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S. B. Ota

doi:10.1103/PhysRevB.43.1237

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Specific heat in the mixed state of superconducting ${YBa}_{2}$ ${Cu}_{3}$ $O_{7 - x}$

S. B. Ota

Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-7000 Stuttgart 80, Federal Republic of Germany

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Phys. Rev. B 43, 1237(R) – Published 1 January, 1991

DOI: https://doi.org/10.1103/PhysRevB.43.1237

Abstract

It is shown that the observed magnetic-field dependence of the specific-heat anomaly near the superconducting transition temperature $T_{c}$ of ${YBa}_{2}$ ${Cu}_{3}$ $O_{7 - x}$ can be understood quantitatively by the Ginzburg-Landau theory of anisotropic type-II superconductors. It is shown, in the London limit, that the change in specific heat by the application of magnetic field $B_{a}$ (∼1T) is approximately linear in ( $B_{a}$ / $T_{c}$ )[t/(1-t)] for temperatures slightly below $T_{c}$ , where t=T/ $T_{c}$ . It is also predicted that the slope of this linear behavior for $B_{a}$ ⊥c axis should be ( $m_{c}$ / $m_{a b}$ $)^{1 / 2}$ times lower than that for $B_{a}$ ∥c axis. Here, $m_{c}$ and $m_{a b}$ are the components of the effective-mass tensor parallel and perpendicular to the c axis, respectively.

References (19)

D. M. Ginsberg et al., Physica C 153-155, 1082 (1988); R. A. Fisher et al., ibid. 153-155, 1092 (1988).
M. B. Salamon et al., Phys. Rev. B 38, 885 (1988).
E. Gmelin, in Studies of High Temperature Superconductors, edited by A. V. Narlikar (Nova, New York, 1989), Vol. 2, p. 95.
The specific-heat jump at $T_{c}$ is practically absent in the HTSC and instead a peak is observed. This is mainly due to the sample inhomogeneities. See for instance, A. Junod, A. Bezinge and J. Müller, Physica C 152, 50 (1988).
B. Serin, in Superconductivity, edited by R. D. Parks (Marcel Dekker, New York, 1969), Vol. 2, Chap. 15, p. 925.
F. Sharifi, J. Giapintzakis, D. M. Ginsberg, and D. J. van Harlingen, Physica C 161, 555 (1989).
L. J. de Jongh, Solid State Commun. 70, 955 (1989).
A. L. Fetter and P. C. Hohenberg, in Superconductivity, edited by R. D. Parks (Marcel Dekker, New York, 1969), Vol. 2, Chap. 14, p. 817.
M. Tinkham and C. J. Lobb, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull (Academic, Orlando, 1989), Vol. 42, p. 91; K. Kamarás et al., Phys. Rev. Lett. 64, 84 (1990).
U. Welp et al., Phys. Rev. Lett. 62, 1908 (1989).
L. Krusin-Elbaum et al., Phys. Rev. Lett. 62, 217 (1989); the uncertainty bounds are $λ_{ab}$ (0) = 1400 +- 500 Å. A. F. Hebard, A. T. Fiory and D. R. Harshman, ibid. 62, 2885 (1989); R. L. Greene, L. Krusin-Elbaum and A. P. Malozemoff, ibid. 62, 2886 (1989).
L. Krusin-Elbaum et al., Phys. Rev. B 39, 2936 (1989).
D. E. Farrell, J. P. Rice, D. M. Ginsberg and J. Z. Liu, Phys. Rev. Lett. 64, 1573 (1990). The intrinsic torque measurement on a YBa ${}_{2}{Cu}_{3}$ $O_{7 - x}$ single crystal reported here gives ( $m_{c}$ / $m_{ab}$ $)^{1 / 2}$ = 7.7 +- 0.2 for 80 < T < 88 K, which is hoped to be reliable. This value is higher than that estimated from ( $m_{c}$ / $m_{ab}$ $)^{1 / 2}$ = $ξ_{ab}$ / $ξ_{c}$ , which is about five. However, the estimate using lambda gives a much lower value [i.e., ( $m_{c}$ / $m_{ab}$ $)^{1 / 2}$ = $λ_{c}$ / $λ_{ab}$ apeq 3 ]. This can be due to the large uncertainty involved in the determination of lambda.
E. H. Brandt, Phys. Rev. Lett. 63, 1106 (1989); Physica C 162-164, 1167 (1989).
V. G. Kogan, Physica C 162-164, 1689 (1989), and the references therein.
W. Bauhofer et al., Phys. Rev. Lett. 63, 2520 (1989). This measurement on untwinned single crystals of YBa ${}_{2}{Cu}_{3}$ $O_{7 - x}$ shows that the anisotropy of $B_{c 2}$ among the a and b axes is about 20% at 85 K.
L. J. Campbell, M. M. Doria and V. G. Kogan, Phys. Rev. B 38, 2439 (1988).
K. S. Athreya et al., Phys. Rev. B 38, 11846 (1988); E. Bonjour et al., Physica C 166, 451 (1990).
M. E. Reeves et al., Phys. Rev. B 40, 4573 (1989).

[c1] D. M. Ginsberg et al., Physica C 153-155, 1082 (1988); R. A. Fisher et al., ibid. 153-155, 1092 (1988).

[c2] M. B. Salamon et al., Phys. Rev. B 38, 885 (1988).

[c3] E. Gmelin, in Studies of High Temperature Superconductors, edited by A. V. Narlikar (Nova, New York, 1989), Vol. 2, p. 95.

[c4] The specific-heat jump at $T_{c}$ is practically absent in the HTSC and instead a peak is observed. This is mainly due to the sample inhomogeneities. See for instance, A. Junod, A. Bezinge and J. Müller, Physica C 152, 50 (1988).

[c5] B. Serin, in Superconductivity, edited by R. D. Parks (Marcel Dekker, New York, 1969), Vol. 2, Chap. 15, p. 925.

[c6] F. Sharifi, J. Giapintzakis, D. M. Ginsberg, and D. J. van Harlingen, Physica C 161, 555 (1989).

[c7] L. J. de Jongh, Solid State Commun. 70, 955 (1989).

[c8] A. L. Fetter and P. C. Hohenberg, in Superconductivity, edited by R. D. Parks (Marcel Dekker, New York, 1969), Vol. 2, Chap. 14, p. 817.

[c9] M. Tinkham and C. J. Lobb, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull (Academic, Orlando, 1989), Vol. 42, p. 91; K. Kamarás et al., Phys. Rev. Lett. 64, 84 (1990).

[c10] U. Welp et al., Phys. Rev. Lett. 62, 1908 (1989).

[c11] L. Krusin-Elbaum et al., Phys. Rev. Lett. 62, 217 (1989); the uncertainty bounds are $λ_{ab}$ (0) = 1400 +- 500 Å. A. F. Hebard, A. T. Fiory and D. R. Harshman, ibid. 62, 2885 (1989); R. L. Greene, L. Krusin-Elbaum and A. P. Malozemoff, ibid. 62, 2886 (1989).

[c12] L. Krusin-Elbaum et al., Phys. Rev. B 39, 2936 (1989).

[c13] D. E. Farrell, J. P. Rice, D. M. Ginsberg and J. Z. Liu, Phys. Rev. Lett. 64, 1573 (1990). The intrinsic torque measurement on a YBa ${}_{2}{Cu}_{3}$ $O_{7 - x}$ single crystal reported here gives ( $m_{c}$ / $m_{ab}$ $)^{1 / 2}$ = 7.7 +- 0.2 for 80 < T < 88 K, which is hoped to be reliable. This value is higher than that estimated from ( $m_{c}$ / $m_{ab}$ $)^{1 / 2}$ = $ξ_{ab}$ / $ξ_{c}$ , which is about five. However, the estimate using lambda gives a much lower value [i.e., ( $m_{c}$ / $m_{ab}$ $)^{1 / 2}$ = $λ_{c}$ / $λ_{ab}$ apeq 3 ]. This can be due to the large uncertainty involved in the determination of lambda.

[c14] E. H. Brandt, Phys. Rev. Lett. 63, 1106 (1989); Physica C 162-164, 1167 (1989).

[c15] V. G. Kogan, Physica C 162-164, 1689 (1989), and the references therein.

[c16] W. Bauhofer et al., Phys. Rev. Lett. 63, 2520 (1989). This measurement on untwinned single crystals of YBa ${}_{2}{Cu}_{3}$ $O_{7 - x}$ shows that the anisotropy of $B_{c 2}$ among the a and b axes is about 20% at 85 K.

[c17] L. J. Campbell, M. M. Doria and V. G. Kogan, Phys. Rev. B 38, 2439 (1988).

[c18] K. S. Athreya et al., Phys. Rev. B 38, 11846 (1988); E. Bonjour et al., Physica C 166, 451 (1990).

[c19] M. E. Reeves et al., Phys. Rev. B 40, 4573 (1989).

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Specific heat in the mixed state of superconducting ${YBa}_{2}$ ${Cu}_{3}$ $O_{7 - x}$

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Specific heat in the mixed state of superconducting YBa2Cu3O7−x

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Specific heat in the mixed state of superconducting ${YBa}_{2}$ ${Cu}_{3}$ $O_{7 - x}$