Theory of upper critical field, fluctuation conductivity, and fluctuation specific heat for high-Tc superconductors in a magnetic field

Abstract

Within the general framework of Bardeen-Cooper-Schrieffer pairing theory we derive coupled gap equations of the Helfand-Werthamer type for two or more order-parameter components having different symmetry. Assuming, for instance, coupled s- and d-wave pairing components, we obtain for certain parameter values a solution for Hc2 perpendicular to the Cu-O planes which accounts qualitatively for the observed upward curvature and yields about 65 T at zero temperature. We calculate also the in-plane fluctuation conductivity of the Lawrence-Doniach type for fields parallel to the c axis. For large fields, the inverse fluctuation conductivity is almost linear in temperature with slope depending sensitively on the ratio of coherence length to unit-cell dimension along the c axis. It seems possible to fit the observed broad resistive transition for different fields with this inverse fluctuation conductivity. Just above the transition temperature, Tc2(H), the inverse ac fluctuation conductivity is approximately a linear function of frequency for small fields, and it is nearly a quadratic function of frequency for large fields. The field dependence of the fluctuation contribution to the specific heat is also discussed in connection with recent measurements.

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