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

The density, current, and spin response functions are investigated above the critical temperature Tc for a system of three-dimensional fermions interacting via an attractive short-range potential, as the strength of this potential is varied from weak to strong coupling. In the strong-coupling (bosonic) limit, we identify the dominant diagrammatic contributions for a “dilute” system of composite bosons which form as bound-fermion pairs, by giving appropriate prescriptions for mapping bosonic onto fermionic diagrams. We then extrapolate these contributions to the weak-coupling limit and compare them with the ordinary (Aslamazov-Larkin, Maki-Thompson, and density of states) terms occurring in the theory of superconducting fluctuations for a clean system above the critical temperature. Specifically, we show that in the strong-coupling limit, at the zeroth order in the diluteness parameter for the composite bosons, the Aslamazov-Larkin term 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 further identified via the above mapping prescriptions at the next order in the diluteness parameter for the composite bosons, where the residual mutual interaction appears explicitly. Numerical comparison of the Aslamazov-Larkin diagram and its leading corrections is presented for a range of temperature above Tc over the whole coupling region. The spin response function is also examined, and it is found to be correctly suppressed in the strong-coupling limit only when appropriate sets of diagrams are considered simultaneously, thus providing a criterion for grouping diagrammatic contributions to the response functions.