Pinning and the intrinsic magnetic-field dependence of the mixed-state Hall conductivity in amorphous Mo{sub 3}Si and YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}}

We have investigated the pinning and magnetic-field dependence of the mixed-state Hall conductivity ${\ensuremath{\sigma}}_{\mathrm{xy}}$ in thin films of two superconductors, amorphous ${\mathrm{Mo}}_{3}\mathrm{Si}$ and ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$ The effects of pinning were varied by measuring at different current densities $j$. In both superconductors, ${\ensuremath{\sigma}}_{\mathrm{xy}}$ is independent of $j$ (and, therefore, pinning) in support of theory. The magnetic-field dependence of ${\ensuremath{\sigma}}_{\mathrm{xy}}$ at large and small magnetic fields strongly supports calculations based on time-dependent Ginzburg-Landau theory. In addition, we find sample inhomogeneities can cause a fictitious current dependence of ${\ensuremath{\sigma}}_{\mathrm{xy}}.$ We argue this explains the conflicting reports of the pinning and magnetic-field dependence of ${\ensuremath{\sigma}}_{\mathrm{xy}}$ found in the literature.