Pseudogap and spectral function from superconducting fluctuations to the bosonic limit

The crossover from weak to strong coupling for a three-dimensional continuum model of fermions interacting via an attractive contact potential is studied above the superconducting critical temperature ${T}_{c}.$ The pair-fluctuation propagator, the one-loop self-energy, and the spectral function are investigated in a systematic way from the superconducting fluctuation regime (weak coupling) to the bosonic regime (strong coupling). Analytic and numerical results are reported. In the strong-coupling regime, where the pair fluctuation propagator has bosonic character, two quite different peaks appear in the spectral function at a given wave vector, a broad one at negative frequencies and a narrow one at positive frequencies. The broad peak is asymmetric about its maximum, with its spectral weight decreasing by increasing coupling and temperature. In this regime, two crossover temperatures ${T}_{1}^{*}$ (at which the two peaks in the spectral function merge in one peak) and ${T}_{0}^{*}$ (at which the maximum of the lower peak crosses zero frequency) can be identified, with ${T}_{c}\ensuremath{\ll}{T}_{0}^{*}l{T}_{1}^{*}.$ By decreasing coupling, the two-peak structure evolves smoothly. In the weak-coupling regime, where the fluctuation propagator has diffusive Ginzburg-Landau character, the overall line shape of the spectral function is more symmetric and the two crossover temperatures approach ${T}_{c}.$ The analysis of the spectral function identifies specific features which allow one to distinguish by ARPES whether a system is in the weak- or strong-coupling regime. Connection of the results of our analysis with the phenomenology of cuprate superconductors is also attempted.