Superconductivity in a system with preformed pairs

We discuss the phenomenology of superconductivity resulting from the Bose condensation of preformed pairs coexisting with unpaired fermions. We show that this transition is more mean-field-like than the usual Bose condensation, i.e., it is characterized by a relatively small value of the Ginzburg parameter. We consider the Hall effect in the vortex-flow regime and in the fluctuational regime above ${\mathrm{T}}_{\mathrm{c}}$, and show that in this situation it is much less than in the transition driven entirely by Bose condensation but much larger than in usual superconductivity. We analyze the available Hall data and conclude that this phenomenology describes reasonably well the data in the underdoped materials of Y-Ba-Cu-O family but is not an appropriate description of optimally doped materials or underdoped La-Sr-Cu-O.