Ginzburg-Landau theory of fluctuation magnetization of two-dimensional superconductors

Large fluctuation-induced magnetization has been observed recently in the quasi-two-dimensional high-Tc materials. A satisfactory theoretical description of this phenomenon is absent at the moment. We present an extensive study of the fluctuation magnetization M₁ of two-dimensional superconductors within the Ginzburg-Landau theory in different regions of the phase diagram. In the normal state one has to distinguish the regions of weak/Gaussian and strong/critical fluctuations. Different kinds of scaling dependencies for M₁ are predicted for these regions. An important feature of the field dependence of M₁ in the weak-fluctuation regime is saturation of the magnetization at high fields. Taking into account both regular and critical contributions to M₁ we obtain an expression that is valid in both regions. In the mixed state at high fields the fluctuation magnetization is completely determined by the thermal elastic fluctuations in the lattice state. Due to suppression of the elastic modulii, M₁ increases mainly as 1/(Hc2-B) as the field approaches the critical region near the upper critical field Hc2. At small fields, B{}Hc2, there are two independent contributions to M₁ which can be treated separately. One comes from the Gaussian excitations in the vortex cores and the other from the thermal motion of the vortices. We demonstrate that the vortex system in this limit is equivalent to the model of the one-component two-dimensional Coulomb plasma. Using Monte Carlo results for this model, we estimate M₁ in the vortex-lattice as well as in the vortex-liquid state.