Measurements of the Shear Modulus of the Superconducting Mixed State of Thin Films

Existence of a shear modulus for the vortex-lattice structure in the superconducting mixed state of several oxygen-doped aluminum films is deduced from observations of the quantum-interference effect. From a detailed study of the widths of the interference transition, it is shown that at low magnetic fields the shear modulus $c_{66}$ is in agreement with a recent theoretical consideration of the thin-film case. In addition, it is found that $c_{66}$ vanishes at $H_{c2}$ in accordance with a theoretical result for the bulk case. Enhanced influence of the pinning effect upon local lattice parameter and velocity fluctuations is observed at small transport velocities, in qualitative agreement with the recent theory of Schmid and Hauger.