The Ginzburg Criterion in High Tc Oxides

  • G. Deutscher

Abstract

The application of the Ginzburg criterion yields for the new high Tc oxides a broad critical region, with a width of order unity. This width could be reduced in the event of large strong coupling corrections Most of the recent theoretical interest in the newly discovered superconducting oxides has been directed towards the various mechanisms that may be responsible for their high critical temperature. In contrast we wish here to point out to a basic feature that differentiates these oxides from ordinary superconductors, irrespective of the mechanism involved. Based upon available data, we show that the Ginzburg criterion yields for the critical region, with a width of order unity. This makes mean field theories inapplicable to the new superconductors. However, this conclusion may be to some extent altered in the event of a very strong coupling correction.

The Ginzburg criterion essentially states that the width of the critical region in a second order phase transition is determined as the range of temperature where the condensation energy per coherence volume is of order unity. It is known that this range is extremely small for superconductors. Expressed in terms of the reduced temperature ɛ = | Tc-T| /TC, it is typically to the order of 10-10. This constitutes the basis for the validity of the mean field theories of superconductivity BCS and Landau Ginzburg.

The width of the critical Region can be calculated from experimental data when cast into the form:
$$ [H{c^2}(\varepsilon )/8\pi ].\xi 3(\varepsilon ) < mu{k_B}{T_c}$$
(1)
From an analysis of the available data (jump of the heat capacity at Tc, critical fields, Hall effect and conductivty), Bardeen concludes that Hc (T=0) = 12,000 Oe and ζ(T=0) = 12A. We note that the value of Hc can be directly obtained from the jump in the heat capacity at Tc, and that the value quoted is consistent with the field mean approximation. Using Hc(ɛ) = 2 Hc(T=0)ɛ and the clean limit result ζ(T)=.74ζ(0)ɛ−1/2, one obtains the width of the critical region ɛ<0.7. Thus, the critical behavior of the new high Tc oxides should be similiar to that of superfluid He4, rather than to that of conventional superconductors. The calculated critical width depends of course on the values used for Hc and ζ, which might have to be modified if more accurate data becomes available. But we expect non mean field behavior to be observable in any case near Tc.
Finally, we note that the width of the critical region is sensitive to strong coupling corrections. Using \(\xi \,(0)\, = 0.18h{v_F}/{k_B}\,Tc,H{c^2}(0)/8\pi = 1/2\,N(0){\Delta ^2}(0)\,and\,2\Delta (0) = 3.5\eta kBTc \), eq.l can be rewritten in the clean limit as:
$$\varepsilon < {\rm{ }}\left[ {(13/\eta )({\rm{kTc}}/{{\rm{E}}_{\rm{F}}})]4} \right.4$$
If strong coupling effects turn out to be important, i.e. if the heat capacity at Tc has been actually underestimated by current experiments, the width of the critical region is significantly reduced. Thus, the observation of a broad or narrow critical region might be indicative respectively of weak or strong coupling behavior. As outlined by Bardeen, this has an immediate bearing on the mechanism of the high Tc in the high Tc oxides.

Keywords

Coherence 

References

  1. 1).
    J. Bardeen, these ProceedingsGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • G. Deutscher
    • 1
  1. 1.Department of Physics and AstronomyTel Aviv UniversityRamat AvivIsreal

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