Absence of the Vortex Solution in Gor'kov's Formalism

It is shown that the Abrikosov’s vortex solution or its corresponding two-particle pair potential is not the solution of the self-consistency equation in Gor’kov’s formalism. Since the self-consistency equation leads to a superposition of different types of off-diagonal long-range order (ODLRO) instead of one type of ODLRO only, it may not handle the vortex problem appropriately. A possible resolution is suggested.