Low-energy collective modes, Ginzburg-Landau theory, and pseudogap behavior in superconductors with long-range pairing interactions

We study the superconducting instability in systems with long- but finite-r anged attractive pairing interactions. We show that such long-ranged superc onductors exhibit a class of fluctuations in which the internal structure o f the Cooper pair wave function is soft, and thus lead to "pseudogap" behav ior in which the actual transition temperature is greatly depressed from it s mean-field value. These fluctuations are riot phase fluctuations of the s tandard superconducting order parameter, and lead to a highly unusual Ginzb urg-Landau description. We suggest that the crossover between the BCS Limit of a short-ranged attraction and our problem is of interest in the context of superconductivity in the underdoped cuprates.