Fluctuations of vortices in layered high-Tcsuperconductors

The temperature ${\mathit{T}}_{\mathit{s}}$ of spontaneous creation of vortex lines in Josephson coupled layered superconductors is obtained by taking into account the entropy contribution to the free energy due to thermal distortions. For Bi- and Ti-based high-${\mathit{T}}_{\mathit{c}}$ superconductors and superlattices, the superconducting critical temperature ${\mathit{T}}_{\mathit{s}}$ lies noticeably below the mean-field transition temperature ${\mathit{T}}_{\mathit{c}0}$(${\mathit{T}}_{\mathit{c}0}$-${\mathit{T}}_{\mathit{s}}$≊4 K or more). The contribution of thermal distortions to the free enery causes significant changes in the temperature and field dependences of magnetization below ${\mathit{T}}_{\mathit{s}}$ seen in Bi compounds.