Theory of diamagnetic response of the vortex liquid phase of two-dimensional superconductors

We calculate the magnetization of a two-dimensional superconductor in a perpendicular magnetic field near its Kosterlitz-Thouless transition and at lower temperatures. We find that the critical behavior is more complex than assumed in the literature and that, in particular, the critical magnetization is not field independent as naive scaling predicts. In the low-temperature phase we find a substantial fluctuation renormalization of the Abrikosov mean-field result. We compare our analysis with the data on the cuprates.