and the quasi-particle injection eect becomes weaker. Thus, the gap suppression decreases, and the gap structure becomes more apparent. In this temperature region (T > 18 K), clear temperature dependence of gap structures can be observed. At higher temperatures, the gap voltage decreases, and the subgap conductance increases. The gap structure disappears slightly
Y. Uematsu et al. / Physica C 367 (2002) 382±387
385
Fig. 3. IVS and DCP of an LSCO c-axis micro-bridge at 10.7.
above Tc . This behavior is very similar to that of a superconducting gap structure. A larger dierence between VG and Vj comes from the dierent temperature dependence at higher temperature for these parameters: VG T is determined by DLSCO T , and Vj T is determined by Ic T . Fig. 3 shows the IVC and DCP for another sample (Sample B, W 20 lm, T 1 lm, L 1 lm) at 10.7 K. For this sample, although a clear gap structure is not seen on the IVCs, a gap structure can be clearly seen on the DCP without a gap suppression. Hence, we can investigate the temperature dependence of the gap voltage in a wide temperature region. Fig. 4 shows the temperature dependence of the DCPs for Sample B. With increasing temperature, the voltage of the gap structure decreases gradually. At a higher temperature, it rapidly decreases, and the structure becomes weak and invisible. For further analysis of the gap structure, the gap voltage vs. the temperature is plotted in Fig. 5. In order to compare the experimental data to the theory, the temperature is normalized by the critical temperature, Tc . The gap voltages at dierent temperatures are normalized by the value at 4.2 K and displayed as squares. As seen in Fig. 5, the temperature dependence of the gap voltage is well ®tted by the BCS theory, which is drawn as a broken line in the ®gure. This behavior strongly suggests that the observed gap structures are the result of a superconducting energy gap. In addition to the gap
Fig. 4. DCPs at dierent temperatures for the sample shown in Fig. 3.
Fig. 5. Temperature dependence of the gap voltage, VG jump voltage, Vj and critical current, Ic . The temperature is normalized by the critical temperature, Tc . VG T ), Vj T , and Ic T are each normalized by the value at low temperature. The broken line, the dotted line, and the solid line represent a theoretical curve for temperature dependence of the superconducting energy gap based on the BCS theory, the A±B relation, and the T±K relation based on the temperature dependence of the gap voltage of our experimental data, respectively. The marks () and ( ) next to the parameters indicate that the values for the parameters are for positive and negative bias, respectively.
386
Y. Uematsu et al. / Physica C 367 (2002) 382±387
structure, a multiple dierential conductance peak structure can be seen below the gap voltage in the DCP. In our opinion, this characteristic structure may be derived from the Josephson plasma oscillation of the LSCO single crystal. Since this structure is irrelevant to the main subject of this paper, it will be presented in detail in another paper [20]. We also analyzed the temperature dependence of the jump voltage, Vj and the critical current, Ic The jump voltages and the critical current at different temperatures are plotted in Fig. 5. These parameters are normalized by the values at 4.2 K. As shown in Fig. 5, Vj and Ic are well ®tted by the dotted line, which represents the Ambegaokar± Barato (A±B) relation [21]. Considering the pairing symmetry of LSCO, we adopted the Tanaka± Kashiwaya (T±K) theory [22], which describes the temperature dependence of the Josephson critical current for SIS-type coupling of a d-wave superconductor along the c-axis, as well. The solid line in Fig. 5 indicates the T±K ®tting based on the gap values of experimental data and assumes a twodimensional limit. As shown in the ®gure, the T±K curve seems to ®t the experimental data better than the A±B ®tting. Because we have only limited and unpersuasive information to con®rm the pairing symmetry of LSCO, we cannot treat the subject here in detail. Consequently, there is considerable validity to the concept that the IJJs of LSCO are SIS-type JJs. Finally, the number of IJJs in the c-axis microbridge are discussed. Usually, the number of IJJs in the c-axis micro-bridges is estimated from the number of quasi-particle branches on the IVCs or from the length of the IJJ stacks. For our LSCO sample, multiple branches corresponding to the number of IJJs were not observed. In this case, the number of IJJs (N) was estimated from the total gap voltage VG (or total jump voltage Vj ) at low temperature (e.g., at 4.2 K). We can say that VG (or Vj ) at low temperature is N times of gap voltage for the elementary junction, Vg . Previously, we reported that a Vg of about 3.5kB Tc =e could be obtained for LSCO IJJs using mesa-type devices [23]. Consequently, the number of IJJs could be obtained by simply dividing VG (or Vj ) by Vg 3:5kB Tc =e. The calculations show a value of about
150±1000 for our samples. These values are several times smaller than the numbers expected from the bridge length (L 1 lm), NL L=s of about 1500, is the spacing between the CuO2 where s 6:6 A layers for LSCO. This dierence seems reasonable considering the reduction in the junction number derived from the angular deviations of the bridges from the c-axis of LSCO. The maximum angle deviation estimated from the dierence in the junction number was less than a few degrees.
4. Conclusion We studied the IVCs of the FIB-patterned caxis micro-bridges of LSCO single crystals in order to characterize the junction properties of LSCO IJJs. The IVCs of the c-axis micro-bridges exhibited a hysteresis with a large single-voltage jump of the ``volt'' order. Gap structures were also observed and showed BCS-like temperature dependence. The temperature dependence of the critical current was in good agreement with the theoretical curves for both s- and d-wave type SIS JJs. These results demonstrate that the intrinsic Josephson junctions of LSCO are characterized as stacked series SIS junctions.
Acknowledgements The authors are thankful to Dr. S.-J. Kim, Dr. T. Tachiki, and Dr. J. Chen for their valuable technical support and participation in fruitful discussions. Y. Uematsu also wishes to thank Dr. C. Buzea for her critical reading of the manuscript.
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