Virial theorem and Abrikosov’s solution of the Ginzburg-Landau equations

Using the virial theorem discovered recently by Doria, Gubernatis, and Rainer [Phys. Rev. B 39, 9573 (1989)], we rederive Abrikosov’s solution of the Ginzburg-Landau equations near ${\mathit{H}}_{\mathit{c}2}$ in a very simple way. We stress the importance of the virial theorem for an intuitive understanding of the vortex state and report a generalized version of it, which is valid within the framework of the quasiclassical theory of superconductivity.