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Doping effect on pairing symmetry in cuprate superconductors
Journal of Physics and Chemistry of Solids 67 (2006) 64–67 www.elsevier.com/locate/jpcs
Doping effect on pairing symmetry in cuprate superconductors C.C. Tsuei a,*, J.R. Kirtley a, G. Hammerl b,*, J. Mannhart b, H. Raffy c, Z.Z. Li c b
a IBM T.J. Watson Research Center, Yorktown Heights, New York, NY 10598, USA Experimental Physics VI, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany c Laboratoire de Physique des Solides, Universite Paris-sud, 91405 Orsay, France
Abstract We have done a series of tricrystal experiments to investigate the doping dependence of pairing symmetry in various hole-doped cuprate superconductors with doping levels ranging from underdoped to overdoped regimes. The results of this work have indicated that the dx2Ky2 pair state is robust against a wide range of doping variation. Our findings underscore the importance of strong on-site Coulomb repulsion in pairing interaction, which favors the dx2Ky2 -wave pairing symmetry over pair states with other symmetries. q 2005 Elsevier Ltd. All rights reserved. Keywords: A. Oxides; A. Superconductors; D. Superconductivity; D. Magnetic properties PACS: 74.60.Ge; 74.72.Bk
1. Introduction A definitive determination of the symmetry of the pair wavefunction in cuprate superconductors represents an important part of the key to the resolution of the mechanism for high-temperature superconductivity. Through the recent advent of phase-sensitive pairing symmetry experiments, and the earlier work on penetration depth, photo-emission, quasiparticle tunneling, . etc., an order parameter with dx2Ky2 symmetry has been established in optimally hole- and electrondoped superconducting cuprates [1]. However, despite numerous theoretical and experimental studies in recent years, the issue of whether there is a doping-induced change in the pairing symmetry of high-temperature superconductors away from optimal doping remains highly controversial. Early measurements of low-temperature in-plane penetration depths have already suggested that the basic nature of the d-wave energy gap is preserved over a wide range of doping in various cuprate systems [2]. More recent work on the doping dependence of pairing symmetry, however, has produced a variety of conflicting results. For example, quasi-particle tunneling spectroscopy indicates a significant fraction
* Corresponding author. Tel.: C1 914 945 2799; fax: C1 914 945 2141. E-mail address: [email protected] (C.C. Tsuei).
0022-3697/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2005.10.041
of s-wave component in the pairing wavefunction of overdoped Y1Kx Cax Ba2 Cu3 O7Kd [3], and a change in pairing symmetry from that of the dx2Ky2 wave pair state to the time-reversal symmetry broken dx2Ky2 C idxy or dx2Ky2 C is pair states in overdoped YBa2Cu3O7 (YBCO) [4,5]. On the other hand, the residual electronic thermal conductivity consistent with a twodimensional d-wave BCS superconductor [6] was observed in La2Kx Srx CuO4 (LSCO) single crystals throughout the entire doping range ð0:05! x% 0:22Þ [7]. An equally confusing situation exists for the electron-doped cuprates. It is by now generally agreed that, based on phase-sensitive tricrystal experiments, Nd2Kx Cex CuO4 (NCCO) and Pr2Kx Cex CuO4 (PCCO) at optimal doping ðx w0:15Þ are superconductors with dx2Ky2 pairing symmetry [8]. Also, recent quasi-particle tunneling data provides strong supporting evidence for d-wave pairing in the optimally electron-doped La2Kx Cex CuO4 (xZ0.112) [9]. Recent penetration depth measurements of PCCO and La2Kx Cex CuO4 (LCCO) suggests a transition from d-wave to s-wave pairing near optimal doping [10]. However, an independent penetration depth study found evidence for d-wave pairing at doping levels covering the underdoped, optimally doped and overdoped regimes in PCCO [11]. The disagreements described above stem mainly from the fact that conventional pairing symmetry tests that utilize measurements of temperature-dependent penetration depth, quasi-particle tunneling characteristics probe the magnitude of the order parameter but not its phase. Further, the data analysis is often model-dependent. In the following, we will present
C.C. Tsuei et al. / Journal of Physics and Chemistry of Solids 67 (2006) 64–67
a series of phase-sensitive tricrystal experiments in search of a doping-induced pairing symmetry change in cuprate superconductors. 2. Tricrystal pairing symmetry experiments As a consequence of nodes in an unconventional gap function such as that in the dx2Ky2 -wave pair state, it is possible to have an odd number of sign changes in the circulating supercurrent in a superconducting loop containing properly configured Josephson junctions made with at least one unconventional (e.g. d-wave) superconductor. Such a loop is characterized by a net phase-shift of p (hence termed a p-loop/ring). The extra cost of Josephson coupling energy arising from the p phase-shift is reduced by the spontaneous generation of a circulating supercurrent which results in a Josephson vortex of half-flux quantum ð1=2F0 Z h=4eZ 1:035 !10K15 WbÞ, threading through the loop. This half-integer flux quantum effect has been the basis of a new class of phase-sensitive tests for pairing symmetry in high-temperature superconductors [1]. In particular, a series of tricrystal experiments have been used to establish the dx2Ky2 wave pairing symmetry in cuprates. Shown in Fig. 1(a) is the basic design of the tricrystal experiments [12]. The crystal orientations were chosen so that the central ring, which contains three grain-boundary junctions, is a p-ring if the cuprate under test is a dx2Ky2 -wave superconductor. Fig. 1(b) shows a scanning SQUID microscope (SSM) [13] image of four optimally doped YBCO rings on a tricrystal (100) SrTiO3 (STO) substrate with the configuration of Fig. 1(a). The fact that spontaneous half-flux magnetization is only observed in the 3-junction ring, but not in the 2- and 0-junction rings, represents strong evidence for d-wave pairing symmetry in YBCO. Since the half-flux quantum effect is a manifestation
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of the ground state in any singly connected superconducting loop with a net phase-shift of p, its observation should be independent of the macroscopic configuration of the loop. Indeed, a Josephson vortex with a total flux of F0 =2 is observed at the tricrystal meeting point in c-axis oriented YBCO films [14] (Fig. 2(a)) and disks [15] (Fig. 2(b)) deposited on the tricrystal STO substrates with the same geometry as that of Fig. 1(a). In recent years, the direct observation of the half-flux quantum effect with a SSM, in unpatterned cuprate films has been employed as an unambiguous signature for establishing the dx2Ky2 pairing symmetry in various optimally hole- and electron-doped cuprate superconductors [1]. 3. Results of doping study The technique of tricrystal pairing symmetry test using unpatterned cuprate films is well adapted for studying the doping effect on pairing symmetry. The robust nature of the dx2Ky2 pairing against a wide range of doping variation has been demonstrated in such tricrystal experiments. For example, the half-flux quantum effect is observed in an overdoped Y0:7 Ca0:3 Ba2 Cu3 O7Kd film (Fig. 3) deposited on a tricrystal STO substrate with the configuration of Fig. 1(a). The over-doped Ca-YBCO films are characterized by sufficiently high grain boundary current densities [16] that Josephson vortices in the grain boundaries and at the tricrystal point are resolution limited with a 4-mm diameter pickup loop. The integrated magnetic flux from the Josephson vortex at the tricrystal point (Fig. 3(a)) can be expressed, in units of F0 , as a function of Aint , the circular area, centered at the tricrystal point, over which the flux is integrated (see Fig. 3(b)). For comparison, the data points for an Abrikosov vortex of F0 inside of a crystal grain of the sample is also shown in Fig. 3(b).
Fig. 1. (a) Schematic of the original tricrystal ring pairing symmetry experiments [12]. The polar plots represent the amplitude and phase of the pairing wavefunction of the cuprate thin-film superconductors, assumed to have dx2Ky2 orbital pairing symmetry, which are epitaxially grown on the Sr2 TiO3 tricrystal substrate, with the (001) tilt grain boundaries between them represented as solid lines. The circles are 50 mm diameter, 10 mm wall thickness, photolithographically patterned optimally doped thin-film Ya2 Cu3 O7Kd rings. (b) Scanning SQUID microscope image of this sample, cooled in zero field and imaged at 4.2 K. The central (p-) ring shows spontaneous magnetization corresponding to half of a superconducting flux quantum trapped in the ring. The three outer control (0-) rings show no spontaneous magnetization.
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Fig. 2. (a) Scanning SQUID microscope image of an unpatterned YBCO film epitaxially grown on a tricrystal substrate with the geometry of Fig. 1(a), cooled in a field of a few mG, and imaged at 4.2 K. Visible are 7 Abrikosov vortices in the crystals, 4 integer Josephson vortices trapped in the grain boundaries, and a half-flux quantum Josephson vortex at the tricrystal meeting point [14]. (b) Similar tricrystal experiment by Sugimoto, Yamaguchi, and Iguchi [15].
A series of tricrystal experiments have been carried out also with Bi2 Sr2 CaCu2 O8Cd (BSCCO) films of various doping concentrations. Through thermal annealing [17], the doping level of a given BSCCO film can be varied to cover the underdoped, through optimal doping, to overdoped regimes. The half-flux quantum effect at the tricrystal point was monitored as a function of such annealing. The dx2Ky2 pairing symmetry was found to persist throughout the entire doping range studied so far (Fig. 4). The crystal structure of all the BSCCO samples studied here is tetragonal equivalent. A dCs mixed pair state in BSCCO is therefore symmetry forbidden [1]. A summary of the results of the BSCCO tricrystal experiments, along with several other cuprate superconductors is displayed in Fig. 5 to show the doping range over which the d-wave pair state prevails. 4. Discussion and concluding remarks The tricrystal experiments described here, combined with previous work establishing d-wave pairing symmetry for
a number of optimally doped hole- and electron-doped cuprates [1], have provided phase-sensitive evidence for the absence of doping-induced pairing symmetry change away from optimal doping in several cuprate systems covering a wide range of doping. It is particularly remarkable that, in the face of competing orders such as charge density wave and antiferromagnetism [19,20], the dx2Ky2 pairing survives in the ultralow doping regime (e.g. as indicated in Fig. 5 for the BSCCO system). A similar conclusion has been reached from a recent study of c-axis penetration depth as a function of temperature and doping in YBa2 Cu3 O7Kd , suggesting that the dx2Ky2 nodal quasi-particles survive to very low doping [21]. The fact that many superconducting and normal-state properties of the cuprate superconductors are doping-dependent [22] while the d-wave pairing symmetry is not requires a generic origin of the doping-independent pairing symmetry in all the cuprates studied so far. We suggest that all evidence points to strong on-site Coulomb repulsion, a characteristic common to all cuprates, which is also responsible for the
Fig. 3. (a) Three-dimensional rendering of the magnetic flux at the tricrystal point for an unpatterned Ya0:7 Ca0:3 Ba2 Cu3 O7Kd film epitaxially grown on a tricrystal substrate with the geometry of Fig. 1(a), cooled in zero field and imaged at 4.2 K. (b) Total integrated magnetic flux from two vortices. The solid points are for the Josephson F0 =2 vortex at the tricrystal point; the open points are for an Abrikosov F0 vortex in the bulk of the sample.
C.C. Tsuei et al. / Journal of Physics and Chemistry of Solids 67 (2006) 64–67
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the dx2Ky2 channel of a Hubbard model is enhanced by an increasing on-site repulsion on the Cu sites and suppressed by inter-site Coulomb interactions [27]. Furthermore, the robust nature of dx2Ky2 pairing over a wide doping range ð0! p% 0:35Þ has been demonstrated by several numerical studies based on Hubbard models [28,29], consistent with the findings of this work. In summary, our phase-sensitive tricrystal experiments have demonstrated the absence of doping-induced pairing symmetry change in a number of superconducting cuprate systems, underscoring the importance of on-site Coulomb repulsion in the making high-temperature superconductivity. Acknowledgements Fig. 4. Examples of a series of tricrystal symmetry pairing experiments from BSCCO films grown epitaxially on a substrate with the geometry of Fig. 1(a), at three different oxygen doping concentrations. In all cases, there is a halfquantum Josephson vortex at the tricrystal point, indicating dx2Ky2 wavefunction pairing symmetry.
We would like to thank B. Chesca, I. Iguchi, R.H. Koch and D.M. Newns for useful discussions. The work of G.H. and J.M. was supported by the BMBF (SFB484) and the ESF (PiShift). References
Fig. 5. Graphical representation of the range of doping covered in the experiments reported in this paper. The vertical positions of the solid points are the measured critical temperatures Tc of the samples. The horizontal positions are the sample hole concentrations p, calculated from Tc using the empirical relation[18] (solid line) Tc ðpÞZ Tc;max ½1K82:6ðpKpc Þ2 . Here Tc,max is the critical temperature of the optimally doped material in each compound, and pcZ0.16.
universally observed Mott metal–insulator transition in perovskites. It is now generally accepted that, as first suggested by Anderson [23,24], a Hubbard model based on strong Coulomb interactions in the CuO2 planes can capture the essence of physics in high-temperature superconductors. With the constraint of no on-site double occupancy, one can show that within the framework of a two-dimensional Hubbard/t–J model, a superconducting ground state with dx2Ky2 symmetry is favored over dxy and extended s-wave (s * ) states [25,26] for parameters relevant to cuprates. Even without knowing the microscopic pairing mechanism, one can show that pairing in
[1] C.C. Tsuei, J.R. Kirtley, Rev. Mod. Phys. 72 (2000) 969. [2] C. Panagopoulos, T. Xiang, Phys. Rev. Lett. 81 (1998) 2336; C. Panagopoulos, et al., Phys. Rev. B 60 (1999) 14617. [3] N.-C. Yeh, et al., Phys. Rev. Lett. 87 (2001) 87003. [4] Y. Dagan, G. Deutscher, Phys. Rev. Lett. 87 (2001) 177004. [5] A. Sharoni, et al., Phys. Rev. B 65 (2002) 134526. [6] P.A. Lee, Phys. Rev. Lett. 71 (1993) 1887; A.C. Durst, P.A. Lee, Phys. Rev. B 62 (2000) 1270. [7] J. Takeya, et al., Phys. Rev. Lett. 88 (2002) 77001. [8] C.C. Tsuei, J.R. Kirtley, Phys. Rev. Lett. 85 (2000) 182. [9] B. Chesca, et al., Phys. Rev. Lett. 90 (2003) 057004; B. Chesca, et al., cond-mat/0402131. [10] J.A. Skinta, et al., Phys. Rev. Lett. 88 (2001) 207005. [11] A. Snezko, et al., Phys. Rev. Lett. 92 (2004) 157005. [12] C.C. Tsuei, et al., Phys. Rev. Lett. 73 (1994) 593. [13] J.R. Kirtley, et al., Appl. Phys. Lett. 66 (1995) 1138. [14] J.R. Kirtley, et al., Phys. Rev. Lett. 76 (1996) 1336. [15] A. Sugimoto, Y. Yamaguchi, I. Iguchi, S. Kasigawa, Physica C 367 (2002) 28. [16] G. Hammerl, et al., Nature 407 (2000) 162. [17] Z. Konstantinovic, Z.Z. Li, H. Raffy, Physica B 259–261 (1999) 567. [18] M.R. Presland, et al., Physica C 176 (1991) 95. [19] S. Sachdev, Rev. Mod. Phys. 75 (2003) 913. [20] M. Vojta, et al., Phys. Rev. B 62 (2000) 6721. [21] H. Hosseini, et al., cond-mat/0312542. [22] J. Orenstein, A.J. Millis, Science 288 (2000) 468. [23] P.W. Anderson, Science 235 (1987) 1196. [24] P.W. Anderson, P.A. Lee, M. Randeria, T.M. Rice, N. Triveda, F.C. Zhang, cond-mat/0311467, and references therein. [25] E. Dagotto, Rev. Mod. Phys. 66 (1994) 763. [26] N. Bulut, Adv. Phys. 51 (2002) 1587 (and references therein). [27] E. Plekhanov, S. Sorella, M. Fabrizio, Phys. Rev. Lett. 90 (2003) 187004. [28] A. Paramekanti, M. Randeria, N. Trivedi, Phys. Rev. Lett. 87 (2001) 217002. [29] S. Sorella, et al., Phys. Rev. Lett. 88 (2002) 117002.
Doping effect on pairing symmetry in cuprate superconductors C.C. Tsuei a,*, J.R. Kirtley a, G. Hammerl b,*, J. Mannhart b, H. Raffy c, Z.Z. Li c b
a IBM T.J. Watson Research Center, Yorktown Heights, New York, NY 10598, USA Experimental Physics VI, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany c Laboratoire de Physique des Solides, Universite Paris-sud, 91405 Orsay, France
Abstract We have done a series of tricrystal experiments to investigate the doping dependence of pairing symmetry in various hole-doped cuprate superconductors with doping levels ranging from underdoped to overdoped regimes. The results of this work have indicated that the dx2Ky2 pair state is robust against a wide range of doping variation. Our findings underscore the importance of strong on-site Coulomb repulsion in pairing interaction, which favors the dx2Ky2 -wave pairing symmetry over pair states with other symmetries. q 2005 Elsevier Ltd. All rights reserved. Keywords: A. Oxides; A. Superconductors; D. Superconductivity; D. Magnetic properties PACS: 74.60.Ge; 74.72.Bk
1. Introduction A definitive determination of the symmetry of the pair wavefunction in cuprate superconductors represents an important part of the key to the resolution of the mechanism for high-temperature superconductivity. Through the recent advent of phase-sensitive pairing symmetry experiments, and the earlier work on penetration depth, photo-emission, quasiparticle tunneling, . etc., an order parameter with dx2Ky2 symmetry has been established in optimally hole- and electrondoped superconducting cuprates [1]. However, despite numerous theoretical and experimental studies in recent years, the issue of whether there is a doping-induced change in the pairing symmetry of high-temperature superconductors away from optimal doping remains highly controversial. Early measurements of low-temperature in-plane penetration depths have already suggested that the basic nature of the d-wave energy gap is preserved over a wide range of doping in various cuprate systems [2]. More recent work on the doping dependence of pairing symmetry, however, has produced a variety of conflicting results. For example, quasi-particle tunneling spectroscopy indicates a significant fraction
* Corresponding author. Tel.: C1 914 945 2799; fax: C1 914 945 2141. E-mail address: [email protected] (C.C. Tsuei).
0022-3697/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2005.10.041
of s-wave component in the pairing wavefunction of overdoped Y1Kx Cax Ba2 Cu3 O7Kd [3], and a change in pairing symmetry from that of the dx2Ky2 wave pair state to the time-reversal symmetry broken dx2Ky2 C idxy or dx2Ky2 C is pair states in overdoped YBa2Cu3O7 (YBCO) [4,5]. On the other hand, the residual electronic thermal conductivity consistent with a twodimensional d-wave BCS superconductor [6] was observed in La2Kx Srx CuO4 (LSCO) single crystals throughout the entire doping range ð0:05! x% 0:22Þ [7]. An equally confusing situation exists for the electron-doped cuprates. It is by now generally agreed that, based on phase-sensitive tricrystal experiments, Nd2Kx Cex CuO4 (NCCO) and Pr2Kx Cex CuO4 (PCCO) at optimal doping ðx w0:15Þ are superconductors with dx2Ky2 pairing symmetry [8]. Also, recent quasi-particle tunneling data provides strong supporting evidence for d-wave pairing in the optimally electron-doped La2Kx Cex CuO4 (xZ0.112) [9]. Recent penetration depth measurements of PCCO and La2Kx Cex CuO4 (LCCO) suggests a transition from d-wave to s-wave pairing near optimal doping [10]. However, an independent penetration depth study found evidence for d-wave pairing at doping levels covering the underdoped, optimally doped and overdoped regimes in PCCO [11]. The disagreements described above stem mainly from the fact that conventional pairing symmetry tests that utilize measurements of temperature-dependent penetration depth, quasi-particle tunneling characteristics probe the magnitude of the order parameter but not its phase. Further, the data analysis is often model-dependent. In the following, we will present
C.C. Tsuei et al. / Journal of Physics and Chemistry of Solids 67 (2006) 64–67
a series of phase-sensitive tricrystal experiments in search of a doping-induced pairing symmetry change in cuprate superconductors. 2. Tricrystal pairing symmetry experiments As a consequence of nodes in an unconventional gap function such as that in the dx2Ky2 -wave pair state, it is possible to have an odd number of sign changes in the circulating supercurrent in a superconducting loop containing properly configured Josephson junctions made with at least one unconventional (e.g. d-wave) superconductor. Such a loop is characterized by a net phase-shift of p (hence termed a p-loop/ring). The extra cost of Josephson coupling energy arising from the p phase-shift is reduced by the spontaneous generation of a circulating supercurrent which results in a Josephson vortex of half-flux quantum ð1=2F0 Z h=4eZ 1:035 !10K15 WbÞ, threading through the loop. This half-integer flux quantum effect has been the basis of a new class of phase-sensitive tests for pairing symmetry in high-temperature superconductors [1]. In particular, a series of tricrystal experiments have been used to establish the dx2Ky2 wave pairing symmetry in cuprates. Shown in Fig. 1(a) is the basic design of the tricrystal experiments [12]. The crystal orientations were chosen so that the central ring, which contains three grain-boundary junctions, is a p-ring if the cuprate under test is a dx2Ky2 -wave superconductor. Fig. 1(b) shows a scanning SQUID microscope (SSM) [13] image of four optimally doped YBCO rings on a tricrystal (100) SrTiO3 (STO) substrate with the configuration of Fig. 1(a). The fact that spontaneous half-flux magnetization is only observed in the 3-junction ring, but not in the 2- and 0-junction rings, represents strong evidence for d-wave pairing symmetry in YBCO. Since the half-flux quantum effect is a manifestation
65
of the ground state in any singly connected superconducting loop with a net phase-shift of p, its observation should be independent of the macroscopic configuration of the loop. Indeed, a Josephson vortex with a total flux of F0 =2 is observed at the tricrystal meeting point in c-axis oriented YBCO films [14] (Fig. 2(a)) and disks [15] (Fig. 2(b)) deposited on the tricrystal STO substrates with the same geometry as that of Fig. 1(a). In recent years, the direct observation of the half-flux quantum effect with a SSM, in unpatterned cuprate films has been employed as an unambiguous signature for establishing the dx2Ky2 pairing symmetry in various optimally hole- and electron-doped cuprate superconductors [1]. 3. Results of doping study The technique of tricrystal pairing symmetry test using unpatterned cuprate films is well adapted for studying the doping effect on pairing symmetry. The robust nature of the dx2Ky2 pairing against a wide range of doping variation has been demonstrated in such tricrystal experiments. For example, the half-flux quantum effect is observed in an overdoped Y0:7 Ca0:3 Ba2 Cu3 O7Kd film (Fig. 3) deposited on a tricrystal STO substrate with the configuration of Fig. 1(a). The over-doped Ca-YBCO films are characterized by sufficiently high grain boundary current densities [16] that Josephson vortices in the grain boundaries and at the tricrystal point are resolution limited with a 4-mm diameter pickup loop. The integrated magnetic flux from the Josephson vortex at the tricrystal point (Fig. 3(a)) can be expressed, in units of F0 , as a function of Aint , the circular area, centered at the tricrystal point, over which the flux is integrated (see Fig. 3(b)). For comparison, the data points for an Abrikosov vortex of F0 inside of a crystal grain of the sample is also shown in Fig. 3(b).
Fig. 1. (a) Schematic of the original tricrystal ring pairing symmetry experiments [12]. The polar plots represent the amplitude and phase of the pairing wavefunction of the cuprate thin-film superconductors, assumed to have dx2Ky2 orbital pairing symmetry, which are epitaxially grown on the Sr2 TiO3 tricrystal substrate, with the (001) tilt grain boundaries between them represented as solid lines. The circles are 50 mm diameter, 10 mm wall thickness, photolithographically patterned optimally doped thin-film Ya2 Cu3 O7Kd rings. (b) Scanning SQUID microscope image of this sample, cooled in zero field and imaged at 4.2 K. The central (p-) ring shows spontaneous magnetization corresponding to half of a superconducting flux quantum trapped in the ring. The three outer control (0-) rings show no spontaneous magnetization.
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C.C. Tsuei et al. / Journal of Physics and Chemistry of Solids 67 (2006) 64–67
Fig. 2. (a) Scanning SQUID microscope image of an unpatterned YBCO film epitaxially grown on a tricrystal substrate with the geometry of Fig. 1(a), cooled in a field of a few mG, and imaged at 4.2 K. Visible are 7 Abrikosov vortices in the crystals, 4 integer Josephson vortices trapped in the grain boundaries, and a half-flux quantum Josephson vortex at the tricrystal meeting point [14]. (b) Similar tricrystal experiment by Sugimoto, Yamaguchi, and Iguchi [15].
A series of tricrystal experiments have been carried out also with Bi2 Sr2 CaCu2 O8Cd (BSCCO) films of various doping concentrations. Through thermal annealing [17], the doping level of a given BSCCO film can be varied to cover the underdoped, through optimal doping, to overdoped regimes. The half-flux quantum effect at the tricrystal point was monitored as a function of such annealing. The dx2Ky2 pairing symmetry was found to persist throughout the entire doping range studied so far (Fig. 4). The crystal structure of all the BSCCO samples studied here is tetragonal equivalent. A dCs mixed pair state in BSCCO is therefore symmetry forbidden [1]. A summary of the results of the BSCCO tricrystal experiments, along with several other cuprate superconductors is displayed in Fig. 5 to show the doping range over which the d-wave pair state prevails. 4. Discussion and concluding remarks The tricrystal experiments described here, combined with previous work establishing d-wave pairing symmetry for
a number of optimally doped hole- and electron-doped cuprates [1], have provided phase-sensitive evidence for the absence of doping-induced pairing symmetry change away from optimal doping in several cuprate systems covering a wide range of doping. It is particularly remarkable that, in the face of competing orders such as charge density wave and antiferromagnetism [19,20], the dx2Ky2 pairing survives in the ultralow doping regime (e.g. as indicated in Fig. 5 for the BSCCO system). A similar conclusion has been reached from a recent study of c-axis penetration depth as a function of temperature and doping in YBa2 Cu3 O7Kd , suggesting that the dx2Ky2 nodal quasi-particles survive to very low doping [21]. The fact that many superconducting and normal-state properties of the cuprate superconductors are doping-dependent [22] while the d-wave pairing symmetry is not requires a generic origin of the doping-independent pairing symmetry in all the cuprates studied so far. We suggest that all evidence points to strong on-site Coulomb repulsion, a characteristic common to all cuprates, which is also responsible for the
Fig. 3. (a) Three-dimensional rendering of the magnetic flux at the tricrystal point for an unpatterned Ya0:7 Ca0:3 Ba2 Cu3 O7Kd film epitaxially grown on a tricrystal substrate with the geometry of Fig. 1(a), cooled in zero field and imaged at 4.2 K. (b) Total integrated magnetic flux from two vortices. The solid points are for the Josephson F0 =2 vortex at the tricrystal point; the open points are for an Abrikosov F0 vortex in the bulk of the sample.
C.C. Tsuei et al. / Journal of Physics and Chemistry of Solids 67 (2006) 64–67
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the dx2Ky2 channel of a Hubbard model is enhanced by an increasing on-site repulsion on the Cu sites and suppressed by inter-site Coulomb interactions [27]. Furthermore, the robust nature of dx2Ky2 pairing over a wide doping range ð0! p% 0:35Þ has been demonstrated by several numerical studies based on Hubbard models [28,29], consistent with the findings of this work. In summary, our phase-sensitive tricrystal experiments have demonstrated the absence of doping-induced pairing symmetry change in a number of superconducting cuprate systems, underscoring the importance of on-site Coulomb repulsion in the making high-temperature superconductivity. Acknowledgements Fig. 4. Examples of a series of tricrystal symmetry pairing experiments from BSCCO films grown epitaxially on a substrate with the geometry of Fig. 1(a), at three different oxygen doping concentrations. In all cases, there is a halfquantum Josephson vortex at the tricrystal point, indicating dx2Ky2 wavefunction pairing symmetry.
We would like to thank B. Chesca, I. Iguchi, R.H. Koch and D.M. Newns for useful discussions. The work of G.H. and J.M. was supported by the BMBF (SFB484) and the ESF (PiShift). References
Fig. 5. Graphical representation of the range of doping covered in the experiments reported in this paper. The vertical positions of the solid points are the measured critical temperatures Tc of the samples. The horizontal positions are the sample hole concentrations p, calculated from Tc using the empirical relation[18] (solid line) Tc ðpÞZ Tc;max ½1K82:6ðpKpc Þ2 . Here Tc,max is the critical temperature of the optimally doped material in each compound, and pcZ0.16.
universally observed Mott metal–insulator transition in perovskites. It is now generally accepted that, as first suggested by Anderson [23,24], a Hubbard model based on strong Coulomb interactions in the CuO2 planes can capture the essence of physics in high-temperature superconductors. With the constraint of no on-site double occupancy, one can show that within the framework of a two-dimensional Hubbard/t–J model, a superconducting ground state with dx2Ky2 symmetry is favored over dxy and extended s-wave (s * ) states [25,26] for parameters relevant to cuprates. Even without knowing the microscopic pairing mechanism, one can show that pairing in
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