From superconducting fluctuations to the bosonic limit in the response functions above the critical temperature

Abstract

We investigate the density, current, and spin response functions above the critical temperature for a system of three-dimensional fermions interacting via an attractive short-range potential. In the strong-coupling (bosonic) limit of this interaction, we identify the dominant diagrammatic contributions for a ``dilute'' system of composite bosons which form as bound-fermion pairs, and compare them with the usual (Aslamazov-Larkin, Maki-Thompson, and density-of-states) terms occurring in the theory of superconducting fluctuations above the critical temperature for a clean system in the weak-coupling limit. We show that, at the zeroth order in the diluteness parameter for the composite bosons, the Aslamazov-Larkin term still represents formally the dominant contribution to the density and current response functions, while the Maki-Thompson and density-of-states terms are strongly suppressed. Corrections to the Aslamazov-Larkin term are then considered at the next order in the diluteness parameter for the composite bosons. The spin response function is also examined, and it is found to be exponentially suppressed in the bosonic limit only when appropriate sets of diagrams are considered simultaneously.