Theory of Pure Type-II Superconductors in High Magnetic Fields. I. Difficulties Associated with Expansions in Powers of the Order Parameter

We consider here the transport properties of a pure type-II superconductor in a field close to the upper critical field $H_{c2\mathrm{}}$, where the order parameter $\Delta \left(\mathbf{r}\right)$ is small and given by Abrikosov's solution. By analyzing the second-order correction in $\Delta \left(\mathbf{r}\right)$ to the ultrasonic attenuation coefficient, it is established that in the calculation the expansion in powers of $\Delta \left(\mathbf{r}\right)$ will not be valid. The above situation is in strong contrast to the case of dirty type-II superconductors.