Critical scaling of the ac conductivity for a superconductor above T c
Critical scaling of the ac conductivity for a superconductor above T c
复制标题
T c 以上超导体交流电导率的临界标度
DOI：
10.1103/physrevb.61.6945
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发表时间：
1999
影响因子：
3.7
通讯作者：
A. Dorsey
中科院分区：
文献类型：
--
作者：
R. Wickham;A. Dorsey
We consider the effects of critical superconducting fluctuations on the scaling of the linear ac conductivity, $\ensuremath{\sigma}(\ensuremath{\omega}),$ of a bulk superconductor slightly above ${T}_{c}$ in zero applied magnetic field. The dynamic renormalization-group method is applied to the relaxational time-dependent Ginzburg-Landau model of superconductivity, with $\ensuremath{\sigma}(\ensuremath{\omega})$ calculated via the Kubo formula to $O({\ensuremath{\epsilon}}^{2})$ in the $\ensuremath{\epsilon}=4\ensuremath{-}d$ expansion. The critical dynamics are governed by the relaxational $\mathrm{XY}$-model renormalization-group fixed point. The scaling hypothesis $\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\xi}}^{2\ensuremath{-}d+z}S(\ensuremath{\omega}{\ensuremath{\xi}}^{z})$ proposed by Fisher, Fisher, and Huse is explicitly verified, with the dynamic exponent $z\ensuremath{\approx}2.015,$ the value expected for the $d=3$ relaxational $\mathrm{XY}$ model. The universal scaling function $S(y)$ is computed and shown to deviate only slightly from its Gaussian form, calculated earlier. The present theory is compared with experimental measurements of the ac conductivity of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ near ${T}_{c},$ and the implications of this theory for such experiments is discussed.
We consider the effects of critical superconducting fluctuations on the scaling of the linear ac conductivity, $\ensuremath{\sigma}(\ensuremath{\omega}),$ of a bulk superconductor slightly above ${T}_{c}$ in zero applied magnetic field. The dynamic renormalization-group method is applied to the relaxational time-dependent Ginzburg-Landau model of superconductivity, with $\ensuremath{\sigma}(\ensuremath{\omega})$ calculated via the Kubo formula to $O({\ensuremath{\epsilon}}^{2})$ in the $\ensuremath{\epsilon}=4\ensuremath{-}d$ expansion. The critical dynamics are governed by the relaxational $\mathrm{XY}$-model renormalization-group fixed point. The scaling hypothesis $\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\xi}}^{2\ensuremath{-}d+z}S(\ensuremath{\omega}{\ensuremath{\xi}}^{z})$ proposed by Fisher, Fisher, and Huse is explicitly verified, with the dynamic exponent $z\ensuremath{\approx}2.015,$ the value expected for the $d=3$ relaxational $\mathrm{XY}$ model. The universal scaling function $S(y)$ is computed and shown to deviate only slightly from its Gaussian form, calculated earlier. The present theory is compared with experimental measurements of the ac conductivity of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ near ${T}_{c},$ and the implications of this theory for such experiments is discussed.