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 Hc2, where the order parameter Δ(r) is small and given by Abrikosov's solution. By analyzing the second-order correction in Δ(r) to the ultrasonic attenuation coefficient, it is established that in the calculation the expansion in powers of Δ(r) will not be valid. The above situation is in strong contrast to the case of dirty type-II superconductors.