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Spin pseudogap and c-axis transport
J. Phys. Chem. So1id.rVol. 56, No. 12, p. 1781, 1995 Copyright @ 1995 ElscvierScienceLtd Printedin Great Britain.All rights mwvcd 0022-3697/95$9.50 + 0.00
Pergamon
00223697(%)00170-O
SPIN PSEUDOGAP
AND c-AXIS TRANSPORT
YUYAO ZHA, S. L. COOPER and DAVID PINES Department of Physics and Science and Technology Center for Superconductivity, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.
Abstract-We present a simple phenomenological model of the c-axis resistivity in the layered cuprates, which accounts for the major features and systematics of experiments on the c-axis resistivity, pc, for Laz_,Sr,CuO4, YBa&I@6+, and BizSr2CaCuzOs We associate the low temperature semiconductor-like upturn in the c-axis resistivity with the suppression of the planar density of states measured in the Knight
shift experiments.
Using eqn (3), we may analyze the existing c-axis resistivity data of La2_,SrXCu04 [2], YBa2Cu306+x [5] and Bi&CaCuzOs [6], since we can obtain N(O), d, -T&, and tl from different magnetic and transport experiments [8], we are left with a two-parameter fit for each cuprate. De tails of these fits are given in Ref. [8], in which we find eqn (3) accounts well for the pc data of the above three types of cuprates at various doping concentrations, and the results for tl and 1/T, are consistent with optical and Raman experiments [7]. In conclusion, we have presented a model for c-axis resistivity of high Tc cuprates, in which the c-axis resistivity consists of contributions from the in-plane dephasing process and the c-axis “barrier” scatterings. As a result, we predict that whenever the spin pseudogap appears in the planar density of states, it will also show up in the c-axis resistivity as a “semiconductor-like” low temperature upturn.
Recent c-axis optical measurements [l] show that the semiconductor-like resistivity “upturn” in underdoped YBazCu,O6+, is actually associated with a uniform suppression of the optical conductivity below - 3OOcm-‘, and the low frequency c-axis conductivity scales with the Knight shift, which has a pseudogap behavior. Since the Knight shift is proportional to the in-plane density of states: I& cy N(O), a phenomenological expression for this contribution to c-axis transport can be written as:
a!” - N(O) L
-
et2 A2
T .l c
where d is the interlayer spacing, N(0) is the in-plane density of states, and tl is the interlayer coupling. Here TVcorresponds to the electron scattering in the “barrier” layer between CuO2 “cells” (i.e. layers, bilayers, trilayers, etc.), which is temperature independent. On the other hand, c-axis transport measurements of La2-,Sr,Cu04 and Bi&CaCuzOs yield pc pi pObat high temperatures [2,3], suggesting that inplane scattering or fluctuations may dominate c-axis transport in this regime. This contribution to c-axis transport can be written [4],
AcknowledgementsSupported by NSF-DMR-9 I-20000 through the Science and Technology Center for Superconductivity.
REFERENCES 1. Homes C. C. et al., Phys. Rev. Let?. 71, 1645 (1993); Basov D. N. et al., Phys. Rev. B 50, 351 I (1994). where rnh can be derived from the planar conductivity ad = wf,,,T,h /47-r, and the temperature-independent quantity, tl, measures the effectiveness of planar fluctuation processes to c-axis transport. Because eqns (1) and (2) describe independent physical processes, it seems natural to consider the corresponding tunneling and/or scattering mechanisms as additive in the resistivity. We are thus led to propose the following expression for pc,
A2 -(‘+
PC = N(O)$d2
t;q,/,
2. Nakamura Y. and Uchida S., Phys. Rev. B 47, 8369 (1993). 3. Hou X. H. et al., Phys. Rev. B 50,496 (1994). 4. Leggett A. J., Braz. 1 Phys. 22, 129 (1992). 5. Takenaka K., Mizuhashi K., Takagi H. and Uchida S., Phys. Rev. B 50, 6534 (1994). 6. Martin S. et al., Appl. Phys. L&r. 54, 72 (1989); Forro L., Ilakovac V. and Keszei B., Phys. Rev. B 41,955l (1990); Xiang X. D. et al., Phys. Rev. Lett. 68, 530 (1992); Yan Y. F., Hrris J.
(3)
M. and Ong N. P., unpublished. 7. Cooper S. L. and Gray K. E., Physical Properties of High Temperature Superconductors IV (Edited by D. M. Ginsberg). World Scientific, Singapore (1994). 8. Zha Y., Cooper S. L. and Pines D., preprint.
in the limit that one mechanism or the other is dominant, it yields the corresponding conductivity given in eqns (1) and (2). 1781
Pergamon
00223697(%)00170-O
SPIN PSEUDOGAP
AND c-AXIS TRANSPORT
YUYAO ZHA, S. L. COOPER and DAVID PINES Department of Physics and Science and Technology Center for Superconductivity, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.
Abstract-We present a simple phenomenological model of the c-axis resistivity in the layered cuprates, which accounts for the major features and systematics of experiments on the c-axis resistivity, pc, for Laz_,Sr,CuO4, YBa&I@6+, and BizSr2CaCuzOs We associate the low temperature semiconductor-like upturn in the c-axis resistivity with the suppression of the planar density of states measured in the Knight
shift experiments.
Using eqn (3), we may analyze the existing c-axis resistivity data of La2_,SrXCu04 [2], YBa2Cu306+x [5] and Bi&CaCuzOs [6], since we can obtain N(O), d, -T&, and tl from different magnetic and transport experiments [8], we are left with a two-parameter fit for each cuprate. De tails of these fits are given in Ref. [8], in which we find eqn (3) accounts well for the pc data of the above three types of cuprates at various doping concentrations, and the results for tl and 1/T, are consistent with optical and Raman experiments [7]. In conclusion, we have presented a model for c-axis resistivity of high Tc cuprates, in which the c-axis resistivity consists of contributions from the in-plane dephasing process and the c-axis “barrier” scatterings. As a result, we predict that whenever the spin pseudogap appears in the planar density of states, it will also show up in the c-axis resistivity as a “semiconductor-like” low temperature upturn.
Recent c-axis optical measurements [l] show that the semiconductor-like resistivity “upturn” in underdoped YBazCu,O6+, is actually associated with a uniform suppression of the optical conductivity below - 3OOcm-‘, and the low frequency c-axis conductivity scales with the Knight shift, which has a pseudogap behavior. Since the Knight shift is proportional to the in-plane density of states: I& cy N(O), a phenomenological expression for this contribution to c-axis transport can be written as:
a!” - N(O) L
-
et2 A2
T .l c
where d is the interlayer spacing, N(0) is the in-plane density of states, and tl is the interlayer coupling. Here TVcorresponds to the electron scattering in the “barrier” layer between CuO2 “cells” (i.e. layers, bilayers, trilayers, etc.), which is temperature independent. On the other hand, c-axis transport measurements of La2-,Sr,Cu04 and Bi&CaCuzOs yield pc pi pObat high temperatures [2,3], suggesting that inplane scattering or fluctuations may dominate c-axis transport in this regime. This contribution to c-axis transport can be written [4],
AcknowledgementsSupported by NSF-DMR-9 I-20000 through the Science and Technology Center for Superconductivity.
REFERENCES 1. Homes C. C. et al., Phys. Rev. Let?. 71, 1645 (1993); Basov D. N. et al., Phys. Rev. B 50, 351 I (1994). where rnh can be derived from the planar conductivity ad = wf,,,T,h /47-r, and the temperature-independent quantity, tl, measures the effectiveness of planar fluctuation processes to c-axis transport. Because eqns (1) and (2) describe independent physical processes, it seems natural to consider the corresponding tunneling and/or scattering mechanisms as additive in the resistivity. We are thus led to propose the following expression for pc,
A2 -(‘+
PC = N(O)$d2
t;q,/,
2. Nakamura Y. and Uchida S., Phys. Rev. B 47, 8369 (1993). 3. Hou X. H. et al., Phys. Rev. B 50,496 (1994). 4. Leggett A. J., Braz. 1 Phys. 22, 129 (1992). 5. Takenaka K., Mizuhashi K., Takagi H. and Uchida S., Phys. Rev. B 50, 6534 (1994). 6. Martin S. et al., Appl. Phys. L&r. 54, 72 (1989); Forro L., Ilakovac V. and Keszei B., Phys. Rev. B 41,955l (1990); Xiang X. D. et al., Phys. Rev. Lett. 68, 530 (1992); Yan Y. F., Hrris J.
(3)
M. and Ong N. P., unpublished. 7. Cooper S. L. and Gray K. E., Physical Properties of High Temperature Superconductors IV (Edited by D. M. Ginsberg). World Scientific, Singapore (1994). 8. Zha Y., Cooper S. L. and Pines D., preprint.
in the limit that one mechanism or the other is dominant, it yields the corresponding conductivity given in eqns (1) and (2). 1781