Precursor diamagnetism in layered and isotropic superconductors

Abstract

The theory of diamagnetic fluctuations in a system of Josephson-coupled superconducting layers is studied using the approach of Kurkij\arvi, Ambegaokar, and Eilenberger, but with a modified treatment of finite frequency fluctuations proposed by Maki and Takayama. Both temperature and field dependence of the fluctuation-induced magnetization above ${T}_{c}$ are discussed. The results are extended to the limit of isotropic superconductors, where they are generally in good agreement with the experimental results of Gollub, Beasley, and Tinkham, for both clean and dirty superconductors. For weakly coupled layers, the temperature dependence of the magnetization for fixed field changes from a ${[T\ensuremath{-}{T}_{c}(B)]}^{\ensuremath{-}\frac{1}{2}}$ behavior near the phase transition, typical of three-dimensional superconductors, to a ${[T\ensuremath{-}{T}_{c}(B)]}^{\ensuremath{-}1}$ behavior of two-dimensional character at higher temperatures, as predicted by Lawrence and Doniach, Similarly, the field dependence at ${T}_{c}$ changes from a $\sqrt{B}$ dependence to a relatively field-in-dependent behavior at higher fields. With increasing layer coupling, these changes take place at higher temperatures and fields, respectively, but they are masked by effects which suppress fluctuations at high fields and temperatures. The numerical results are consistent with the layer-compound data of Prober, Beasley, and Schwall, but they show that these compounds behave much more like three-dimensional than like two-dimensional systems, in spite of the apparent Curie-Weiss-like temperature dependence of the susceptibility.