Relating the ac complex resistivity of the pinned vortex lattice to its shear modulus

作者：N. Phuan Ong, Hui Wu · 发表于：Physical review. B, Condensed matter · 年份：1997 · DOI：10.1103/physrevb.56.458 · 被引用次数：12 · 研究领域：Physics of Superconductivity and Magnetism、Advanced Condensed Matter Physics、Superconducting Materials and Applications

We propose a way to determine the shear rigidity of the pinned vortex lattice in high-purity crystals from the dependence of its complex resistivity $\ensuremath{\rho}\^{}$ on frequency $(\ensuremath{\omega})$. The lattice is modeled as an elastic medium pinned by a sparse, random distribution of defects. We relate $\ensuremath{\rho}\^{}$ to the velocity of the small subset of pinned vortices via the lattice propagator $G(\mathbf{R},\ensuremath{\omega})$. Measuring $\ensuremath{\rho}\^{}$ versus $\ensuremath{\omega}$ is equivalent to determining $G(\mathbf{R},\ensuremath{\omega})$ versus $R$. The range of $G(\mathbf{R},\ensuremath{\omega})$ depends sensitively on the shear and tilt moduli. We describe the evaluation of $G(\mathbf{R},\ensuremath{\omega})$ in two-dimensional (2D) and 3D lattices. The 2D analysis provides a close fit to the frequency dependence of Re$\ensuremath{\rho}\^{}$ measured in an untwinned crystal of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ at 89 K in a field of 0.5 and 1.0 T. We compare our results with earlier models.